In the reaction between solid calcium carbonate and excess hydrochloric acid, 31.7 g of calcium carbonate produces approximately 6.49 L of carbon dioxide gas, collected over water at 25.0 °C with a total pressure of 911.0 mmHg (23.8 mmHg vapor pressure of water).
To calculate the volume of CO₂ gas collected over water, we need to apply Dalton's Law of partial pressures to find the partial pressure of CO₂. The equation is:
\[ P_{\text{total}} = P_{\text{CO}_2} + P_{\text{H}_2\text{O}} \]
Given:
- Total pressure (\( P_{\text{total}} \)): 911.0 mmHg
- Vapor pressure of water (\( P_{\text{H}_2\text{O}} \)): 23.8 mmHg
We can find \( P_{\text{CO}_2} \) by subtracting the vapor pressure of water from the total pressure:
\[ P_{\text{CO}_2} = P_{\text{total}} - P_{\text{H}_2\text{O}} \]
\[ P_{\text{CO}_2} = 911.0 \, \text{mmHg} - 23.8 \, \text{mmHg} \]
\[ P_{\text{CO}_2} = 887.2 \, \text{mmHg} \]
Now, we can use the ideal gas law to find the volume of CO₂:
\[ PV = nRT \]
Where:
- \( P \) is the pressure in atm (converted from mmHg),
- \( V \) is the volume in liters,
- \( n \) is the moles of gas,
- \( R \) is the ideal gas constant (0.0821 L·atm/(mol·K)),
- \( T \) is the temperature in Kelvin.
First, convert pressures to atm:
\[ P_{\text{CO}_2} = 887.2 \, \text{mmHg} \times \left(\frac{1 \, \text{atm}}{760 \, \text{mmHg}}\right) \]
\[ P_{\text{CO}_2} \approx 1.167 \, \text{atm} \]