7. Calculate the partial pressure of oxygen and nitrogen in a mixture of 35.0 g of oxygen gas and 31.5 g of nitrogen gas in a 2.0 L container at 45 °C.

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**Problem Statement:**

Calculate the partial pressure of oxygen and nitrogen in a mixture of 35.0 g of oxygen gas and 31.5 g of nitrogen gas in a 2.0 L container at 45 °C.

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**Solution Process:**

To find the partial pressures of oxygen (O₂) and nitrogen (N₂), we will use the ideal gas law and the concept of partial pressures.

1. **Convert Mass to Moles:**
   - Molar mass of O₂ = 32.00 g/mol
   - Moles of O₂ = 35.0 g / 32.00 g/mol = 1.094 moles
   
   - Molar mass of N₂ = 28.02 g/mol
   - Moles of N₂ = 31.5 g / 28.02 g/mol = 1.124 moles

2. **Use the Ideal Gas Law:**
   - Ideal gas law: PV = nRT
   - P = nRT/V
  
   - R (ideal gas constant) = 0.0821 L·atm/mol·K
   - T = 45 °C = 318 K (Kelvin conversion: °C + 273)
   - V = 2.0 L

3. **Calculate Partial Pressure of Each Gas:**
   - Partial pressure of O₂ (P₁) = (1.094 moles) × (0.0821 L·atm/mol·K) × (318 K) / 2.0 L
   
   - Partial pressure of N₂ (P₂) = (1.124 moles) × (0.0821 L·atm/mol·K) × (318 K) / 2.0 L

4. **Calculate Total Pressure (if needed):**
   - Total pressure (P_total) = P₁ + P₂

The partial pressures and total pressure can be calculated using the above formulas. This process illustrates the key applications of the ideal gas law in conjunction with Dalton's Law of Partial Pressures in gas mixtures.
Transcribed Image Text:**Problem Statement:** Calculate the partial pressure of oxygen and nitrogen in a mixture of 35.0 g of oxygen gas and 31.5 g of nitrogen gas in a 2.0 L container at 45 °C. --- **Solution Process:** To find the partial pressures of oxygen (O₂) and nitrogen (N₂), we will use the ideal gas law and the concept of partial pressures. 1. **Convert Mass to Moles:** - Molar mass of O₂ = 32.00 g/mol - Moles of O₂ = 35.0 g / 32.00 g/mol = 1.094 moles - Molar mass of N₂ = 28.02 g/mol - Moles of N₂ = 31.5 g / 28.02 g/mol = 1.124 moles 2. **Use the Ideal Gas Law:** - Ideal gas law: PV = nRT - P = nRT/V - R (ideal gas constant) = 0.0821 L·atm/mol·K - T = 45 °C = 318 K (Kelvin conversion: °C + 273) - V = 2.0 L 3. **Calculate Partial Pressure of Each Gas:** - Partial pressure of O₂ (P₁) = (1.094 moles) × (0.0821 L·atm/mol·K) × (318 K) / 2.0 L - Partial pressure of N₂ (P₂) = (1.124 moles) × (0.0821 L·atm/mol·K) × (318 K) / 2.0 L 4. **Calculate Total Pressure (if needed):** - Total pressure (P_total) = P₁ + P₂ The partial pressures and total pressure can be calculated using the above formulas. This process illustrates the key applications of the ideal gas law in conjunction with Dalton's Law of Partial Pressures in gas mixtures.
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