Question

you have a mixture of hydrogen gas (h₂) and oxygen gas (o₂). the mixture contains 0.5 moles of hydrogen gas and 1.5 moles of oxygen gas. the mixture is in a 10.0 l container at 25.0 °c (298k). use the ideal gas law to find the partial pressure of hydrogen gas in the mixture. (r=0.0821)
the total pressure of the gas mixture is 879 mm, using the partial pressure of hydrogen gas calculated above, what is the partial pressure of oxygen gas (o₂)? show your work.
( p_{\text{total}} = p_{\text{h}_2} + p_{\text{o}_2} )

Explanation:

Step1: Recall Dalton's Law

Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of its individual components, i.e., \( P_{\text{total}} = P_{\text{H}_2} + P_{\text{O}_2} \). (Assuming the mixture is of hydrogen and oxygen, and we know \( P_{\text{H}_2} = 40 \, \text{mmHg} \) from the context, \( P_{\text{total}} = 870 \, \text{mmHg} \))

Step2: Rearrange the formula to solve for \( P_{\text{O}_2} \)

We can rearrange the formula as \( P_{\text{O}_2} = P_{\text{total}} - P_{\text{H}_2} \).

Step3: Substitute the known values

Substitute \( P_{\text{total}} = 870 \, \text{mmHg} \) and \( P_{\text{H}_2} = 40 \, \text{mmHg} \) into the formula: \( P_{\text{O}_2} = 870 - 40 \).

Step4: Calculate the result

\( 870 - 40 = 830 \, \text{mmHg} \).

Answer:

The partial pressure of oxygen gas is \( \boldsymbol{830 \, \text{mmHg}} \).