Chemistry - The Ideal Gas Law and Stoichiometry

Understanding the Relationship

Gas stoichiometry combines the principles of chemical reactions with the properties of gases. In high school chemistry, you have already learned how to use the Ideal Gas Law (PV = nRT) to find properties of a single gas. Stoichiometry allows you to use the balanced chemical equation to relate the amount of one substance to another. When these two concepts meet, you can calculate the volume of a gas produced in a reaction or determine how much of a solid reactant is needed to produce a specific pressure of gas.

The key link between these two worlds is the mole (n). Stoichiometry uses mole ratios from balanced equations, and the Ideal Gas Law solves for moles based on pressure (P), volume (V), and temperature (T).

The Ideal Gas Law Formula: PV = nRT

P is Pressure (commonly in atm or kPa)

V is Volume (must be in Liters)

n is Number of Moles

R is the Ideal Gas Constant (0.0821 L atm / mol K or 8.314 L kPa / mol K)

T is Temperature (must be in Kelvin; K = Celsius + 273)

Steps for Gas Stoichiometry Problems

1. Write or check the balanced chemical equation.

2. Identify the given information. Is it gas data (P, V, T) or mass/mole data?

3. Convert your "Given" to Moles. If you start with gas data, use n = PV / RT. If you start with mass, use the molar mass.

4. Use the Mole Ratio from the balanced equation to find the moles of the "Unknown" substance. 

5. Convert the Moles of the Unknown to the final units requested (Volume, Mass, or Pressure).

Practice Problems

1. The combustion of propane follows the equation: C3H8 + 5 O2 --> 3 CO2 + 4 H2O. If 5.00 grams of propane (C3H8) is burned, what volume of CO2 gas will be produced at 1.00 atm and 298 K?

2. Solid calcium carbonate decomposes into calcium oxide and carbon dioxide gas: CaCO3 --> CaO + CO2.  How many grams of CaCO3 are needed to produce 15.0 L of CO2 at a pressure of 105 kPa and a temperature of 300 K?

3. Hydrogen gas is produced by reacting zinc with sulfuric acid: Zn + H2SO4 --> ZnSO4 + H2. If 12.0 grams of zinc react completely, what will be the pressure of the hydrogen gas if it is collected in a 4.00 L flask at 27 degrees Celsius?

4. In the reaction 2 NaN3 --> 2 Na + 3 N2, used in car airbags, how many grams of NaN3 are required to provide 65.0 L of nitrogen gas at 1.15 atm and 30 degrees Celsius?

5. Ammonia is produced via the Haber process: N2 + 3 H2 --> 2 NH3. If 20.0 L of nitrogen gas at 200 kPa and 500 K reacts with excess hydrogen, how many moles of ammonia are produced?

Answer Key

1. 8.32 L of CO2

   Steps: Convert 5.00g C3H8 to moles (0.113 mol). Use 3:1 ratio to get 0.339 mol CO2. Use V = nRT/P.

2. 63.2 grams of CaCO3

   Steps: Use n = PV/RT to find moles of CO2 (0.631 mol). Use 1:1 ratio to find moles of CaCO3. Multiply by molar mass (100.09 g/mol).

3. 1.13 atm

   Steps: Convert 12.0g Zn to moles (0.184 mol). Use 1:1 ratio to get 0.184 mol H2. Use P = nRT/V with T=300K.

4. 130.5 grams of NaN3

   Steps: Use n = PV/RT to find moles of N2 (3.01 mol). Use 2:3 ratio to find moles of NaN3 (2.007 mol). Multiply by molar mass (65.01 g/mol).

5. 1.93 moles of NH3

   Steps: Use n = PV/RT to find moles of N2 (0.963 mol). Use 2:1 mole ratio to find moles of NH3.

Chemistry - Practice Problems on Gas Laws

Boyle’s Law (P1V1 = P2V2)

1. A sample of oxygen gas occupies 10.0 L at a pressure of 101.3 kPa. What will its volume be if the pressure is increased to 202.6 kPa?

