A mixture of hydrogen gas and oxygen gas exerts a total pressure of 3.0 atm on the walls of its container. If the partial pressure of hydrogen is 1.65 atm, find the mole fraction of oxygen in the mixture.
The Correct Answer and Explanation is :
To find the mole fraction of oxygen in the mixture, we can apply Dalton’s Law of Partial Pressures. Dalton’s Law states that the total pressure of a gas mixture is the sum of the partial pressures of the individual gases:
[
P_{\text{total}} = P_{\text{H}2} + P{\text{O}_2}
]
Where:
- ( P_{\text{total}} = 3.0 \, \text{atm} ) (total pressure of the gas mixture)
- ( P_{\text{H}_2} = 1.65 \, \text{atm} ) (partial pressure of hydrogen gas)
Step 1: Calculate the partial pressure of oxygen gas
To find the partial pressure of oxygen, we rearrange the equation:
[
P_{\text{O}2} = P{\text{total}} – P_{\text{H}_2}
]
Substitute the given values:
[
P_{\text{O}_2} = 3.0 \, \text{atm} – 1.65 \, \text{atm} = 1.35 \, \text{atm}
]
Step 2: Calculate the mole fraction of oxygen
The mole fraction of a component in a mixture is the ratio of the partial pressure of that component to the total pressure of the mixture:
[
X_{\text{O}2} = \frac{P{\text{O}2}}{P{\text{total}}}
]
Substitute the known values:
[
X_{\text{O}_2} = \frac{1.35 \, \text{atm}}{3.0 \, \text{atm}} = 0.45
]
Conclusion:
The mole fraction of oxygen (( X_{\text{O}_2} )) in the mixture is 0.45.
Explanation:
The mole fraction gives a way to express the proportion of a particular gas in a mixture. By using Dalton’s Law, we first calculated the partial pressure of oxygen and then determined its mole fraction by dividing its partial pressure by the total pressure. This result means that 45% of the gas mixture is oxygen by moles.
I’ll generate an image to visually explain this.
Here is a visual representation of Dalton’s Law of Partial Pressures, showing how the partial pressures of hydrogen and oxygen gases relate to the total pressure and the calculation of the mole fraction of oxygen. Let me know if you’d like further explanation!
