ChemGem

Home › Lessons › Chapter 6

Chapter 6 · Free lesson

Solutions and aqueous reactions

The full lesson, free. For instant answer checking, hints and progress tracking, open the interactive version.

START A NEW CHAPTER
YOUR CHAPTER PLAN

What you will study

  1. Concentration describes amount per volume
  2. Dilution conserves the dissolved amount
  3. What stays dissolved and what reacts
  4. Acid–base reactions: see the particles in water
  5. Solution stoichiometry and titration
  6. Redox: electron transfer

By the end, you can…

  1. Calculate molarity using liters of solution.
  2. Solve a dilution using conserved solute moles.
  3. Predict common precipitates, write a net ionic equation, and identify spectator ions.
  4. Compare strong electrolytes, weak electrolytes, and nonelectrolytes in water.
  5. Explain an acid and a strong base in water, identify the reacting ions, and write their neutralization equation.
  6. Use balanced ratios with moles from solution amounts, including acid–base titrations.
  7. Identify oxidation and reduction from changing charges.

These are the skills to check, not just pages to finish. Use the section goals while studying, then try the chapter checks without hints.

Read the idea first. Then notice the clue, follow the route, and make a choice you can explain. You can return to the worked example if a practice question feels unfamiliar.

6.1 Concentration describes amount per volume

A solution has a dissolved substance spread evenly through a liquid. Molarity says how many moles of that substance sit in each liter of solution. This lesson calculates molarity from moles and liters.

What you’ll use from earlier
  • Moles (Chapter 4); mL → L and rearranging equations (Math first).

Need a refresher? Open the table of contents and revisit that topic before starting.

The idea
Three words for one mixture
TermMeaningSalt water
SoluteWhat dissolvesNaCl
SolventWhat it dissolves inWater
SolutionTheir uniform mixtureSalt water
Molarity = moles of solute ÷ liters of solution
M = n (mol)V (L)
M is concentration in mol/L. n is moles of solute. V is the total solution volume, in liters.
Need moles instead? Multiply.
n = M × V    molL × L = mol
Liters cancel and moles remain.
Same 0.30 mol of solute, three solution volumes
in 0.300 L1.0 Min 0.600 L0.50 Min 1.20 L0.25 MMolarity (mol/L)
More volume spreads the same moles thinner, so molarity falls.
Water surrounds ions with the correct end facing inward. Four nearby water molecules are schematic, not a fixed hydration number. Water is polar; NaCl does not become neutral Na and Cl atoms.
Water is polar; its matching end faces each ion. Four water molecules are schematic, not a fixed number. NaCl does not become neutral Na and Cl atoms.
Molarity counts solute, not particle type
Sugar
Stays as whole molecules.
NaCl
Separates into ions:
NaCl → Na+ + Cl−
A weighed solute needs a mass-to-mole conversion. NaCl contains one Na and one Cl: about 22.99 + 35.45 = 58.44 g/mol. If solute is given in grams, first divide by 58.44 g/mol; then divide moles by liters for molarity. If solute moles are already given, use them directly. The solution volume comes from the question.
Solute given in grams? Divide by molar mass first (NaCl: 58.44 g/mol), then by liters. Moles given? Use them directly. Use supplied masses when a question gives them.
1 · Recognize the clue
Look for this:moles (or grams) of solute plus a solution volume, and a question asking for molarity, M, or moles from M and volume.
2 · Follow the route
  1. Find the moles of solute and the solution volume.
  2. Convert the volume to liters.
  3. Divide moles by liters.

On the periodic table: Sodium (Na) is in Group 1, so it forms Na+. Chlorine (Cl) is in Group 17, so it forms Cl−.

On the periodic table: Molar masses come from the table: Na 22.99 and Cl 35.45, so NaCl is 22.99 + 35.45 = 58.44 g/mol.

On the periodic table: Atomic number gives the proton count (Na 11, Cl 17). The decimal mass is an average, not an isotope’s mass number.

Worked example

Find molarity for 0.30 mol solute in 600 mL of solution.

The solute is unspecified and its moles are supplied, so no molar mass is needed. Conversion factor: 1 L / 1000 mL.

  1. 1
    Convert the volume

    Molarity uses liters of final solution, not milliliters.

    600 mL × 1 L1000 mL = 0.600 L
  2. 2
    Write the relationship

    n is solute moles; V is liters of solution.

    M = nV
  3. 3
    Divide

    Moles per liter is the requested concentration.

    M = 0.30 mol0.600 L = 0.50 mol/L
  4. 4
    Write the short unit

    Capital M is short for molarity.

    0.50 mol/L = 0.50 M
  5. ✓
    Answer

    0.50 M

6.2 Dilution conserves the dissolved amount

Dilution means adding solvent, usually water, without adding solute. The moles of solute stay the same while the volume grows, so the concentration falls. That one fact gives the dilution equation.

What you’ll use from earlier
  • Molarity (6.1); solve for an unknown (Math first).

Need a refresher? Open the table of contents and revisit that topic before starting.

The idea
Before: one spoonful of sugar dissolved in half a cup of coffee, represented by six gold markers. After adding only water: a full cup with the same six sugar markers spread through more liquid. The sugar amount stays constant and its concentration decreases.
Same sugar, more liquid. Each gold dot is an equal amount of dissolved sugar. Adding water lowers the concentration. A second spoonful would add solute: a different comparison.
Before dilution = after dilution: same solute moles
M1V1 = M2V2
M is molarity; V is solution volume. Subscript 1 means before; 2 means after.
What changes and what does not
Before (1)After (2)
Solute moles0.100 mol0.100 mol
Volume50.0 mL200 mL
Molarity2.00 M0.500 M
Numbers from the worked example: 2.00 M × 0.0500 L = 0.500 M × 0.200 L = 0.100 mol.
Fixed solute moles: more volume, lower molarity
00.511.5201002003004000.100 mol solute50 mL, 2.00 M100 mL, 1.00 M200 mL, 0.500 MFinal volume (mL)Molarity (M)
Doubling the final volume halves the concentration.
Rules for using M1V1 = M2V2
  • Both volumes must use the same units (both mL or both L).
  • V2 is the final total volume, not the water added.
  • It applies to the same solute with no reaction and no loss.
1 · Recognize the clue
Look for this:a stock solution being diluted: a starting M and volume, plus a final M or final total volume to find.
2 · Follow the route
  1. Check that only solvent is added, so solute moles stay constant.
  2. Write M1V1 = M2V2 and solve for the unknown.
  3. Insert values with matching volume units.
  4. Check: lower concentration means larger final volume.

On the periodic table: No element values are needed here. Concentrations and volumes supply M1V1 = M2V2.

Worked example

Dilute 50.0 mL of 2.00 M stock to 0.500 M. What final volume is needed?

  1. 1
    Name what stays constant

    Only solvent is added, so solute moles stay the same.

    moles before = moles after → M1V1 = M2V2
  2. 2
    Solve for final volume

    Divide both sides by the final concentration, M2.

    V2 = M1V1M2
  3. 3
    Insert the known values

    Both volumes can stay in mL because the units match.

    V2 = 2.00 M × 50.0 mL0.500 M
  4. 4
    Calculate and interpret

    Concentration becomes one quarter as large, so volume becomes four times as large.

    V2 = 2.00 × 102 mL final solution
  5. ✓
    Answer

    Bring the total solution volume to 2.00 × 102 mL (200 mL).

