Question: The vapor pressure of water at 40.0ºC is 7.34×103 N/m2. Using the ideal gas law, calculate the density of water vapor in g/m3 that creates a partial pressure equal to this vapor pressure. The result should be the same as the saturation vapor density at that temperature (51.1 g/m3).
The density of water vapor is 50.746 g/m3.
Ideal gas law states that the product of pressure and volume of a gas is equal to the product of temperature in Kelvin and the universal gas constant. It is expressed as;
Where is the pressure, is the volume, is the number of moles,is the universal gas constant, and is the temperature in Kelvin.
The value of pressure and temperature are given.
The value of is 8.314 Jmol-1K-1. No of moles is the ratio of a given mass of a substance to the molar mass. It is expressed as;
The molar mass of water is 18g. Substitute this in equation (2).
The density of water vapor can be derived from the ideal gas formula.
Substitute equation (3) in equation (1)
The ratio of mass to volume is the density. Therefore,
This value is approximately equal to 51.1 g/m3, which is the saturation vapor density at the given temperature. The small variation is due to the error caused by rounding the values.
So, the calculated vapor density is equal to 50.746 g/m3.
A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.40 x 107 N/m2 and a temperature of . Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature () to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.0 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?
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