2. A gas has a volume of 500 mL at 0.95 atm. What is the pressure (in atm) if the volume is compressed to 125 mL?

3. A balloon is filled with 2.5 L of air at sea level (101.3 kPa). If it rises to 75.0 kPa, what is the new volume? 

4. If a gas at 3.0 atm is compressed from 4.0 L to 1.5 L, what is the final pressure?

5. A syringe contains 60.0 mL of gas at 100.0 kPa. To what volume must the gas be expanded to reach 40.0 kPa?

6. A diver exhales a 20.0 mL bubble at a depth where the pressure is 3.5 atm. What is the volume of the bubble when it reaches the surface (1.0 atm)?

7. A 2.0 L tank of helium is at a pressure of 15,000 kPa. If this gas is transferred to a 12.0 L tank, what is the new pressure? 

8. A gas sample at 800 mmHg occupies 300 mL. If the pressure is reduced to 600 mmHg, what is the new volume? 

9. A 5.0 L container holds nitrogen at 2.5 atm. If the volume is changed so that the pressure becomes 1.25 atm, what is the new volume? 

10. If the volume of a gas is tripled, what happens to the pressure? Show the mathematical relationship.

Charles’ Law (V1/T1 = V2/T2)

11. A sample of neon gas occupies 2.0 L at 293 K. What will be its volume at 350 K?

12. A balloon has a volume of 1.5 L at 25°C. What is its volume if placed in a freezer at -10°C?

13. A gas occupies 5.0 L at 100°C. At what temperature (in °C) will the volume be 2.5 L?

14. If a 450 mL sample of gas at 273 K is heated to 546 K, what is the new volume?

15. A container holds 12.0 L of gas at 50°C. If the volume expands to 18.0 L, what is the new temperature in Celsius?

16. A gas at 20°C has a volume of 0.75 L. To what temperature must it be heated to double its volume?

17. A sample of hydrogen occupies 100 mL at 27°C. What is its volume at 127°C?

18. At 0°C, a gas has a volume of 25.0 L. If the volume decreases to 20.0 L, what is the new temperature in Kelvin?

19. A 2.2 L balloon at 300 K is moved to an environment at 250 K. What is the new volume?

20. A gas sample occupies 8.0 L at 27°C. What volume will it occupy at 227°C?

Ideal Gas Law (PV = nRT)

21. How many moles of gas are in a 5.0 L flask at 200 kPa and 30°C?

22. What is the pressure (in kPa) exerted by 0.50 moles of CO2 in a 10.0 L container at 25°C?

23. What volume will 2.5 moles of nitrogen occupy at 1.2 atm and 310 K?

24. A 2.0 L bottle contains 0.40 moles of gas at 5.0 atm. What is the temperature in Kelvin?

25. Find the mass of oxygen (O2) in a 15.0 L tank at 150 kPa and 27°C. (Molar mass O2 = 32.0 g/mol).

26. A 500 mL flask is filled with 0.15 moles of helium at 22°C. What is the pressure in atm?

27. Calculate the moles of gas in a 25.0 L container at STP (273 K and 101.3 kPa).

28. What is the temperature (in °C) of 1.2 moles of gas that occupies 20.0 L at 1.5 atm?

29. A gas sample has a mass of 10.0 g and occupies 4.0 L at 2.0 atm and 300 K. What is its molar mass?

30. How many moles of gas are in a 0.25 L container at 10.0 kPa and 150 K?

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Answer Key

1. 5.0 L

2. 3.8 atm

3. 3.38 L

4. 8.0 atm

5. 150.0 mL

6. 70.0 mL

7. 2,500 kPa

8. 400 mL

9. 10.0 L

10. P2 = 1/3 P1

11. 2.39 L

12. 1.32 L

13. -86.5°C

14. 900 mL

15. 211.5°C

16. 313°C

17. 133.3 mL

18. 218.4 K

19. 1.83 L

20. 13.3 L

21. 0.40 mol

22. 123.9 kPa

23. 53.0 L

24. 304.5 K

25. 28.9 g

26. 7.26 atm

27. 1.11 mol

28. 31.6°C

29. 30.8 g/mol

30. 0.002 mol