6.3 What stays dissolved and what reacts

When two solutions mix, start by asking which particles are in the water. Some ions pair up into an insoluble solid, a precipitate; others stay dissolved and unchanged. This lesson predicts the solid and writes only the change that happens.

What you’ll use from earlier
  • Ionic compounds and ion charges (Chapter 2).

Need a refresher? Open the table of contents and revisit that topic before starting.

The idea
What a dissolved substance puts in the water
TypeParticles in waterConducts?Examples
Strong electrolyteBreaks apart completely into ionsYesDissolved ionic compounds: NaCl → Na+ + Cl−
Weak electrolyteMostly whole molecules, a few ionsWeaklyWeak bases such as ammonia, NH3
NonelectrolyteWhole, neutral molecules; no ionsNoSugar (C12H22O11), ethanol
Moving ions carry charge, so only solutions with ions conduct electricity.
  • Ionic compounds that dissolve break into ions, so they are strong electrolytes.
  • Most molecular compounds stay as molecules, so they are nonelectrolytes.
  • Exceptions: acids and weak bases such as NH3 are molecular but form ions in water (6.4).
Solubility rules for this course
Ion groupUsuallyExceptions
Nitrates (NO3−), Group 1 salts, common ammonium (NH4+) saltsSolubleNone
Chlorides, bromides, iodidesSolubleAg+, Pb2+, Hg22+
Sulfates (SO42−)SolubleBa2+, Sr2+, Pb2+, Hg22+; CaSO4 is sparingly soluble
Carbonates, phosphates, hydroxidesPoorly solubleGroup 1 and NH4+ salts dissolve (first row); Ba(OH)2 and Sr(OH)2 are also soluble, Ca(OH)2 slightly; check your course table for others
Use this table before predicting a solid.
Before: Ag⁺, NO₃⁻, Na⁺ and Cl⁻ are dissolved, and Ag⁺ and Cl⁻ attract. After: Ag⁺ and Cl⁻ pack into solid AgCl while Na⁺ and NO₃⁻ stay dissolved as spectators. No electrons move; every ion keeps its charge. Net ionic equation: Ag⁺(aq) + Cl⁻(aq) → AgCl(s).
Ag+ and Cl− pack into solid AgCl; Na+ and NO3− stay dissolved. The solid is a repeating ionic lattice, not one AgCl molecule. Water is omitted.
Precipitation route
  • Swap ion partners.
  • Make neutral formulas.
  • Check each new formula for a solid.
  • Balance.
Writing the complete ionic equation
Split into ions
Aqueous (aq) strong electrolytes.
Keep together
Solids, liquids, gases and weak electrolytes.
From complete ionic to net ionic
  • Spectator ions: unchanged on both sides. Cross them out.
  • What remains is the net ionic equation.
  • Check both atoms and total charge.
Groups can help you recognize ions and spectators. Na is a group 1 metal, commonly forming Na⁺; Cl commonly forms Cl⁻. In AgNO₃ + NaCl, Na⁺ stays dissolved while Ag⁺ and Cl⁻ form AgCl(s). Use solubility rules and physical states. Periodic position alone does not identify every precipitate.
Groups help you recognize ions and spectators. Periodic position alone does not identify every precipitate; use the solubility rules and states.
1 · Recognize the clue
Look for this:two aqueous salts mixed, words like precipitate, spectator, net ionic, conducts, or electrolyte.
2 · Follow the route
  1. Identify each substance’s state.
  2. Separate aqueous strong electrolytes into ions.
  3. Cancel the spectator ions.
  4. Check atoms and total charge.

On the periodic table: Group 1 is the far-left column below hydrogen: lithium (Li), sodium (Na), potassium (K) and the elements under them.

On the periodic table: Barium (Ba) and strontium (Sr) are in Group 2, so they form Ba2+ and Sr2+.

On the periodic table: Sodium (Na) is in Group 1, so it forms Na+. Chlorine (Cl) is in Group 17, so it forms Cl−.

On the periodic table: Ag is silver, atomic number 47 (Group 11).

Worked example

AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq). Find the net ionic equation.

  1. 1
    Separate dissolved ionic compounds

    Split the aqueous strong electrolytes. Keep the precipitate AgCl together.

    Ag+ + NO3− + Na+ + Cl− → AgCl(s) + Na+ + NO3−
  2. 2
    Find the unchanged ions

    Na+ and NO3− stay dissolved and do not form the solid.

    ParticleLeft sideRight sideRole
    Ag+dissolvedin AgCl(s)reacts
    Cl−dissolvedin AgCl(s)reacts
    Na+dissolveddissolvedspectator
    NO3−dissolveddissolvedspectator
  3. 3
    Cancel the spectators

    Remove the unchanged ions to show only what reacts.

    Ag+(aq) + Cl−(aq) → AgCl(s)
  4. 4
    Check conservation

    Both atoms and total charge must balance.

    LeftRight
    Ag atoms11
    Cl atoms11
    Total charge(+1) + (−1) = 00
  5. ✓
    Answer

    Ag+(aq) + Cl−(aq) → AgCl(s). Ag+ and Cl− form the precipitate; Na+ and NO3− are spectators.

Section practice · 4 questions · tap to open

What this set is for: practicing the method from this section while it’s fresh. Every problem uses only what this section has taught.

Practice 1

Will AgNO3(aq) + NaCl(aq) form a precipitate?

Give me a hint

Swap ion partners to make two new formulas. Check each one against the solubility rules, including the exceptions.

Check the answer

Answer: Yes, AgCl(s)

Explain the worked problem to me

What you know: AgNO3(aq) and NaCl(aq) are mixed. What you want: whether a solid forms.

  1. List the dissolved ions: Ag+, NO3−, Na+, Cl−.
  2. Swap partners to get the two new neutral formulas: NaNO3 and AgCl.
  3. Check the solubility rules. NaNO3 is a nitrate and a Group 1 salt, so it dissolves. Most chlorides dissolve, but Ag+ is an exception to that rule.
  4. So a precipitate forms: Yes, AgCl(s).

Check: Ag+ (+1) and Cl− (−1) combine 1 : 1, so AgCl is neutral.

Watch out: "Chlorides dissolve" is not the whole rule. Always check the exceptions: Ag+, Pb2+, Hg22+.

On the periodic table: Sodium (Na) is in Group 1, so it forms Na⁺. Chlorine (Cl) is in Group 17, so it forms Cl⁻.

That’s right: Yes, AgCl(s)

YOUR PERIODIC-TABLE REFERENCE

11NaSodium22.99Group 1 · Period 3
47AgSilver107.87Group 11 · Period 5

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 2

Course solubility rules: nitrates, Group 1 salts, and common ammonium salts are soluble. Name a soluble polyatomic group in these rules.

Give me a hint

Pick a soluble group that is made of more than one atom.

Check the answer

Answer: Nitrate (ammonium also counts)

Explain the worked problem to me

What you know: the course solubility rules. What you want: a polyatomic ion whose salts are soluble.

  1. Read the "soluble" line of the rules: nitrates, Group 1 salts, and common ammonium salts.
  2. Pick the ones that are polyatomic (more than one atom). Nitrate is NO3−, one N and three O atoms.
  3. Nitrate salts have no exceptions in these rules, so the answer is Nitrate. Ammonium (NH4+) is also polyatomic and soluble, so it counts too.

Why it matters: If a nitrate appears in a mixing problem, it stays dissolved. It is often a spectator ion.

Watch out: Group 1 is a column of elements, not a polyatomic ion.

