Question

Solve the following, show all work and units for your calculation: Let's say we have a mixture of hydrogen gas
(H2), and oxygen gas (O2). The mixture contains 6.7 mol hydrogen gas and 3.3 mol oxygen gas. The mixture is
in a 300 L container at 273 K and the total pressure of the gas mixture is 0.75 atm. What is the partial
pressure for each gas?​

Answer 1

Answer: The partial pressure of hydrogen gas is 0.503 atm and that of oxygen gas is 0.248 atm

Explanation:

We are given:

Moles of hydrogen gas = 6.7 moles

Moles of oxygen gas = 3.3 moles

Mole fraction of a substance is given by:

$\chi_A=\frac{n_A}{n_A+n_B}$

Mole fraction of hydrogen gas, $\chi_{H_2}=\frac{6.7}{6.7+3.3}=0.67$

Mole fraction of oxygen gas, $\chi_{O_2}=\frac{3.3}{6.7+3.3}=0.33$

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

$p_{A}=p_T\times \chi_{A}$

where,

$p_A$ = partial pressure of substance

$p_T$ = total pressure

$\chi_A$ = mole fraction of substance

• For hydrogen gas:

We are given:

$\chi_{H_2}=0.67\\p_T=0.75atm$

Putting values in above equation, we get:

$p_{H_2}=0.75atm\times 0.67=0.503atm$

• For oxygen gas:

We are given:

$\chi_{O_2}=0.33\\p_T=0.75atm$

Putting values in above equation, we get:

$p_{O_2}=0.75atm\times 0.33=0.248atm$

Hence, the partial pressure of hydrogen gas is 0.503 atm and that of oxygen gas is 0.248 atm