How to Calculate Volume of Gas Produced in a Reaction

📚 Understanding Gas Volume in Chemical Reactions

Calculating the volume of gas produced in a chemical reaction involves stoichiometry, the ideal gas law, and understanding the reaction's conditions. Let's break it down.

🧪 Key Principles

• ⚖️Stoichiometry: Begin with a balanced chemical equation. The coefficients in the balanced equation indicate the mole ratios between reactants and products.
• 🌡️Ideal Gas Law: The ideal gas law, $PV = nRT$, relates pressure ($P$), volume ($V$), number of moles ($n$), ideal gas constant ($R$), and temperature ($T$). This law is crucial for relating moles of gas to its volume.
• 🔢Moles Calculation: Determine the number of moles of the gas produced using stoichiometry based on the limiting reactant.
• ⚙️Applying the Ideal Gas Law: Use the ideal gas law to calculate the volume of the gas produced. Rearrange the equation to solve for $V$: $V = \frac{nRT}{P}$.

⚗️ Step-by-Step Calculation

1. 📝 Write the Balanced Chemical Equation: Ensure the chemical equation is correctly balanced. For example: $2H_2(g) + O_2(g) \rightarrow 2H_2O(g)$
2. 🔍 Identify the Limiting Reactant: Determine which reactant limits the amount of product formed.
3. 🔢 Calculate Moles of Gas Produced: Use stoichiometry to find the moles of gas produced from the limiting reactant.
4. 🌡️ Determine the Conditions (T and P): Note the temperature (in Kelvin) and pressure (in atm, kPa, or mmHg) at which the gas is collected.
5. ⚙️ Apply the Ideal Gas Law: Use $V = \frac{nRT}{P}$ to calculate the volume. The ideal gas constant $R$ is $0.0821 \frac{L \cdot atm}{mol \cdot K}$ if $P$ is in atm, or $8.314 \frac{L \cdot kPa}{mol \cdot K}$ if $P$ is in kPa.

🌍 Real-world Example

Consider the decomposition of sodium azide ($NaN_3$) in airbags:

$2NaN_3(s) \rightarrow 2Na(s) + 3N_2(g)$

If 50 grams of $NaN_3$ decompose at 25°C (298 K) and 1 atm, let's calculate the volume of $N_2$ produced.

1. ⚖️ Moles of $NaN_3$: Molar mass of $NaN_3$ = 65 g/mol. Moles of $NaN_3 = \frac{50 \text{ g}}{65 \text{ g/mol}} = 0.769 \text{ mol}$
2. ⚗️ Moles of $N_2$: From the balanced equation, 2 moles of $NaN_3$ produce 3 moles of $N_2$. Moles of $N_2 = 0.769 \text{ mol } NaN_3 \times \frac{3 \text{ mol } N_2}{2 \text{ mol } NaN_3} = 1.154 \text{ mol}$
3. ⚙️ Volume of $N_2$: Using $V = \frac{nRT}{P}$, $V = \frac{1.154 \text{ mol } \times 0.0821 \frac{L \cdot atm}{mol \cdot K} \times 298 \text{ K}}{1 \text{ atm}} = 28.2 \text{ L}$

💡 Important Considerations

• 💧 Water Vapor Pressure: If the gas is collected over water, correct for the vapor pressure of water. Subtract the vapor pressure of water at the given temperature from the total pressure to find the partial pressure of the gas.
• 🌡️ Real Gases: The ideal gas law works best at low pressures and high temperatures. Under other conditions, more complex equations of state may be needed.

📝 Conclusion

Calculating the volume of gas produced in a reaction combines stoichiometry with the ideal gas law. By carefully following these steps and understanding the underlying principles, you can confidently solve these types of problems.