Question

A mixture of helium and methane gases, at a total pressure of 821 mm Hg, contains 0.723 grams of helium and 3.43 grams of methane. What is the partial pressure of each gas in the mixture?

PHe = mm Hg
PCH4 = mm Hg

2.) A mixture of nitrogen and carbon dioxide gases contains nitrogen at a partial pressure of 363 mm Hg and carbon dioxide at a partial pressure of 564 mm Hg. What is the mole fraction of each gas in the mixture?

XN2 =
XCO2 =

Answer 1

For 1: The partial pressure of helium is 376 mmHg and that of methane gas is 445 mmHg

For 2: The mole fraction of nitrogen gas is 0.392 and that of carbon dioxide gas is 0.608

Step-by-step explanation:

For 1:

To calculate the number of moles, we use the equation:

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}` .....(1)

• For helium:

Given mass of helium = 0.723 g

Molar mass of helium = 4 g/mol

Putting values in equation 1, we get:

`\text{Moles of helium}=(0.723g)/(4g/mol)=0.181mol`

• For methane gas:

Given mass of methane gas = 3.43 g

Molar mass of methane gas = 16 g/mol

Putting values in equation 1, we get:

`\text{Moles of methane gas}=(3.43g)/(16g/mol)=0.214mol`

To calculate the mole fraction , we use the equation:

`\chi_A=(n_A)/(n_A+n_B)` .......(2)

To calculate the partial pressure of gas, we use the equation given by Raoult's law, which is:

`p_(A)=p_T* \chi_(A)` ......(3)

• For Helium gas:

We are given:

`n_(He)=0.181mol\\n_(CH_4)=0.214mol`

Putting values in equation 2, we get:

`\chi_(He)=(0.181)/(0.181+0.214)=0.458`

Calculating the partial pressure by using equation 3, we get:

`p_T=821mmHg\\\\\chi_(He)=0.458`

Putting values in equation 3, we get:

`p_(He)=0.458* 821mmHg=376mmHg`

• For Methane gas:

We are given:

`n_(He)=0.181mol\\n_(CH_4)=0.214mol`

Putting values in equation 2, we get:

`\chi_(CH_4)=(0.214)/(0.181+0.214)=0.542`

Calculating the partial pressure by using equation 3, we get:

`p_T=821mmHg\\\\\chi_(CH_4)=0.542`

Putting values in equation 3, we get:

`p_(CH_4)=0.542* 821mmHg=445mmHg`

Hence, the partial pressure of helium is 376 mmHg and that of methane gas is 445 mmHg

• For 2:

We are given:

Partial pressure of nitrogen gas = 363 mmHg

Partial pressure of carbon dioxide gas = 564 mmHg

Total pressure = (363 + 564) mmHg = 927 mmHg

Calculating the mole fraction of the gases by using equation 3:

For nitrogen gas:

`363=\chi_(N_2)* 927\\\\\chi_(N_2)=(363)/(927)=0.392`

For carbon dioxide gas:

`564=\chi_(CO_2)* 927\\\\\chi_(CO_2)=(564)/(927)=0.608`

Hence, the mole fraction of nitrogen gas is 0.392 and that of carbon dioxide gas is 0.608