Amixture 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 =

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

Explanation:

For 1:

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

    .....(1)

Given mass of helium = 0.723 g

Molar mass of helium = 4 g/mol

Putting values in equation 1, we get:

Given mass of methane gas = 3.43 g

Molar mass of methane gas = 16 g/mol

Putting values in equation 1, we get:

To calculate the mole fraction , we use the equation:

    .......(2)

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

      ......(3)

We are given:

Putting values in equation 2, we get:

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

Putting values in equation 3, we get:

We are given:

Putting values in equation 2, we get:

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

Putting values in equation 3, we get:

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

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:

For carbon dioxide gas:

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

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