Gas Stoichiometry
Related Examples and Practice Problems
Topic Summary & Highlights
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Core Concept
Gas stoichiometry is the study of the relationships between volumes, moles, and masses of gaseous reactants and products in a chemical reaction. Using gas laws and stoichiometric principles, you can predict the amounts of gases involved in reactions, whether they are measured in moles, liters, or grams.
Practice Tips
Use Ideal Gas Law for Non-STP Conditions: When conditions differ from STP, use PV=nRT to find moles or volume.
Use Volume Ratios at STP: At STP, you can use the mole ratio as a volume ratio for gases.
Convert Units Carefully: Always check if you need to convert between grams, moles, or liters.
Temperature in Kelvin: Always use Kelvin in gas law calculations.
Key Concepts
Ideal Gas Law:
The ideal gas law relates pressure, volume, temperature, and moles of a gas: PV=nRT
P = Pressure (usually in atm), V = Volume (L), n = Moles of gas, R = Ideal gas constant (0.0821 L⋅atm⋅K⁻¹⋅mol⁻¹), T = Temperature (K).
Molar Volume of a Gas at STP:
At Standard Temperature and Pressure (STP), 1 mole of any ideal gas occupies 22.4 L.
STP Conditions: 0C (273.15 K) and 1 atm pressure.
Stoichiometry and Mole Ratios:
Just like in standard stoichiometry, the coefficients in a balanced chemical equation represent the mole ratios of the reactants and products.
These mole ratios allow you to relate moles of one substance to moles of another.
Volume Ratios:
In reactions where all reactants and products are gases at the same temperature and pressure, you can use the mole ratio as a volume ratio.
In the reaction 2H₂ + O₂ → 2H₂O, 2 liters of H₂ react with 1 liter of O₂ to produce 2 liters of H₂O vapor.
Steps for Solving Gas Stoichiometry Problems
Write and Balance the Chemical Equation:
Start with a balanced chemical equation to find the mole ratios.
Convert Known Quantities to Moles:
If you’re given grams of a gas, convert to moles using molar mass.
If you’re given volume (at STP), convert to moles using the molar volume (22.4 L/mol).
For other conditions, use the ideal gas law to find moles.
Use Mole Ratios to Find Unknown Quantities:
Use the mole ratio from the balanced equation to relate the known substance to the unknown substance.
Convert Moles of Desired Gas to Required Units:
Convert moles to volume at STP (using 22.4 L/mol) or use the ideal gas law if the gas is not at STP.
If mass is required, multiply moles by molar mass.
Example Problem: Gas Stoichiometry at STP
Problem: How many liters of CO₂ are produced when 5.0 g of C₂H₅OH (ethanol) combusts completely at STP?
C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O
Solution:
Write and Balance the Equation:
The equation is already balanced.
Convert Given Mass to Moles:
Molar mass of C₂H₅OH = 46.07 g/mol
Moles of C₂H₅OH = (5.0 g) / (46.07 g/mol) = 0.108 mol
Use Mole Ratio to Find Moles of CO₂:
From the balanced equation, 1 mol C₂H₅OH produces 2 mol CO₂.
Moles of CO₂ = (0.108 mol C₂H₅OH) * (2 mol CO₂ / 1 mol C₂H₅OH) = 0.216 mol CO₂
Convert Moles of CO₂ to Volume at STP:
At STP, use the molar volume (22.4 L/mol) to convert to volume.
Volume of CO₂ = (0.216 mol CO₂) * (22.4 L/mol) = 4.84 L CO₂
Answer: 4.84 liters of CO₂ are produced at STP.
Example Problem: Gas Stoichiometry Using Ideal Gas Law
Problem: How many grams of O₂ are needed to produce 15.0 L of NO₂ at 2.00 atm and 298 K in the following reaction?
2NO + O₂ → 2NO₂
Solution:
Write and Balance the Equation:
The equation is balanced as written.
Convert Volume of NO₂ to Moles Using the Ideal Gas Law:
Rearrange the ideal gas law to solve for n: n = PV/RT
Given: P = 2.00 atm, V = 15.0 L, T = 298 K, R = 0.0821 L⋅atm⋅K⁻¹⋅mol⁻¹
Moles of NO₂ = (2.00 atm * 15.0 L) / (0.0821 L⋅atm⋅K⁻¹⋅mol⁻¹ * 298 K) = 1.23 mol NO₂
Use Mole Ratio to Find Moles of O₂:
From the balanced equation, 2 mol NO₂ requires 1 mol O₂.
Moles of O₂ = (1.23 mol NO₂) * (1 mol O₂ / 2 mol NO₂) = 0.615 mol O₂
Convert Moles of O₂ to Grams:
Molar mass of O₂ = 32.00 g/mol
Mass of O₂ = (0.615 mol O₂) * (32.00 g/mol) = 19.68 g O₂
Answer: 19.68 grams of O₂ are needed.
