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7. Gases
The Ideal Gas Law Applications
Multiple Choice
45.4 liters of hydrogen are collected over water at 76.0°C and has a pressure of 498 torr. What would the pressure (in torr) of the 'dry' hydrogen at 22.2°C in an 11.6 liter container be? (Water Vapor Pressure at 76.0°C is 301.4 torr)
A
312.4 torr
B
196.6 torr
C
152.3 torr
D
245.8 torr
Verified step by step guidance1
First, determine the pressure of the 'dry' hydrogen gas by subtracting the water vapor pressure from the total pressure. Use the formula: P_dry = P_total - P_water, where P_total is 498 torr and P_water is 301.4 torr.
Next, use the ideal gas law to relate the initial and final conditions of the hydrogen gas. The formula is: (P1 * V1) / T1 = (P2 * V2) / T2, where P1 is the initial pressure of dry hydrogen, V1 is the initial volume, T1 is the initial temperature in Kelvin, P2 is the final pressure, V2 is the final volume, and T2 is the final temperature in Kelvin.
Convert the temperatures from Celsius to Kelvin by adding 273.15. So, T1 = 76.0 + 273.15 and T2 = 22.2 + 273.15.
Substitute the known values into the rearranged ideal gas law equation to solve for the final pressure P2: P2 = (P1 * V1 * T2) / (V2 * T1).
Calculate the final pressure P2 using the values obtained from the previous steps. This will give you the pressure of the 'dry' hydrogen gas in the 11.6-liter container at 22.2°C.
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