Question

The gaseous mixture contains 1 mol of methane, 3mol of carbon dioxide, and1 mole of hydrogen sulfide. The pressure in the room increased from 1 atm by 1 bar.a.What are the mole fractions and partial pressures of the gases?

Answer 1

This is an incomplete question, here is a complete question.

The gaseous mixture contains 1 mol of methane, 3 mol of carbon dioxide, and 1 mole of hydrogen sulfide. The total pressure in the room 1 atm. What are the mole fractions and partial pressures of the gases?

Answer :

The mole fraction of $CH_4,CO_2$ and $H_2S$ gases are, 0.2, 0.6 and 0.2 respectively.

The partial pressure of $CH_4,CO_2$ and $H_2S$ gases are, 0.2, 0.6 and 0.2 atm respectively.

Explanation : Given,

Moles of $CH_4$ = 1 mole

Moles of $CO_2$ = 3 mole

Moles of $H_2S$ = 1 mole

Now we have to calculate the mole fraction of $CH_4,CO_2$ and $H_2S$ gases.

$\text{Mole fraction of }CH_4=\frac{\text{Moles of }CH_4}{\text{Moles of }CH_4+\text{Moles of }CO_2+\text{Moles of }H_2S}$

$\text{Mole fraction of }CH_4=\frac{1}{1+3+1}=0.2$

and,

$\text{Mole fraction of }CO_2=\frac{\text{Moles of }CO_2}{\text{Moles of }CH_4+\text{Moles of }CO_2+\text{Moles of }H_2S}$

$\text{Mole fraction of }CO_2=\frac{3}{1+3+1}=0.6$

and,

$\text{Mole fraction of }H_2S=\frac{\text{Moles of }H_2S}{\text{Moles of }CH_4+\text{Moles of }CO_2+\text{Moles of }H_2S}$

$\text{Mole fraction of }H_2S=\frac{1}{1+3+1}=0.2$

Thus, the mole fraction of $CH_4,CO_2$ and $H_2S$ gases are, 0.2, 0.6 and 0.2 respectively.

Now we have to calculate the partial pressure of $CH_4,CO_2$ and $H_2S$ gases.

According to the Raoult's law,

$p_i=X_i\times p_T$

where,

$p_i$ = partial pressure of gas

$p_T$ = total pressure of gas  = 1 atm

$X_i$ = mole fraction of gas

$p_{CH_4}=X_{CH_4}\times p_T$

$p_{CH_4}=0.2\times 1atm=0.2atm$

and,

$p_{CO_2}=X_{CO_2}\times p_T$

$p_{CO_2}=0.6\times 1atm=0.6atm$

and,

$p_{H_2S}=X_{H_2S}\times p_T$

$p_{H_2S}=0.2\times 1atm=0.2atm$

Thus, the partial pressure of $CH_4,CO_2$ and $H_2S$ gases are, 0.2, 0.6 and 0.2 atm respectively.