That’s right: Nitrate

Practice 3

Sugar, C12H22O11, dissolved in water: strong electrolyte, weak electrolyte, or nonelectrolyte?

Give me a hint

Is sugar ionic or molecular? Does it form ions?

Check the answer

Answer: Nonelectrolyte

Explain the worked problem to me

What you know: sugar, C12H22O11, dissolves in water. What you want: its electrolyte type.

  1. Look at the formula. It has only C, H and O, all nonmetals. So sugar is a molecular compound, not ionic.
  2. Most molecular compounds dissolve as whole, neutral molecules. Sugar is not an acid or a base, so it forms no ions.
  3. No ions means nothing carries charge. Sugar is a Nonelectrolyte.

Why it matters: A sugar solution does not conduct electricity, unlike a salt solution.

Watch out: Dissolving is not the same as forming ions. Sugar dissolves well but stays as molecules.

That’s right: Nonelectrolyte

Practice 4

Which solution conducts electricity: KBr(aq) or C2H5OH(aq) (ethanol)?

Give me a hint

Which one is ionic?

Check the answer

Answer: KBr(aq)

Explain the worked problem to me

What you know: two solutions, KBr(aq) and C2H5OH(aq). What you want: which one conducts.

  1. Classify each compound. KBr is a metal (K) plus a nonmetal (Br), so it is ionic. Ethanol has only C, H and O, so it is molecular.
  2. A dissolved ionic compound breaks apart: KBr → K+ + Br−. It is a strong electrolyte.
  3. Ethanol stays as neutral molecules. It is a nonelectrolyte.
  4. Moving ions carry charge, so the conductor is KBr(aq).

Why it matters: Conductivity is a quick test for whether ions are present.

Watch out: The OH in ethanol is not a hydroxide ion. It is bonded inside the molecule.

That’s right: KBr(aq)

6.4 Acid–base reactions: see the particles in water

An acid in water makes hydronium, H3O+. A strong base releases hydroxide, OH−. Mixed, these two ions make water: neutralization.

What you’ll use from earlier
  • Positive and negative ions, ionic formulas, and polyatomic ions (Chapter 2).
  • Net ionic equations and spectator ions (6.3).

Need a refresher? Open the table of contents and revisit that topic before starting.

The idea
HCl transfers its gold hydrogen as H⁺ to H₂O, producing H₃O⁺ and Cl⁻.
1. Acid in water: the gold H moves from HCl to water.
HCl + H2O → H3O+ + Cl−
HCl donates H+, a proton. Water accepts it, becoming hydronium (+1).
Strong acid vs weak acid in water
Strong acid (HCl)
Essentially every molecule gives up its proton.
Holds H3O+ and Cl− in water.
Weak acid
Only some molecules do.
Holds many unchanged acid molecules.

H2SO4 is strong for its first proton only: H2SO4 + H2O → H3O+ + HSO4−.

Left: Na⁺ and OH⁻ ions packed together in a solid. Right: the same ions spread apart in a beaker of water, with a few water molecules drawn among them.
2. Base in water: Na+ and OH− separate; OH− stays one ion.
NaOH(s) → Na+(aq) + OH−(aq)
NaOH is ionic: Na+ plus polyatomic OH−.
  • Base solutions are usually dissolved metal hydroxides.
  • Strong base: the dissolved part separates completely into ions.
  • “Strong” means full separation, not high concentration.
One H₃O⁺ and one OH⁻ react to form two H₂O molecules.
3. Mix: OH− takes H+ from H3O+. Two waters form; charges cancel.
Neutralization: HCl(aq) + NaOH(aq)
Full ionic: H3O+ + Cl− + Na+ + OH− → 2H2O + Cl− + Na+
Net ionic: H3O+ + OH− → 2H2O
Shorthand: H+ + OH− → H2O
Cross out unchanged Na+ and Cl− for the net ionic equation. H+ is shorthand for the proton in water.
1 · Recognize the clue
Look for this:an acid and a strong base mixed in water, asking which ions react, which are spectators, or what forms.
2 · Follow the route
  1. Acid in water: find H3O+.
  2. Base in water: find OH−.
  3. Combine only the ions that change.

On the periodic table: Sodium (Na) is a Group 1 metal, so it forms Na+.

Worked example

Given H3O+ and OH−, find the product and balanced particle counts.

  1. 1
    Count the atoms

    Add up what the two ions bring together.

    IonH atomsO atomsCharge
    H3O+31+1
    OH−11−1
    Total420
  2. 2
    Build the product

    Two H2O molecules use exactly 4 H and 2 O.

    2 H2O = 2 × (2 H + 1 O) = 4 H + 2 O
  3. 3
    Check the charge

    Starting charge is zero; water is neutral.

    (+1) + (−1) = 0 → 2H2O has charge 0
  4. ✓
    Answer

    H3O+ + OH− → 2H2O

6.4a Solution stoichiometry and titration

Molarity turns a solution volume into moles. The balanced equation turns those into moles of another substance. A titration uses both steps to find an unknown amount.

What you’ll use from earlier
  • Moles from molarity: n = M × V (6.1).
  • Mole ratios from a balanced equation (5.2–5.3).
  • Acids, bases and neutralization (6.4).

Need a refresher? Open the table of contents and revisit that topic before starting.

The idea
Moles in a solution = molarity × liters
n = M × V
n in moles, M in mol/L, V in liters. Convert mL to L first.
A two-step text diagram. Step 1 finds moles in the solution with n = M × V, volume in liters. Step 2 uses the balanced equation: moles of B = moles of A × (coefficient of B ÷ coefficient of A).
Volume → moles (n = M × V) → moles of the other substance (balanced ratio).
A titration setup
Buretteknown molarityvolume read hereFlaskmeasured sample+ indicatoradd drop by drop
Add the known solution until the indicator changes color.
Titration words
TermMeaning
TitrationFinds an unknown amount with a measured solution.
EquivalenceThe balanced mole ratio is met.
EndpointThe observed signal, such as an indicator color change.
At equivalence: reactants match the balanced mole ratio
MA × VAcoefficient A = MB × VBcoefficient B
Use liters for both volumes and the balanced coefficients.
Full neutralization ratios
AcidBalanced reactionAcid : NaOH
HClHCl + NaOH → NaCl + H2O1 : 1
H2SO4H2SO4 + 2NaOH → Na2SO4 + 2H2O1 : 2
1 · Recognize the clue
Look for this:a volume and molarity of one solution, a second solution's molarity, and words like neutralized, titration, or mole ratio.
2 · Follow the route
  1. Convert volumes to liters.
  2. Find moles of the known: n = M × V.
  3. Use the balanced ratio for moles of the other.
  4. Convert to the volume or molarity asked for.

On the periodic table: No table values are needed when molarity and volume are given.

On the periodic table: Given grams instead? Get molar mass from the periodic table first, e.g. NaOH: 22.99 + 16.00 + 1.008 = 40.00 g/mol.

Worked example

25.0 mL of 0.100 M HCl is titrated with 0.200 M NaOH. Find the moles of HCl and the NaOH volume needed.

  1. 1
    Convert the volume

    Molarity is per liter.

    25.0 mL × 1 L1000 mL = 0.0250 L
  2. 2
    Find moles of HCl

    Use n = M × V.

    nHCl = 0.100 molL × 0.0250 L = 0.00250 mol HCl
  3. 3
    Apply the 1 : 1 ratio

    HCl + NaOH → NaCl + H2O, so one NaOH per HCl.

