To calculate the pressure of a dry gas collected over water, you subtract the vapor pressure of water at the given temperature from the total pressure of the gas mixture. This is based on Dalton's Law of Partial Pressures.
Here's a breakdown of the process:
Understanding the Concepts
- Dalton's Law of Partial Pressures: This law states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. In this case, the total pressure is the sum of the pressure of the dry gas and the pressure of the water vapor.
- Vapor Pressure of Water: Water molecules are always evaporating. In a closed container, this evaporation reaches an equilibrium where the pressure exerted by the water vapor is constant at a given temperature. This is the vapor pressure of water. The vapor pressure depends solely on the temperature of the water. You can find vapor pressure values in reference tables.
- Dry Gas: The gas of interest without any water vapor mixed in. We want to know the pressure this gas would exert if water vapor wasn't present.
The Formula
The formula to calculate the pressure of dry gas (Pdry gas) is:
Pdry gas = Ptotal - PH2O
Where:
- Ptotal is the total pressure of the gas mixture (the pressure reading you obtain when collecting the gas over water).
- PH2O is the vapor pressure of water at the temperature of the experiment. You'll need to look this up in a table or chart.
Steps to Calculate Dry Gas Pressure
- Measure the Total Pressure (Ptotal): This is usually done with a barometer or manometer.
- Measure the Temperature of the Water: The temperature of the water is crucial because the vapor pressure of water is temperature-dependent.
- Find the Vapor Pressure of Water (PH2O): Look up the vapor pressure of water at the measured temperature in a reference table. These tables are readily available online or in chemistry textbooks.
- Calculate the Dry Gas Pressure (Pdry gas): Subtract the vapor pressure of water from the total pressure using the formula: Pdry gas = Ptotal - PH2O
Example
Let's say you collect oxygen gas over water at 25°C. The total pressure is 760 mmHg. You look up the vapor pressure of water at 25°C and find it to be 23.8 mmHg.
Then, the pressure of the dry oxygen gas is:
PO2 = 760 mmHg - 23.8 mmHg = 736.2 mmHg
Important Considerations
- Units: Ensure that all pressure values are in the same units (e.g., mmHg, atm, kPa) before performing the calculation.
- Temperature Accuracy: The accuracy of the dry gas pressure calculation depends on the accuracy of the temperature measurement and the corresponding vapor pressure value.
- Reference Tables: Always use a reliable vapor pressure table or chart. Different sources may have slight variations, but a reputable source should provide accurate values.
By following these steps and understanding the underlying concepts, you can accurately calculate the pressure of dry gas collected over water.
