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Ideal Gas Law 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: Amount (n)
- Absolute pressure (P): 1 atm
- Volume (V): 24 L
- Temperature (T): 0 °C
Find: Amount of gas
Answer
2.
Problem 2.
- Solve for: Temperature (T)
- Absolute pressure (P): 1 atm
- Volume (V): 17 L
- Amount of gas (n): 1 mol
- Show temperature in: Celsius (°C)
Find: Temperature
Answer
3.
Problem 3.
- Solve for: Volume (V)
- Absolute pressure (P): 1 atm
- Amount of gas (n): 1 mol
- Temperature (T): 0 °C
- Show volume in: Milliliters (mL)
Find: Volume
Answer
4.
Problem 4.
- Solve for: Volume (V)
- Absolute pressure (P): 2 atm
- Amount of gas (n): 1 mol
- Temperature (T): 0 °C
- Show volume in: Cubic feet (ft³)
Find: Volume
Answer
5.
Problem 5.
- Solve for: Amount (n)
- Absolute pressure (P): 1 atm
- Volume (V): 25 L
- Temperature (T): 0 °C
Find: Amount of gas
Answer
6.
Problem 6.
- Solve for: Amount (n)
- Absolute pressure (P): 1 atm
- Volume (V): 32.5 L
- Temperature (T): 0 °C
Find: Amount of gas
Answer
7.
Problem 7.
- Solve for: Temperature (T)
- Absolute pressure (P): 1 atm
- Volume (V): 28 L
- Amount of gas (n): 1 mol
- Show temperature in: Kelvin (K)
Find: Temperature
Answer
8.
Problem 8.
- Solve for: Pressure (P)
- Volume (V): 18 L
- Amount of gas (n): 1 mol
- Temperature (T): 0 °C
- Show pressure in: Megapascals (MPa)
Find: Pressure
Answer
9.
Problem 9.
- Solve for: Temperature (T)
- Absolute pressure (P): 1 atm
- Volume (V): 22 L
- Amount of gas (n): 1 mol
- Show temperature in: Kelvin (K)
Find: Temperature
Answer
10.
Problem 10.
- Solve for: Amount (n)
- Absolute pressure (P): 1 atm
- Volume (V): 20 L
- Temperature (T): 0 °C
Find: Amount of gas
Answer

Answer key: Ideal Gas Law worksheet

1. Amount of gas: 1.07 mol
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $0 °C + 273.15$ $= 273.15 K$
2. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $1 atm \times 101,325$ $= 101,325 Pa$
3. Convert volume to m³, the standard unit the formula needs (1 L = 0.001 m³)
  $24 L \times 0.001$ $= 0.024 m³$
4. Find the moles of gas: multiply pressure by volume, then divide by R times the temperature
  $\frac{101,325 \times 0.024}{8.314462618 \times 273.15}$ $= 1.0707608 mol$
2. Temperature: -65.98 °C
1. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $1 atm \times 101,325$ $= 101,325 Pa$
2. Convert volume to m³, the standard unit the formula needs (1 L = 0.001 m³)
  $17 L \times 0.001$ $= 0.017 m³$
3. Find the temperature: multiply pressure by volume, then divide by the moles times the gas constant R
  $\frac{101,325 \times 0.017}{1 \times 8.314462618}$ $= 207.172138 K$
4. Change the answer back to Celsius: subtract 273.15
  $207.172138 K - 273.15$ $= −65.977862 °C$
3. Volume: 22,413.97 mL
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $0 °C + 273.15$ $= 273.15 K$
2. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $1 atm \times 101,325$ $= 101,325 Pa$
3. Find the volume: multiply the moles, the gas constant R and the temperature, then divide by the pressure
  $\frac{1 \times 8.314462618 \times 273.15}{101,325}$ $= 0.0224139695 m³$
4. Convert to mL, the unit you chose: divide by 0.000001
  $\frac{0.0224139695}{0.000001}$ $= 22,413.969545 mL$
4. Volume: 0.4 ft³
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $0 °C + 273.15$ $= 273.15 K$
2. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $2 atm \times 101,325$ $= 202,650 Pa$
3. Find the volume: multiply the moles, the gas constant R and the temperature, then divide by the pressure
  $\frac{1 \times 8.314462618 \times 273.15}{202,650}$ $= 0.0112069848 m³$
4. Convert to ft³, the unit you chose: divide by 0.028316846592
  $\frac{0.0112069848}{0.028316846592}$ $= 0.395771 ft³$
5. Amount of gas: 1.12 mol
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $0 °C + 273.15$ $= 273.15 K$
2. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $1 atm \times 101,325$ $= 101,325 Pa$
3. Convert volume to m³, the standard unit the formula needs (1 L = 0.001 m³)
  $25 L \times 0.001$ $= 0.025 m³$
4. Find the moles of gas: multiply pressure by volume, then divide by R times the temperature
  $\frac{101,325 \times 0.025}{8.314462618 \times 273.15}$ $= 1.11537584 mol$
6. Amount of gas: 1.45 mol
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $0 °C + 273.15$ $= 273.15 K$
2. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $1 atm \times 101,325$ $= 101,325 Pa$
3. Convert volume to m³, the standard unit the formula needs (1 L = 0.001 m³)
  $32.5 L \times 0.001$ $= 0.0325 m³$
4. Find the moles of gas: multiply pressure by volume, then divide by R times the temperature
  $\frac{101,325 \times 0.0325}{8.314462618 \times 273.15}$ $= 1.44998859 mol$
7. Temperature: 341.22 K
1. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $1 atm \times 101,325$ $= 101,325 Pa$
2. Convert volume to m³, the standard unit the formula needs (1 L = 0.001 m³)
  $28 L \times 0.001$ $= 0.028 m³$
3. Find the temperature: multiply pressure by volume, then divide by the moles times the gas constant R
  $\frac{101,325 \times 0.028}{1 \times 8.314462618}$ $= 341.224698 K$
8. Pressure: 0.13 MPa
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $0 °C + 273.15$ $= 273.15 K$
2. Convert volume to m³, the standard unit the formula needs (1 L = 0.001 m³)
  $18 L \times 0.001$ $= 0.018 m³$
3. Find the pressure: multiply the moles, the gas constant R and the temperature, then divide by the volume
  $\frac{1 \times 8.314462618 \times 273.15}{0.018}$ $= 126,171.970228 Pa$
4. Convert to MPa, the unit you chose: divide by 1,000,000
  $\frac{126,171.970228}{1,000,000}$ $= 0.126172 MPa$
9. Temperature: 268.11 K
1. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $1 atm \times 101,325$ $= 101,325 Pa$
2. Convert volume to m³, the standard unit the formula needs (1 L = 0.001 m³)
  $22 L \times 0.001$ $= 0.022 m³$
3. Find the temperature: multiply pressure by volume, then divide by the moles times the gas constant R
  $\frac{101,325 \times 0.022}{1 \times 8.314462618}$ $= 268.10512 K$
10. Amount of gas: 0.89 mol
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $0 °C + 273.15$ $= 273.15 K$
2. Convert pressure to Pa, the standard unit the formula needs (1 atm = 101,325 Pa)
  $1 atm \times 101,325$ $= 101,325 Pa$
3. Convert volume to m³, the standard unit the formula needs (1 L = 0.001 m³)
  $20 L \times 0.001$ $= 0.02 m³$
4. Find the moles of gas: multiply pressure by volume, then divide by R times the temperature
  $\frac{101,325 \times 0.02}{8.314462618 \times 273.15}$ $= 0.89230067 mol$