    0.00250 mol HCl × 1 mol NaOH1 mol HCl = 0.00250 mol NaOH
  4. 4
    Find the NaOH volume

    Rearrange n = M × V to V = n ÷ M.

    V = 0.00250 mol0.200 mol/L = 0.0125 L = 12.5 mL
  5. ✓
    Answer

    0.00250 mol HCl, which needs 0.00250 mol NaOH, or 12.5 mL of 0.200 M NaOH

Section practice · 8 questions · tap to open

What this set is for: practicing the method from this section while it’s fresh. Every problem uses only what this section has taught.

Practice 1

10.0 mL of 0.100 M HCl is neutralized by 0.200 M NaOH. Find NaOH volume; the ratio is 1:1.

Give me a hint

Convert acid volume to liters before calculating moles.

Check the answer

Answer: 5.00 mL

Explain the worked problem to me

What you know: 10.0 mL of 0.100 M HCl; 0.200 M NaOH; HCl : NaOH = 1 : 1. What you want: the NaOH volume.

  1. Convert the acid volume to liters: 10.0 mL × (1 L / 1000 mL) = 0.0100 L.
  2. Find moles of HCl with n = M × V: 0.100 mol/L × 0.0100 L = 0.00100 mol HCl. The L units cancel.
  3. Use the 1 : 1 ratio: 0.00100 mol HCl needs 0.00100 mol NaOH.
  4. Find the base volume with V = n ÷ M: 0.00100 mol ÷ 0.200 mol/L = 0.00500 L. Then 0.00500 L × (1000 mL / 1 L) = 5.00 mL. Three significant figures, like the data.

Check: The base is twice as concentrated as the acid, so it needs half the volume: 10.0 ÷ 2 = 5.00 mL.

Watch out: Use liters in n = M × V. Using 10.0 mL directly gives moles 1000 times too big.

That’s right: 5.00 mL

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 2

20.0 mL of 0.100 M HCl is neutralized by 0.200 M NaOH. Find NaOH volume; the ratio is 1:1.

Give me a hint

Convert acid volume to liters before calculating moles.

Check the answer

Answer: 10.0 mL

Explain the worked problem to me

What you know: 20.0 mL of 0.100 M HCl; 0.200 M NaOH; HCl : NaOH = 1 : 1. What you want: the NaOH volume.

  1. Convert the acid volume to liters: 20.0 mL × (1 L / 1000 mL) = 0.0200 L.
  2. Find moles of HCl with n = M × V: 0.100 mol/L × 0.0200 L = 0.00200 mol HCl. The L units cancel.
  3. Use the 1 : 1 ratio: 0.00200 mol HCl needs 0.00200 mol NaOH.
  4. Find the base volume with V = n ÷ M: 0.00200 mol ÷ 0.200 mol/L = 0.0100 L. Then 0.0100 L × (1000 mL / 1 L) = 10.0 mL. Three significant figures, like the data.

Check: The base is twice as concentrated as the acid, so it needs half the volume: 20.0 ÷ 2 = 10.0 mL.

Watch out: Use liters in n = M × V. Using 20.0 mL directly gives moles 1000 times too big.

That’s right: 10.0 mL

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 3

30.0 mL of 0.100 M HCl is neutralized by 0.200 M NaOH. Find NaOH volume; the ratio is 1:1.

Give me a hint

Convert acid volume to liters before calculating moles.

Check the answer

Answer: 15.0 mL

Explain the worked problem to me

What you know: 30.0 mL of 0.100 M HCl; 0.200 M NaOH; HCl : NaOH = 1 : 1. What you want: the NaOH volume.

  1. Convert the acid volume to liters: 30.0 mL × (1 L / 1000 mL) = 0.0300 L.
  2. Find moles of HCl with n = M × V: 0.100 mol/L × 0.0300 L = 0.00300 mol HCl. The L units cancel.
  3. Use the 1 : 1 ratio: 0.00300 mol HCl needs 0.00300 mol NaOH.
  4. Find the base volume with V = n ÷ M: 0.00300 mol ÷ 0.200 mol/L = 0.0150 L. Then 0.0150 L × (1000 mL / 1 L) = 15.0 mL. Three significant figures, like the data.

Check: The base is twice as concentrated as the acid, so it needs half the volume: 30.0 ÷ 2 = 15.0 mL.

Watch out: Use liters in n = M × V. Using 30.0 mL directly gives moles 1000 times too big.

That’s right: 15.0 mL

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 4

40.0 mL of 0.100 M HCl is neutralized by 0.200 M NaOH. Find NaOH volume; the ratio is 1:1.

Give me a hint

Convert acid volume to liters before calculating moles.

Check the answer

Answer: 20.0 mL

Explain the worked problem to me

What you know: 40.0 mL of 0.100 M HCl; 0.200 M NaOH; HCl : NaOH = 1 : 1. What you want: the NaOH volume.

  1. Convert the acid volume to liters: 40.0 mL × (1 L / 1000 mL) = 0.0400 L.
  2. Find moles of HCl with n = M × V: 0.100 mol/L × 0.0400 L = 0.00400 mol HCl. The L units cancel.
  3. Use the 1 : 1 ratio: 0.00400 mol HCl needs 0.00400 mol NaOH.
  4. Find the base volume with V = n ÷ M: 0.00400 mol ÷ 0.200 mol/L = 0.0200 L. Then 0.0200 L × (1000 mL / 1 L) = 20.0 mL. Three significant figures, like the data.

Check: The base is twice as concentrated as the acid, so it needs half the volume: 40.0 ÷ 2 = 20.0 mL.

Watch out: Use liters in n = M × V. Using 40.0 mL directly gives moles 1000 times too big.

That’s right: 20.0 mL

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 5

50.0 mL of 0.100 M HCl is neutralized by 0.200 M NaOH. Find NaOH volume; the ratio is 1:1.

Give me a hint

Convert acid volume to liters before calculating moles.

Check the answer

Answer: 25.0 mL

Explain the worked problem to me

What you know: 50.0 mL of 0.100 M HCl; 0.200 M NaOH; HCl : NaOH = 1 : 1. What you want: the NaOH volume.

  1. Convert the acid volume to liters: 50.0 mL × (1 L / 1000 mL) = 0.0500 L.
  2. Find moles of HCl with n = M × V: 0.100 mol/L × 0.0500 L = 0.00500 mol HCl. The L units cancel.
  3. Use the 1 : 1 ratio: 0.00500 mol HCl needs 0.00500 mol NaOH.
  4. Find the base volume with V = n ÷ M: 0.00500 mol ÷ 0.200 mol/L = 0.0250 L. Then 0.0250 L × (1000 mL / 1 L) = 25.0 mL. Three significant figures, like the data.

Check: The base is twice as concentrated as the acid, so it needs half the volume: 50.0 ÷ 2 = 25.0 mL.

Watch out: Use liters in n = M × V. Using 50.0 mL directly gives moles 1000 times too big.

That’s right: 25.0 mL

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 6

How many mol NaOH fully neutralize 1 mol H2SO4?

Give me a hint

Count the H+ each H2SO4 can give. Each OH− takes one.

Check the answer

Answer: 2 mol

Explain the worked problem to me

What you know: 1 mol H2SO4. What you want: moles of NaOH for full neutralization.

  1. Count the acidic H in H2SO4: there are 2. Each OH− neutralizes one H+.
  2. Write the balanced equation: H2SO4 + 2NaOH → Na2SO4 + 2H2O.
  3. Use the ratio: 1 mol H2SO4 × (2 mol NaOH / 1 mol H2SO4) = 2 mol.

