Question

A mixture of $ 1.0g $ of $ {H_2} $ and $ 1.0g $ of $ He $ is placed in a $ 1.0L $ container at $ {27^0}C $ . What is the partial pressure of each gas and the total pressure?

Answer 1

Hint: Given the mass of each gas, temperature, and volume of container. The number of moles can be calculated from the mass and molar mass. Substitute these values in the ideal gas equation to get the partial pressure of hydrogen and helium. The sum of these two partial pressures gives the total pressure.

Complete answer:
According to Dalton’s law the sum of the partial pressure of each gas in a container is equal to the total pressure.
The ideal gas equation can be given as $ PV = nRT $
The volume is given as $ 1.0L $
The temperature is $ {27^0}C $ which means $ 27 + 273 = 300K $
The ideal gas constant value is $ 0.0821atm.L.{\left( {K.mol} \right)^{ - 1}} $
Number of moles will be obtained by dividing the mass of the compound with the molar mass of that compound.
The number of moles for hydrogen gas will be $ \dfrac{1}{2} = 0.5moles $
The number of moles for helium will be $ \dfrac{1}{4} = 0.25moles $
Substitute these values in the pressure,
 $ {P_{{H_2}}} = \dfrac{{0.5 \times 0.0821 \times 300}}{1} = 12atm $
 $ {P_{He}} = \dfrac{{0.25 \times 0.0821 \times 300}}{1} = 6atm $
Thus, the pressure of hydrogen gas is $ 12atm $ and the pressure of helium is $ 6atm $ . The sum of both pressures gives the total pressure.
Total pressure is $ 6 + 12 = 18atm $
Thus, total pressure is $ 18atm $ .

Note:
While calculating the pressure of each gas from ideal gas equation, the volume must be in litres, the temperature should be in kelvins and number of moles should be in moles as the ideal gas constant value we have taken is $ 0.0821atm.L.{\left( {K.mol} \right)^{ - 1}} $ means it is in litres, atm, kelvin and moles.