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Dilution worksheet

Grades 10–11 · CCSS HSA.CED.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: C₂: final concentration
- Stock concentration (C₁): 1 M
- Volume of stock (V₁): 10 mL
- Final volume (V₂): 120 mL
Find: C₂: final concentration
Answer
2.
Problem 2.
- Solve for: C₁: stock concentration
- Volume of stock (V₁): 8 mL
- Final concentration (C₂): 0.1 M
- Final volume (V₂): 90 mL
Find: C₁: stock concentration
Answer
3.
Problem 3.
- Solve for: C₁: stock concentration
- Volume of stock (V₁): 10 mL
- Final concentration (C₂): 0.1 M
- Final volume (V₂): 120 mL
Find: C₁: stock concentration
Answer
4.
Problem 4.
- Solve for: C₁: stock concentration
- Volume of stock (V₁): 8 mL
- Final concentration (C₂): 0.1 M
- Final volume (V₂): 110 mL
Find: C₁: stock concentration
Answer
5.
Problem 5.
- Solve for: C₂: final concentration
- Stock concentration (C₁): 1 M
- Volume of stock (V₁): 14 mL
- Final volume (V₂): 90 mL
Find: C₂: final concentration
Answer
6.
Problem 6.
- Solve for: C₁: stock concentration
- Volume of stock (V₁): 13 mL
- Final concentration (C₂): 0.1 M
- Final volume (V₂): 100 mL
Find: C₁: stock concentration
Answer
7.
Problem 7.
- Solve for: C₁: stock concentration
- Volume of stock (V₁): 10 mL
- Final concentration (C₂): 0.1 M
- Final volume (V₂): 95 mL
Find: C₁: stock concentration
Answer
8.
Problem 8.
- Solve for: V₁: volume of stock to use
- Stock concentration (C₁): 1 M
- Final concentration (C₂): 0.1 M
- Final volume (V₂): 90 mL
Find: V₁: volume of stock
Answer
9.
Problem 9.
- Solve for: V₁: volume of stock to use
- Stock concentration (C₁): 2 M
- Final concentration (C₂): 0.1 M
- Final volume (V₂): 120 mL
Find: V₁: volume of stock
Answer
10.
Problem 10.
- Solve for: V₁: volume of stock to use
- Stock concentration (C₁): 2 M
- Final concentration (C₂): 0.1 M
- Final volume (V₂): 110 mL
Find: V₁: volume of stock
Answer

Answer key: Dilution worksheet

1. C₂: final concentration: 0.08 M
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get C₂ on its own
  $C₂$ $= \frac{C₁ \times V₁}{V₂}$
2. Put in your numbers and work it out
  $C₂$ $= \frac{1 M \times 10 mL}{120 mL}$ $= 0.0833333333 M$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $120 - 10$ $= 110 mL$
2. C₁: stock concentration: 1.13 M
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get C₁ on its own
  $C₁$ $= \frac{C₂ \times V₂}{V₁}$
2. Put in your numbers and work it out
  $C₁$ $= \frac{0.1 M \times 90 mL}{8 mL}$ $= 1.125 M$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $90 - 8$ $= 82 mL$
3. C₁: stock concentration: 1.2 M
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get C₁ on its own
  $C₁$ $= \frac{C₂ \times V₂}{V₁}$
2. Put in your numbers and work it out
  $C₁$ $= \frac{0.1 M \times 120 mL}{10 mL}$ $= 1.2 M$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $120 - 10$ $= 110 mL$
4. C₁: stock concentration: 1.38 M
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get C₁ on its own
  $C₁$ $= \frac{C₂ \times V₂}{V₁}$
2. Put in your numbers and work it out
  $C₁$ $= \frac{0.1 M \times 110 mL}{8 mL}$ $= 1.375 M$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $110 - 8$ $= 102 mL$
5. C₂: final concentration: 0.16 M
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get C₂ on its own
  $C₂$ $= \frac{C₁ \times V₁}{V₂}$
2. Put in your numbers and work it out
  $C₂$ $= \frac{1 M \times 14 mL}{90 mL}$ $= 0.1555555556 M$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $90 - 14$ $= 76 mL$
6. C₁: stock concentration: 0.77 M
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get C₁ on its own
  $C₁$ $= \frac{C₂ \times V₂}{V₁}$
2. Put in your numbers and work it out
  $C₁$ $= \frac{0.1 M \times 100 mL}{13 mL}$ $= 0.7692307692 M$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $100 - 13$ $= 87 mL$
7. C₁: stock concentration: 0.95 M
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get C₁ on its own
  $C₁$ $= \frac{C₂ \times V₂}{V₁}$
2. Put in your numbers and work it out
  $C₁$ $= \frac{0.1 M \times 95 mL}{10 mL}$ $= 0.95 M$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $95 - 10$ $= 85 mL$
8. V₁: volume of stock: 9 mL
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get V₁ on its own
  $V₁$ $= \frac{V₂ \times C₂}{C₁}$
2. Put in your numbers and work it out
  $V₁$ $= \frac{90 mL \times 0.1 M}{1 M}$ $= 9 mL$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $90 - 9$ $= 81 mL$
9. V₁: volume of stock: 6 mL
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get V₁ on its own
  $V₁$ $= \frac{V₂ \times C₂}{C₁}$
2. Put in your numbers and work it out
  $V₁$ $= \frac{120 mL \times 0.1 M}{2 M}$ $= 6 mL$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $120 - 6$ $= 114 mL$
10. V₁: volume of stock: 5.5 mL
1. The amount of dissolved substance stays the same (C₁V₁ = C₂V₂), so rearrange it to get V₁ on its own
  $V₁$ $= \frac{V₂ \times C₂}{C₁}$
2. Put in your numbers and work it out
  $V₁$ $= \frac{110 mL \times 0.1 M}{2 M}$ $= 5.5 mL$
3. Find the solvent to add: the final volume minus the stock you already put in, in mL
  $110 - 5.5$ $= 104.5 mL$