Hydrogen gas at a temperature of 22.00C that is confined is a 5.00-L cylinder exerts a pressure of 4.20 atm. If the gas is released into a 10.0-L reaction vessel at a temperature of 33.60C, what will be the pressure inside the reaction vessel? Hydrogen gas at a temperature of 22.00C that is confined is a 5.00-L cylinder exerts a pressure of 4.20 atm. If the gas is released into a 10.0-L reaction vessel at a temperature of 33.60C, what will be the pressure inside the reaction vessel?
The Correct Answer and Explanation is :
Solution:
We will use the combined gas law:
[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
]
Where:
- (P_1, V_1, T_1) are the initial pressure, volume, and temperature.
- (P_2, V_2, T_2) are the final pressure, volume, and temperature.
Given:
- (P_1 = 4.20 \, \text{atm})
- (V_1 = 5.00 \, \text{L})
- (T_1 = 22.00 \, ^\circ \text{C} = 22.00 + 273.15 = 295.15 \, \text{K})
- (V_2 = 10.0 \, \text{L})
- (T_2 = 33.60 \, ^\circ \text{C} = 33.60 + 273.15 = 306.75 \, \text{K})
- (P_2 = ?)
Step 1: Rearrange the equation to solve for (P_2):
[
P_2 = P_1 \times \frac{V_1}{V_2} \times \frac{T_2}{T_1}
]
Step 2: Substitute the values:
[
P_2 = 4.20 \, \text{atm} \times \frac{5.00 \, \text{L}}{10.0 \, \text{L}} \times \frac{306.75 \, \text{K}}{295.15 \, \text{K}}
]
Step 3: Perform the calculations:
- (\frac{V_1}{V_2} = \frac{5.00}{10.0} = 0.50)
- (\frac{T_2}{T_1} = \frac{306.75}{295.15} \approx 1.0393)
- (P_2 = 4.20 \times 0.50 \times 1.0393 \approx 2.18 \, \text{atm})
Final Answer:
The pressure in the reaction vessel is approximately 2.18 atm.
Explanation:
The combined gas law relates the pressure, volume, and temperature of a gas system. When hydrogen gas is transferred to the reaction vessel, its volume doubles (from 5.00 L to 10.0 L), reducing the pressure since volume and pressure are inversely proportional. However, the temperature also increases, which increases the pressure as temperature and pressure are directly proportional.
In this problem, the effects of increased volume and temperature oppose each other. The increase in volume (from 5.00 L to 10.0 L) halves the pressure, but the temperature increase (from 22.00°C to 33.60°C) slightly raises the pressure. The result is a final pressure of 2.18 atm, which is less than the initial pressure of 4.20 atm due to the dominant effect of the increased volume.