The compressibility factor Z=PV/RT for 1 mol of a real gas is greater than unity at a pressure of 1 atm and 273.15 K. The molar volume of the gas at STP will be :
Question
The compressibility factor Z=PV/RT for 1 mol of a real gas is greater than unity at a pressure of 1 atm and 273.15 K. The molar volume of the gas at STP will be :
Solution
The compressibility factor (Z) is a measure of how much a real gas deviates from ideal gas behavior. It is given by the equation Z = PV/RT, where P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature.
In this case, we are told that Z > 1 for 1 mol of a real gas at a pressure of 1 atm and a temperature of 273.15 K.
The molar volume of a gas is the volume occupied by one mole of that gas. At standard temperature and pressure (STP), which is defined as a temperature of 273.15 K and a pressure of 1 atm, an ideal gas occupies a volume of 22.4 L/mol.
However, since we know that Z > 1 for this gas under these conditions, this means that the gas is less compressible than an ideal gas. Therefore, it occupies a larger volume than an ideal gas would under the same conditions.
So, the molar volume of the gas at STP will be greater than 22.4 L/mol. The exact volume would depend on the specific value of Z for this gas, which is not provided in the question.
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