Check: Atoms balance: 2 Na, 1 S, 6 O and 4 H on each side.

Watch out: Do not assume 1 : 1 for every acid. The 1 : 1 ratio is for HCl and NaOH.

That’s right: 2 mol

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1
11NaSodium22.99Group 1 · Period 3
16SSulfur32.06Group 16 · Period 3

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 7

Is an endpoint identical by definition to equivalence?

Give me a hint

Equivalence comes from the mole ratio. The endpoint is what the indicator shows.

Check the answer

Answer: No

Explain the worked problem to me

What you know: the definitions of endpoint and equivalence point. What you want: whether endpoint and equivalence mean the same thing.

  1. Equivalence is a stoichiometric condition: the added base exactly matches the acid in the balanced mole ratio.
  2. The endpoint is what you observe, such as an indicator changing color.
  3. A good indicator makes the endpoint land very close to equivalence. But one is a signal and the other is a mole ratio, so they are not identical by definition. The answer is No.

Why it matters: The endpoint is how you estimate equivalence in the lab.

Watch out: "Close in practice" is not the same as "the same by definition."

That’s right: No

Practice 8

Equal volumes of 0.100 M and 0.200 M solutions: equal moles?

Give me a hint

Moles = molarity × volume.

Check the answer

Answer: No

Explain the worked problem to me

What you know: equal volumes, one 0.100 M and one 0.200 M. What you want: whether the moles are equal.

  1. Use n = M × V for each. Call the shared volume V.
  2. First solution: 0.100 mol/L × V. Second: 0.200 mol/L × V.
  3. The second has twice the molarity at the same volume, so it holds twice the moles. The answer is No.

Check: Try V = 1.00 L: 0.100 mol versus 0.200 mol.

Watch out: Equal volumes need not mean equal moles. Molarity tells you how much solute is packed into each liter.

That’s right: No

6.5 Redox: electron transfer

In a redox reaction, electrons move from one substance to another. One side loses electrons while the other gains them. This lesson tracks changing charges to name which is which.

What you’ll use from earlier
  • Ion charge and electron counts (Chapter 1); ionic formulas (Chapter 2).

Need a refresher? Open the table of contents and revisit that topic before starting.

The idea
Two halves of one transfer
Oxidation
Loss of electrons.
Oxidation number goes up.
Reduction
Gain of electrons.
Oxidation number goes down.
Zinc loses two electrons to become Zn²⁺; copper ions gain those two electrons to become copper. Nuclei remain unchanged.
Oxidation and reduction are paired: the 2 electrons zinc loses are the 2 that Cu2+ gains. Nuclei do not change.
Zn + Cu2+ → Zn2+ + Cu, split in two
Zn → Zn2+ + 2e−   (oxidation)
Cu2+ + 2e− → Cu   (reduction)
They happen together. Proton counts do not change.
Assigning oxidation numbers
RuleExample
An element alone is 0.Zn metal: 0; Cu metal: 0
A monatomic ion has its ion charge.Zn2+: +2; Cl−: −1
In a compound or polyatomic ion, the numbers add up to the overall charge.SO42−: S + 4(−2) = −2, so S = +6
Oxygen is usually −2.O in SO42−: −2
Read the change on a number line
−10+1+2+3oxidation numberZn: 0 → +2 · oxidation · loses 2e−Cu: +2 → 0 · reduction · gains 2e−
Up the line is oxidation; down the line is reduction.
Periodic-table tiles for magnesium (12, Mg, 24.31) and oxygen (8, O, 16.00). Notes say Mg keeps its 12 protons when it loses electrons, and Mg → Mg²⁺ + 2e⁻ is oxidation.
A second case: Mg → Mg2+ + 2e− is oxidation. Mg keeps its 12 protons, so the element does not change.
1 · Recognize the clue
Look for this:words like oxidized, reduced, oxidation number, or a reaction where a metal or ion changes charge.
2 · Follow the route
  1. Assign oxidation numbers before and after.
  2. An increase means oxidation; a decrease means reduction.
  3. Check that electrons lost equal electrons gained.

On the periodic table: Zinc (Zn) is atomic number 30 and copper (Cu) is 29. Atomic number does not change in redox.

On the periodic table: Magnesium (Mg) is atomic number 12, so Mg2+ still has 12 protons.

Worked example

In Zn + Cu2+ → Zn2+ + Cu, identify oxidation and reduction.

  1. 1
    Track zinc

    Its oxidation number increases. More positive means it lost electrons.

    Zn: 0 → +2
  2. 2
    Name zinc’s change

    Oxidation means electron loss.

    Zn → Zn2+ + 2e−   oxidation
  3. 3
    Track copper

    Its oxidation number decreases as it gains electrons.

    Cu: +2 → 0
  4. 4
    Name copper’s change

    Reduction means electron gain. Cu2+ accepts electrons, so it is the oxidizing agent.

    Cu2+ + 2e− → Cu   reduction
  5. ✓
    Answer

    Zinc is oxidized and copper(II) is reduced. Cu2+ is the oxidizing agent.

    ChangeElectrons
    Zn0 → +2 (oxidized)2 lost
    Cu+2 → 0 (reduced)2 gained
    The two electron counts match.

Mixed chapter review

Answer in your notebook before revealing help. Keep your first attempt separate from an answer corrected with help.

Mixed chapter review · 14 questions · tap to open

What this set is for: problems from every section of the chapter, mixed together and not labeled, the way a test asks them. Your job is to pick the right method yourself. Do this before the skill check.

Practice 1

A solution contains 1.2 mol solute in 2.4 L solution. What is molarity?

Give me a hint

Moles and solution volume are given.

Check the answer

Answer: 0.50 M

Explain the worked problem to me

What you know: 1.2 mol solute in 2.4 L of solution. What you want: molarity.

  1. Molarity means moles of solute per liter of solution: M = moles ÷ liters.
  2. The volume is already in liters, so divide: 1.2 mol ÷ 2.4 L = 0.50 mol/L = 0.50 M. Keep two significant figures, matching the data.

Check: 2.4 L is twice 1.2, so the answer is one half: 0.50 × 2.4 = 1.2 mol.

Watch out: Divide moles by liters, not liters by moles. Flipping it gives 2 L/mol, which is not a molarity.

Your route: Moles ÷ Liters of solution

That’s right: 0.50 M

Practice 2

A solution contains 1.4 mol solute in 2.8 L solution. What is molarity?

Give me a hint

Moles and solution volume are given.

Check the answer

Answer: 0.50 M

Explain the worked problem to me

What you know: 1.4 mol solute in 2.8 L of solution. What you want: molarity.

  1. Molarity means moles of solute per liter of solution: M = moles ÷ liters.
  2. The volume is already in liters, so divide: 1.4 mol ÷ 2.8 L = 0.50 mol/L = 0.50 M. Keep two significant figures, matching the data.

Check: 2.8 L is twice 1.4, so the answer is one half: 0.50 × 2.8 = 1.4 mol.

Watch out: Divide moles by liters, not liters by moles. Flipping it gives 2 L/mol, which is not a molarity.

Your route: Moles ÷ Liters of solution

That’s right: 0.50 M

Practice 3

0.3 mol solute is in 600 mL solution. What is molarity?

Give me a hint

The solution volume is in milliliters.

Check the answer

Answer: 0.5 M

Explain the worked problem to me

What you know: 0.3 mol solute in 600 mL of solution. What you want: molarity.

