Question

Calculate the total pressure in a 10 liter cylinder which contains $ 0\cdot 4 $ g He, $ 1\cdot 6 $ g oxygen and $ 1\cdot 4 $ g nitrogen at $ 27{}^\circ \text{C} $ . Also calculate the partial pressure of He gas in the cylinder. Assume ideal behavior for gases.

Answer 1

Hint: First find the no. of moles for helium, oxygen and nitrogen. The moles can be found by dividing the given mass by the molar mass of the respective gases. After finding moles, use the ideal gas equation to find the total pressure. Once the total pressure is found we will find the partial pressure. Partial pressure for any ideal gas is given by the product of total pressure and the mole fraction of that gas.

Formula used: $ PV=nRT $
 $ P_{He}^{'}=P\times {{x}_{He}} $
Where P is total pressure
V is total volume
n is total no. of moles
R is universal gas constant
T is temperature in kelvin
 $ P_{He}^{'} $ is partial pressure of He
 $ {{x}_{He}} $ is a mole fraction of He.

Complete Step By Step Solution
Given volume of cylinder= 10 L
Mass of He $ =0\cdot 4g $ , No. of moles for He $ =\dfrac{0\cdot 4}{4}=0\cdot 1 $ (Molar mass of He is 4)
Mass of oxygen $ =1\cdot 6g $ , No. of moles for oxygen $ =\dfrac{1\cdot 6}{32}=0\cdot 05 $ (Molar mass of oxygen is 32)
Mass of nitrogen $ =1\cdot 4g $ , No. of moles for nitrogen $ =\dfrac{1\cdot 4}{28}=0\cdot 05 $ (Molar mass of nitrogen is 28)
Total no. of moles (n) $ =0\cdot 1+0\cdot 05+0\cdot 05 $
 $ =0\cdot 2 $
Temperature is given as $ 27{}^\circ \text{C} $ . Converting it into kelvin we get, T $ =273+27=300K $ (Add 273 to given temperature for converting it from Celsius to kelvin)
Using ideal gas equation-
 $ PV=nRT $ $ (R=0.082litreatm{{K}^{-1}}mol{{e}^{-1}}) $
 $ P\times 10=0\cdot 2\times 0\cdot 082\times 300 $
 $ P\times 10=4\cdot 92 $
 $ P=\dfrac{4\cdot 92}{10}=0\cdot 492atm $
Calculating mole fraction for He $ ({{x}_{He}})=\dfrac{0\cdot 1}{0\cdot 1+0\cdot 05+0\cdot 05}=\dfrac{0\cdot 1}{0\cdot 2}=0\cdot 5 $
Calculating partial pressure we have, $ P_{He}^{'}=P\times {{x}_{He}}=0\cdot 492\times 0\cdot 5=0\cdot 246atm $ .

Additional Information
Boyle’s Law states the inverse relationship between pressure and volume of a gas at a constant temperature.
Charles’s Law states that the volume and temperature (in Kelvin) are directly proportional to each other when the pressure is constant.
Avagadro’s Law states that volume of a gas is directly proportional to the amount of gas at a constant temperature and pressure.

Note
An ideal gas is a hypothetical gas in which intermolecular forces do not exist. The term is called the compression factor and it is a measure of the ideality of the gas. An ideal gas will have value equal to 1 for this factor. The greater the deviation is from the number 1, the more a given gas will behave like a real gas rather than an ideal gas. R will have different values for different units of pressure and volume. Using the correct value of R according to the units given in the question will lead to the correct answer. It is simply a constant.