Question

Four gases were combined in a gas cylinder with these partial pressures: 3.5 atm N2, 2.8 atm O2, 0.25 atm Ar, and 0.15 atm He. What is the total pressure inside the cylinder? What is the mole fraction of N2 in the mixture?

Answer 1

Answer :

The total pressure inside the cylinder is, 6.7 atm

The mole fraction of $N_2$ in the mixture is, 0.52

Solution :

First we have to calculate the total pressure inside the cylinder.

According to the Dalton's law, the total pressure of the gas is equal to the sum of the partial pressure of the mixture of gasses.

$P_T=p_{N_2}+p_{O_2}+p_{Ar}+p_{He}$

Now put all the given values is expression, we get the total pressure inside the cylinder.

$P_T=3.5+2.8+0.25+0.15=6.7atm$

Now we have to calculate the mole fraction of $N_2$ in the mixture.

Formula used :

$p_{N_2}=X_{N_2}\times P_T$

where,

$P_T$ = total pressure = 6.7 atm

$p_{N_2}$ = partial pressure of nitrogen gas = 3.5 atm

$X_{N_2}$ = mole fraction of nitrogen gas = ?

Now put all the given values in the above formula, we get

$3.5atm=X_{N_2}\times 6.7atm$

$X_{N_2}=0.52$

Therefore, the total pressure inside the cylinder is, 6.7 atm and the mole fraction of $N_2$ in the mixture is, 0.52