  1. Molarity uses liters, so convert: 600 mL × (1 L / 1000 mL) = 0.6 L. The mL units cancel.
  2. Divide moles by liters: 0.3 mol ÷ 0.6 L = 0.5 mol/L = 0.5 M.

Check: 0.5 mol/L × 0.6 L = 0.3 mol, the amount given.

Watch out: Dividing by 600 mL gives 0.0005, which is 1000 times too small.

Your route: mL ÷ 1000 → Moles ÷ L

That’s right: 0.5 M

Practice 4

0.35 mol solute is in 700 mL solution. What is molarity?

Give me a hint

The solution volume is in milliliters.

Check the answer

Answer: 0.50 M

Explain the worked problem to me

What you know: 0.35 mol solute in 700 mL of solution. What you want: molarity.

  1. Molarity uses liters, so convert: 700 mL × (1 L / 1000 mL) = 0.700 L. The mL units cancel.
  2. Divide moles by liters: 0.35 mol ÷ 0.700 L = 0.50 mol/L = 0.50 M. Keep two significant figures, matching 0.35 mol.

Check: 0.50 mol/L × 0.700 L = 0.35 mol, the amount given.

Watch out: Dividing by 700 mL gives 0.0005, which is 1000 times too small.

Your route: mL ÷ 1000 → Moles ÷ L

That’s right: 0.50 M

Practice 5

How many moles are in 0.2 L of 4 M solution?

Give me a hint

A concentration and a volume are given.

Check the answer

Answer: 0.8 mol

Explain the worked problem to me

What you know: 0.2 L of 4 M solution. What you want: moles of solute.

  1. 4 M means 4 mol of solute in every liter of solution.
  2. Use n = M × V: 4 mol/L × 0.2 L = 0.8 mol. The L units cancel, leaving mol.

Check: 0.2 L is less than 1 L, so the moles should be less than 4. 0.8 is less than 4.

Watch out: Multiply, do not divide. 4 ÷ 0.2 gives 20, which has the wrong units.

Your route: Molarity × Liters → Moles

That’s right: 0.8 mol

Practice 6

How many moles are in 0.2 L of 4.5 M solution?

Give me a hint

A concentration and a volume are given.

Check the answer

Answer: 0.9 mol

Explain the worked problem to me

What you know: 0.2 L of 4.5 M solution. What you want: moles of solute.

  1. 4.5 M means 4.5 mol of solute in every liter of solution.
  2. Use n = M × V: 4.5 mol/L × 0.2 L = 0.9 mol. The L units cancel, leaving mol.

Check: 0.2 L is less than 1 L, so the moles should be less than 4.5. 0.9 is less than 4.5.

Watch out: Multiply, do not divide. 4.5 ÷ 0.2 gives 22.5, which has the wrong units.

Your route: Molarity × Liters → Moles

That’s right: 0.9 mol

Practice 7

80 mL of 2.0 M stock is diluted to 320 mL total volume. What is final concentration?

Give me a hint

Only solvent is added.

Check the answer

Answer: 0.50 M

Explain the worked problem to me

What you know: M1 = 2.0 M, V1 = 80 mL, V2 = 320 mL. What you want: M2.

  1. Only solvent is added, so solute moles stay the same. That gives M1V1 = M2V2.
  2. Solve for M2: M2 = M1V1 ÷ V2.
  3. Substitute: 2.0 M × 80 mL ÷ 320 mL = 160 ÷ 320 = 0.50 M (two significant figures, like 2.0 M). The mL units cancel, so you do not need to convert to liters here.

Check: The volume grew 4 times (320 ÷ 80 = 4), so the concentration drops to one quarter: 2.0 ÷ 4 = 0.50 M.

Watch out: V2 is the total final volume, 320 mL. Do not use the 240 mL of water added.

Your route: Same solute → M1V1 = M2V2

That’s right: 0.50 M

Practice 8

90 mL of 2.0 M stock is diluted to 360 mL total volume. What is final concentration?

Give me a hint

Only solvent is added.

Check the answer

Answer: 0.50 M

Explain the worked problem to me

What you know: M1 = 2.0 M, V1 = 90 mL, V2 = 360 mL. What you want: M2.

  1. Only solvent is added, so solute moles stay the same. That gives M1V1 = M2V2.
  2. Solve for M2: M2 = M1V1 ÷ V2.
  3. Substitute: 2.0 M × 90 mL ÷ 360 mL = 180 ÷ 360 = 0.50 M (two significant figures, like 2.0 M). The mL units cancel, so you do not need to convert to liters here.

Check: The volume grew 4 times (360 ÷ 90 = 4), so the concentration drops to one quarter: 2.0 ÷ 4 = 0.50 M.

Watch out: V2 is the total final volume, 360 mL. Do not use the 270 mL of water added.

Your route: Same solute → M1V1 = M2V2

That’s right: 0.50 M

Practice 9

Mixing two aqueous salts gives PbI2(s); K+ and NO3− stay dissolved. Which net ionic equation describes precipitation?

Give me a hint

A precipitate is named.

Check the answer

Answer: Pb2+ + 2I− → PbI2(s)

Explain the worked problem to me

What you know: PbI2(s) forms; K+ and NO3− stay dissolved. What you want: the net ionic equation.

  1. Write the complete ionic equation. Split the aqueous salts into ions and keep the solid together: Pb2+ + 2NO3− + 2K+ + 2I− → PbI2(s) + 2K+ + 2NO3−.
  2. Cross out the ions that are unchanged on both sides: 2K+ and 2NO3−. These are spectators.
  3. What remains is Pb2+ + 2I− → PbI2(s).

Check: Atoms: 1 Pb and 2 I on each side. Charge: (+2) + 2(−1) = 0 on the left, and the solid is 0.

Watch out: Pb2+ needs two I−. Writing Pb2+ + I− leaves the charge unbalanced.

Your route: Separate aqueous strong electrolytes → Cancel spectators

On the periodic table: Potassium (K) is in Group 1, so it forms K⁺. Iodine (I) is in Group 17, so it forms I⁻.

That’s right: Pb2+ + 2I− → PbI2(s)

YOUR PERIODIC-TABLE REFERENCE

7NNitrogen14.01Group 15 · Period 2
19KPotassium39.10Group 1 · Period 4
53IIodine126.90Group 17 · Period 5

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 10

When dilute aqueous HCl and NaOH neutralize, which net ionic pair produces water?

Give me a hint

A strong acid and base neutralize.

Check the answer

Answer: H+ + OH−

Explain the worked problem to me

What you know: HCl(aq) and NaOH(aq), a strong acid and a strong base. What you want: the ions that make water.

  1. Split both into ions: HCl gives H+ and Cl−; NaOH gives Na+ and OH−.
  2. Na+ and Cl− stay dissolved and unchanged. They are spectators.
  3. The reacting pair is H+ + OH−, which gives H+ + OH− → H2O.

Check: Atoms: 2 H and 1 O on each side. Charge: (+1) + (−1) = 0, and water is neutral.

Watch out: In water, H+ is really carried as H3O+. H+ is the short way to write it.

Your route: Identify acid/base ions → Balance neutralization

That’s right: H+ + OH−

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1
8OOxygen16.00Group 16 · Period 2

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 11

In Al + 3Ag+ → Al3+ + 3Ag, which reactant is oxidized?

Give me a hint

An electron-transfer reaction is given.

Check the answer

Answer: Al

Explain the worked problem to me

What you know: Al + 3Ag+ → Al3+ + 3Ag. What you want: the reactant that is oxidized.

