Question

A mixture of 0.5 mol of CH4, 0.5 mol of H2, and 0.5 mol of SO2 is introduced into a 10.0 L container at 25 *C.

Answer 1

Answer: The partial pressure of individual components in the container will be same, that is $p_{SO_2}=p_{CH_4}=p_{H_2}$

Explanation:

To calculate the total pressure, we use the equation given by ideal gas equation:

$PV=nRT$

where,

P = pressure of the gas

V = Volume of gas = 10.0 L

n = Number of moles = $(n_{CH_4}+n_{H_2}+n_{SO_2})=(0.5+0.5+0.5)=1.5mol$

R = Gas constant = $0.0821\text{ L atm }mol^{-1}K^{-1}$

T = temperature of the gas = $25^oC=[25+273]K=298K$

Putting values in above equation, we get:

$P\times 10L=1.5\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times 298K\\\\P=\frac{1.5\times 0.0821\times 298}{10}=3.67atm$

The partial pressure of a gas is given by Raoult's law, which is:

$p_A=p_T\times \chi_A$     ......(1)

where,

$p_A$ = partial pressure of substance A

$p_T$ = total pressure

$\chi_A$ = mole fraction of substance A

To calculate the mole fraction of a substance, we use the equation:

$\chi_A=\frac{n_{A}}{n_{A}+n_B}$       .......(2)

We are given:

Moles of methane = 0.5 moles

Moles of hydrogen = 0.5 moles

Moles of sulfur dioxide = 0.5 moles

• For methane:

Using equation 2, we get:

$\chi_{CH_4}=\frac{n_{CH_4}}{n_{CH_4}+n_{H_2}+n_{SO_2}}=\frac{0.5}{1.5}=\frac{1}{3}$

Using equation 1, we get:

$p_{CH_4}=3.67\times \frac{1}{3}=1.22atm$

Partial pressure of methane = 1.22 atm

• For hydrogen gas:

Using equation 2, we get:

$\chi_{H_2}=\frac{n_{H_2}}{n_{CH_4}+n_{H_2}+n_{SO_2}}=\frac{0.5}{1.5}=\frac{1}{3}$

Using equation 1, we get:

$p_{H_2}=3.67\times \frac{1}{3}=1.22atm$

Partial pressure of hydrogen gas = 1.22 atm

• For sulfur dioxide:

Using equation 2, we get:

$\chi_{SO_2}=\frac{n_{SO_2}}{n_{CH_4}+n_{H_2}+n_{SO_2}}=\frac{0.5}{1.5}=\frac{1}{3}$

Using equation 1, we get:

$p_{SO_2}=3.67\times \frac{1}{3}=1.22atm$

Partial pressure of sulfur dioxide = 1.22 atm

Hence, the partial pressure of individual components in the container will be same, that is $p_{SO_2}=p_{CH_4}=p_{H_2}$