A gas is collected over water at 20 degrees Celsius at a pressure of 752 mm. What is the pressure of the pure gas?
At the conditions listed
Ptotal = pgas + pH2O vapor. You need to look in your text and find the vapor pressure of H2O at 20C. That is pH2O. You know total P = 752 torr.
30L
To find the pressure of the pure gas, we need to correct for the vapor pressure of water at 20 degrees Celsius. The vapor pressure of water at 20 degrees Celsius is approximately 17.5 mmHg.
We can use Dalton's Law of partial pressures, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each component gas. In this case, the gas collected and the water vapor are the two components.
So, the pressure of the pure gas can be calculated as follows:
Pressure of Pure Gas = Total Pressure - Vapor Pressure of Water
Total Pressure = 752 mmHg
Vapor Pressure of Water = 17.5 mmHg
Pressure of Pure Gas = 752 mmHg - 17.5 mmHg
Pressure of Pure Gas = 734.5 mmHg
Therefore, the pressure of the pure gas is approximately 734.5 mmHg.
To find the pressure of the pure gas, we need to calculate the partial pressure of water vapor at 20 degrees Celsius and subtract it from the total pressure.
The partial pressure of water vapor can be determined using the vapor pressure of water at that temperature. We can refer to a vapor pressure chart or use the Antoine equation to calculate it.
One commonly used form of the Antoine equation is:
log10(P) = A - (B / (T + C))
Where P is the vapor pressure in mmHg, T is the temperature in degrees Celsius, and A, B, and C are constants specific to the substance. For water, the values of A, B, and C are 8.07131, 1730.63, and 233.426, respectively.
Plugging in the values for T = 20 degrees Celsius, we can solve for P using the equation:
log10(P) = 8.07131 - (1730.63 / (20 + 233.426))
Now, we can calculate the value of P:
P = 10^(8.07131 - (1730.63 / (20 + 233.426)))
This will give us the partial pressure of water vapor at 20 degrees Celsius.
Finally, we can find the pressure of the pure gas by subtracting the partial pressure of water vapor from the total pressure:
Pressure of pure gas = Total pressure - Partial pressure of water vapor
Plug in the values of the total pressure (752 mm) and the partial pressure of water vapor obtained from the above calculation into this formula to find the pressure of the pure gas.