  1. Assign oxidation numbers. An element alone is 0, and a monatomic ion has its ion charge.
  2. Track Al: 0 → +3. It increases, so Al loses 3 electrons. That is oxidation.
  3. Track Ag: +1 → 0. It decreases, so Ag+ gains electrons. That is reduction.
  4. The oxidized reactant is Al.

Check: Electrons lost equal electrons gained: Al loses 3, and 3 Ag+ each gain 1.

Watch out: Losing electrons makes the number go up, not down. Electrons are negative.

Your route: Compare oxidation numbers → Increase means oxidation

On the periodic table: Aluminum (Al) is in Group 13 and loses 3 electrons, so it forms Al³⁺.

That’s right: Al

YOUR PERIODIC-TABLE REFERENCE

13AlAluminum26.98Group 13 · Period 3

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Practice 12

Assign oxygen −2 in ClO3−. What is chlorine’s oxidation number?

Give me a hint

An ion charge and oxygen assignment are supplied.

Check the answer

Answer: +5

Explain the worked problem to me

What you know: ClO3− has an overall charge of −1, and each O is −2. What you want: the oxidation number of Cl.

  1. In a polyatomic ion, the oxidation numbers add up to the ion's charge. Let Cl = x.
  2. Set up the sum: x + 3(−2) = −1, so x − 6 = −1.
  3. Add 6 to both sides: x = −1 + 6 = +5.

Check: (+5) + 3(−2) = +5 − 6 = −1, the ion's charge.

Watch out: The sum equals −1, not 0. Setting it to 0 gives +6, which is wrong for an ion.

Your route: Sum oxidation numbers → Equal species charge

On the periodic table: Oxygen (O) is in Group 16, so it usually takes −2, the same as the charge of its O²⁻ ion.

That’s right: +5

Practice 13

For HCl + NaOH → NaCl + H2O, what volume of 0.10 M NaOH neutralizes 45 mL of 0.20 M HCl?

Give me a hint

Concentrations and an acid amount are given.

Check the answer

Answer: 90 mL

Explain the worked problem to me

What you know: 45 mL of 0.20 M HCl; 0.10 M NaOH; ratio 1 : 1. What you want: the NaOH volume.

  1. Find moles of HCl. Convert first: 45 mL × (1 L / 1000 mL) = 0.045 L. Then 0.20 mol/L × 0.045 L = 0.0090 mol HCl.
  2. The balanced equation is 1 : 1, so 0.0090 mol NaOH is needed.
  3. Find the base volume: 0.0090 mol ÷ 0.10 mol/L = 0.090 L. Convert: 0.090 L × (1000 mL / 1 L) = 90 mL.

Check: The base is half as concentrated as the acid, so it needs twice the volume: 2 × 45 mL = 90 mL.

Watch out: A less concentrated base means more volume, not less. If your answer is smaller than 45 mL, the division is upside down.

Your route: Balanced acid/base ratio → Moles acid → Base volume

That’s right: 90 mL

Practice 14

For HCl + NaOH → NaCl + H2O, what volume of 0.10 M NaOH neutralizes 50 mL of 0.20 M HCl?

Give me a hint

Concentrations and an acid amount are given.

Check the answer

Answer: 100 mL

Explain the worked problem to me

What you know: 50 mL of 0.20 M HCl; 0.10 M NaOH; ratio 1 : 1. What you want: the NaOH volume.

  1. Find moles of HCl. Convert first: 50 mL × (1 L / 1000 mL) = 0.050 L. Then 0.20 mol/L × 0.050 L = 0.010 mol HCl.
  2. The balanced equation is 1 : 1, so 0.010 mol NaOH is needed.
  3. Find the base volume: 0.010 mol ÷ 0.10 mol/L = 0.10 L. Convert: 0.10 L × (1000 mL / 1 L) = 100 mL.

Check: The base is half as concentrated as the acid, so it needs twice the volume: 2 × 50 mL = 100 mL.

Watch out: A less concentrated base means more volume, not less. If your answer is smaller than 50 mL, the division is upside down.

Your route: Balanced acid/base ratio → Moles acid → Base volume

That’s right: 100 mL

Skill check: the chapter’s key skills

Try each fresh question without the worked examples. Record your first answer and whether you used a hint. Explain the route as well as the answer.

Skill check · 7 questions · tap to open

What this set is for: one question on each key skill from this chapter. Try each on your own, without hints, then mark how it went in the tracker below. A miss tells you which section to review.

Skill 1: Calculate molarity using liters of solution.

0.20 mol in 400 mL: molarity?

Give me a hint

Convert solution volume to liters, then divide solute moles by solution liters.

Check the answer

400 mL = 0.400 L; 0.20/0.400 = 0.50 M.

Explain the worked problem to me

What you know: 0.20 mol solute in 400 mL of solution. What you want: molarity.

  1. Molarity uses liters of solution, so convert: 400 mL × (1 L / 1000 mL) = 0.400 L.
  2. Divide moles by liters: 0.20 mol ÷ 0.400 L = 0.50 M. Keep two significant figures, matching 0.20 mol.

Check: 0.50 mol/L × 0.400 L = 0.20 mol, the amount given.

Watch out: 0.20 ÷ 400 = 0.00050, which is 1000 times too small. Convert mL to L first.

That’s right: 400 mL = 0.400 L; 0.20/0.400 = 0.50 M.

Skill 2: Solve a dilution using conserved solute moles.

Dilute 20 mL of 2.0 M to 0.50 M. Final volume?

Give me a hint

Solute moles stay constant during dilution. Use M1V1 = M2V2 and isolate the requested value.

Check the answer

2.0 × 20/0.50 = 80 mL final solution.

Explain the worked problem to me

What you know: M1 = 2.0 M, V1 = 20 mL, M2 = 0.50 M. What you want: V2, the final volume.

  1. Only solvent is added, so solute moles stay the same: M1V1 = M2V2.
  2. Divide both sides by M2: V2 = M1V1 ÷ M2.
  3. Substitute: 2.0 M × 20 mL ÷ 0.50 M = 40 ÷ 0.50 = 80 mL of final solution. The M units cancel, leaving mL.

Check: The concentration drops to one quarter (2.0 → 0.50), so the volume must grow 4 times: 4 × 20 = 80 mL.

Watch out: 80 mL is the total volume. You add only 80 − 20 = 60 mL of water.

That’s right: 2.0 × 20/0.50 = 80 mL final solution.

Skill 3: Predict common precipitates, write a net ionic equation, and identify spectator ions.

Ag+ + NO3− + Na+ + Cl− → AgCl(s) + Na+ + NO3−: remove spectators.

Give me a hint

Separate dissolved strong electrolytes into ions. Cancel species unchanged on both sides; preserve atom and charge balance.

Check the answer

Ag+ + Cl− → AgCl(s); Na+ and NO3− are spectators.

Explain the worked problem to me

What you know: the complete ionic equation, with AgCl(s) as the solid. What you want: the net ionic equation and the spectators.

  1. The aqueous ions are already split. AgCl stays together because it is a solid.
  2. Find ions that appear unchanged on both sides: Na+ and NO3−. Cross them out.
  3. What remains is Ag+ + Cl− → AgCl(s); Na+ and NO3− are spectators.

Check: Atoms: 1 Ag and 1 Cl on each side. Charge: (+1) + (−1) = 0 on the left, and the solid is 0.

Watch out: Do not split AgCl(s) into ions. Only dissolved strong electrolytes are split.

