Textbook Question
Imagine that you have two identical flasks, one containing chlorine gas and the other containing argon at the same temperature and pressure. How can you tell which is which without opening them?
7. Gases
The Ideal Gas Law Applications
Multiple Choice
39.9 liters of hydrogen are collected over water at 76.0°C and have a pressure of 439 torr. What would the pressure (in torr) of the 'dry' hydrogen at 29.4°C in an 18.5 liter container be? (Water Vapor Pressure at 76.0°C is 301.4 torr)
A
450 torr
B
550 torr
C
512 torr
D
400 torr
Verified step by step guidance1
Start by understanding that the problem involves gas collected over water, which means the total pressure includes both the pressure of the hydrogen gas and the water vapor pressure. Use Dalton's Law of Partial Pressures to find the pressure of the dry hydrogen gas: \( P_{\text{dry}} = P_{\text{total}} - P_{\text{water vapor}} \).
Calculate the pressure of the dry hydrogen at 76.0°C using the given total pressure and water vapor pressure: \( P_{\text{dry}} = 439 \text{ torr} - 301.4 \text{ torr} \).
Apply the Combined Gas Law to find the new pressure of the dry hydrogen at 29.4°C in an 18.5 liter container. The Combined Gas Law is \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \), where \( P_1 \) and \( V_1 \) are the initial pressure and volume, \( T_1 \) is the initial temperature in Kelvin, and \( P_2 \), \( V_2 \), and \( T_2 \) are the final conditions.
Convert the temperatures from Celsius to Kelvin: \( T_1 = 76.0 + 273.15 \) and \( T_2 = 29.4 + 273.15 \).
Rearrange the Combined Gas Law to solve for the final pressure \( P_2 \): \( P_2 = \frac{P_1 V_1 T_2}{V_2 T_1} \). Substitute the known values to find \( P_2 \).
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