Question
How do I calculate the pressure of a pure gas collected over water?
Answers
GPT-4o mini
To calculate the pressure of a pure gas collected over water, you need to account for the vapor pressure of water at the temperature at which the gas is collected. The total pressure measured will be the sum of the partial pressure of the gas and the vapor pressure of the water.
Here's how to do it step-by-step:
1. **Measure the total pressure**: Use a barometer or manometer to measure the total pressure of the gas collected in the container (P_total).
2. **Determine the vapor pressure of water**: Look up the vapor pressure of water at the temperature of your experiment. This value can often be found in tables or textbooks. The vapor pressure changes with temperature, so ensure you have the correct value for the specific temperature.
3. **Apply Dalton's Law of Partial Pressures**: According to Dalton's Law, the total pressure (P_total) is equal to the sum of the partial pressures of the components in the gas mixture. In this case, it's the pressure of the gas (P_gas) and the vapor pressure of the water (P_water):
\[
P_{\text{total}} = P_{\text{gas}} + P_{\text{water}}
\]
4. **Calculate the pressure of the pure gas**:
Rearranging the equation gives you the pressure of the gas:
\[
P_{\text{gas}} = P_{\text{total}} - P_{\text{water}}
\]
### Example Calculation:
Assume you measure the total pressure (P_total) of the collected gas to be 760 mmHg and the temperature is 25°C, where the vapor pressure of water (P_water) is approximately 23.8 mmHg.
1. Measure total pressure: \(P_{\text{total}} = 760 \, \text{mmHg}\)
2. Vapor pressure of water at 25°C: \(P_{\text{water}} = 23.8 \, \text{mmHg}\)
3. Calculate the pressure of the gas:
\[
P_{\text{gas}} = 760 \, \text{mmHg} - 23.8 \, \text{mmHg} = 736.2 \, \text{mmHg}
\]
Thus, the pressure of the pure gas collected over water is approximately 736.2 mmHg.
Here's how to do it step-by-step:
1. **Measure the total pressure**: Use a barometer or manometer to measure the total pressure of the gas collected in the container (P_total).
2. **Determine the vapor pressure of water**: Look up the vapor pressure of water at the temperature of your experiment. This value can often be found in tables or textbooks. The vapor pressure changes with temperature, so ensure you have the correct value for the specific temperature.
3. **Apply Dalton's Law of Partial Pressures**: According to Dalton's Law, the total pressure (P_total) is equal to the sum of the partial pressures of the components in the gas mixture. In this case, it's the pressure of the gas (P_gas) and the vapor pressure of the water (P_water):
\[
P_{\text{total}} = P_{\text{gas}} + P_{\text{water}}
\]
4. **Calculate the pressure of the pure gas**:
Rearranging the equation gives you the pressure of the gas:
\[
P_{\text{gas}} = P_{\text{total}} - P_{\text{water}}
\]
### Example Calculation:
Assume you measure the total pressure (P_total) of the collected gas to be 760 mmHg and the temperature is 25°C, where the vapor pressure of water (P_water) is approximately 23.8 mmHg.
1. Measure total pressure: \(P_{\text{total}} = 760 \, \text{mmHg}\)
2. Vapor pressure of water at 25°C: \(P_{\text{water}} = 23.8 \, \text{mmHg}\)
3. Calculate the pressure of the gas:
\[
P_{\text{gas}} = 760 \, \text{mmHg} - 23.8 \, \text{mmHg} = 736.2 \, \text{mmHg}
\]
Thus, the pressure of the pure gas collected over water is approximately 736.2 mmHg.