On the periodic table: Sodium (Na) is in Group 1, so it forms Na⁺. Chlorine (Cl) is in Group 17, so it forms Cl⁻.

That’s right: Ag+ + Cl− → AgCl(s); Na+ and NO3− are spectators.

YOUR PERIODIC-TABLE REFERENCE

7NNitrogen14.01Group 15 · Period 2
11NaSodium22.99Group 1 · Period 3
17ClChlorine35.45Group 17 · Period 3
47AgSilver107.87Group 11 · Period 5

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Skill 4: Explain an acid and a strong base in water, identify the reacting ions, and write their neutralization equation.

Mix HCl(aq) and NaOH(aq). Which ions react, which are spectators, and what forms?

Give me a hint

Separate dissolved strong electrolytes into ions. Cancel species unchanged on both sides; preserve atom and charge balance.

Check the answer

H3O+ and OH− react: H3O+ + OH− → 2H2O. Na+ and Cl− remain dissolved as spectator ions. The acid supplies the extra proton in hydronium.

Explain the worked problem to me

What you know: HCl(aq) and NaOH(aq) are mixed. What you want: the reacting ions, the spectators, and the product.

  1. In water, HCl gives its H+ to H2O, making H3O+ and Cl−. NaOH splits into Na+ and OH−.
  2. OH− takes the extra proton from H3O+. Hydronium becomes one water and hydroxide becomes another: H3O+ + OH− → 2H2O.
  3. Na+ and Cl− are unchanged on both sides. So H3O+ and OH− react to form 2H2O; Na+ and Cl− are spectator ions.

Check: Atoms: 4 H and 2 O on each side. Charge: (+1) + (−1) = 0, and water is neutral.

Watch out: Do not draw solid NaCl forming. Na+ and Cl− stay dissolved.

On the periodic table: Sodium (Na) is in Group 1, so it forms Na⁺. Chlorine (Cl) is in Group 17, so it forms Cl⁻.

That’s right: H3O+ and OH− react: H3O+ + OH− → 2H2O. Na+ and Cl− remain dissolved as spectator ions. The acid supplies the extra proton in hydronium.

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1
8OOxygen16.00Group 16 · Period 2
11NaSodium22.99Group 1 · Period 3
17ClChlorine35.45Group 17 · Period 3

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Skill 5: Use balanced ratios with moles from solution amounts, including acid–base titrations.

25.0 mL of 0.100 M HCl is neutralized by 0.200 M NaOH (HCl : NaOH = 1 : 1). What volume of NaOH is needed?

Give me a hint

Convert each volume to liters and find moles with n = M × V. Use the balanced equation’s mole ratio to get moles of the other substance, then convert to the requested volume or amount.

Check the answer

25.0 mL of 0.100 M HCl contains 0.00250 mol HCl. It needs 0.00250 mol NaOH, or 12.5 mL of 0.200 M NaOH.

Explain the worked problem to me

What you know: 25.0 mL of 0.100 M HCl; 0.200 M NaOH; HCl : NaOH = 1 : 1. What you want: the NaOH volume.

  1. Convert to liters: 25.0 mL × (1 L / 1000 mL) = 0.0250 L.
  2. Find moles of acid with n = M × V: 0.100 mol/L × 0.0250 L = 0.00250 mol HCl.
  3. Use the 1 : 1 ratio: 0.00250 mol HCl needs 0.00250 mol NaOH.
  4. Find the base volume: 0.00250 mol ÷ 0.200 mol/L = 0.0125 L. Convert: 0.0125 L × (1000 mL / 1 L) = 12.5 mL of 0.200 M NaOH.

Check: The base is twice as concentrated, so it needs half the volume: 25.0 ÷ 2 = 12.5 mL.

Watch out: The ratio is not always 1 : 1. For H2SO4 and NaOH it is 1 : 2.

That’s right: 25.0 mL of 0.100 M HCl contains 0.00250 mol HCl. It needs 0.00250 mol NaOH, or 12.5 mL of 0.200 M NaOH.

YOUR PERIODIC-TABLE REFERENCE

1HHydrogen1.008Group 1 · Period 1
11NaSodium22.99Group 1 · Period 3

Atomic number identifies proton count. The decimal mass is an average, not an isotope’s mass number. Use supplied rounded masses when a problem gives them.

Skill 6: Identify oxidation and reduction from changing charges.

Mg → Mg2+: oxidation or reduction?

Give me a hint

Compare oxidation numbers before and after: an increase means oxidation; a decrease means reduction.

Check the answer

Oxidation: loses electrons and its oxidation number increases.

Explain the worked problem to me

What you know: Mg → Mg2+. What you want: oxidation or reduction.

  1. Assign oxidation numbers. Mg alone is an element, so it is 0. Mg2+ is a monatomic ion, so it is +2.
  2. The number goes from 0 to +2. An increase means oxidation.
  3. To become more positive, Mg must lose 2 electrons: Mg → Mg2+ + 2e−. So it is Oxidation: Mg loses electrons and its oxidation number increases.

Check: Charge balances: 0 on the left; (+2) + 2(−1) = 0 on the right.

Watch out: Gaining a positive charge comes from losing electrons, not gaining protons. Mg keeps its 12 protons.

That’s right: Oxidation: loses electrons and its oxidation number increases.

Skill 7: Compare strong electrolytes, weak electrolytes, and nonelectrolytes in water.

Classify each dissolved solute as a strong electrolyte, weak electrolyte, or nonelectrolyte: CaCl2(aq), NH3(aq), and glucose, C6H12O6(aq).

Give me a hint

Ask two questions for each: is it ionic (metal + nonmetal) or molecular? If molecular, is it a weak acid or a weak base, like ammonia, that forms only some ions?

Check the answer

CaCl2: strong electrolyte; NH3: weak electrolyte; C6H12O6: nonelectrolyte.

Explain the worked problem to me

What you know: CaCl2, NH3, and C6H12O6 each dissolve in water. What you want: the electrolyte type of each.

  1. CaCl2 is a metal (Ca) plus a nonmetal (Cl), so it is ionic. It breaks apart completely: CaCl2 → Ca2+ + 2Cl−. It is a strong electrolyte.
  2. NH3 is molecular, but it is a weak base. Only some molecules react with water to form NH4+ and OH−; most stay as whole NH3 molecules. It is a weak electrolyte.
  3. Glucose has only C, H and O, so it is molecular. It is not an acid or a base, so it dissolves as whole, neutral molecules and forms no ions. It is a nonelectrolyte.

Check: Conductivity ranks them the same way: CaCl2(aq) conducts strongly, NH3(aq) weakly, and glucose(aq) not at all.

Watch out: Dissolving well is not the same as forming ions. Glucose dissolves easily but stays as molecules, and NH3 is mostly molecules even though it makes some ions.

On the periodic table: Calcium (Ca) is in Group 2, so it forms Ca²⁺. Chlorine (Cl) is in Group 17, so it forms Cl⁻.

That’s right: CaCl2: strong electrolyte; NH3: weak electrolyte; C6H12O6: nonelectrolyte.

What to do next

Mark each skill: “I can do it independently,” “I needed help,” or “I need another explanation.” Revisit the section with the same goal for any skill needing help, then try a different question. A successful first attempt is evidence of progress; one answer alone does not establish lasting mastery.

Final coming up?

Take the 70-question practice final

Modeled on standardized first-term general chemistry finals: 70 questions, 110 minutes. Timed or untimed. Full feedback on every question, plus your score by topic. The first 20 are free; the full final is $7.99 for 2 weeks.

Original ChemGem questions.