Chapter 14, Problem 4STP

Interpretation Introduction

Interpretation: The partial pressure of oxygen and hydrogen is to be determined.

Concept introduction: Boyle's law relates the pressure of a gas and its volume. When a constant temperature is maintained, a decrease in pressure occurs as volume increases and an increase in volume decreases.

Answer to Problem 4STP

The correct option is (A) Oxygen is $101\text{ kPa}$ ; hydrogen is $505\text{ kPa}$ .

Explanation of Solution

Oxygen gas from a $10\text{ L}$ container at a pressure of $202\text{ kPa}$ is added to a $20\text{ L}$ container of hydrogen gas at a pressure of $505\text{ kPa}$ .

The given options are as follows:

1. Oxygen is $101\text{ kPa}$ ; hydrogen is $505\text{ kPa}$ .
2. Oxygen is $202\text{ kPa}$ ; hydrogen is $505\text{ kPa}$ .
3. Oxygen is $101\text{ kPa}$ ; hydrogen is $253\text{ kPa}$ .
4. Oxygen is $202\text{ kPa}$ ; hydrogen is $253\text{ kPa}$ .

Reason for the correct option:

The equation of Boyle's law is as follows:

  $P_1{V}_1=P_2{V}_2$

Where,

• $P_1$ and $P_2$ are the pressures.
• $V_1$ and $V_2$ are the volumes.

Substitute the values of $V_1$ , $V_2$ and $P_1$ in the above equation as follows:

  $\begin{array}{c}{P}_1{V}_1=P_2{V}_2\\ P_2=\frac{P_1{V}_1}{V_2}\\ =\frac{202\text{ kPa}\times 10\bcancel{\text{L}}}{20\bcancel{\text{L}}}\\ =101\text{ kPa}\end{array}$

Therefore, the partial pressure of oxygen gas is $101\text{ kPa}$ .

The final partial pressure of hydrogen gas does not change because it remains in the same container with the same volume. Therefore, the partial pressure of hydrogen gas is $505\text{ kPa}$ .

Hence, the correct option is (A) Oxygen is $101\text{ kPa}$; hydrogen is

Conclusion

Reason for the incorrect options

The partial pressure of oxygen and hydrogen gas is $101\text{ kPa}$ and $505\text{ kPa}$ , respectively.