Questions: A 0.750 mol sample of Xe gas is confined in a 18.7 liter container at 30.8°C. If the temperature of the gas sample is lowered to 8.10°C holding the volume constant, the average molecular speed will increase decrease remain the same not enough information to answer the question

Solution Steps

The average molecular speed of a gas is related to its temperature. According to the kinetic molecular theory, the average speed of gas molecules is proportional to the square root of the absolute temperature (in Kelvin). The formula for the average speed \( v \) of gas molecules is given by:

\[ v \propto \sqrt{T} \]

where \( T \) is the absolute temperature in Kelvin.

First, convert the given temperatures from Celsius to Kelvin:

• Initial temperature: \( 30.8^\circ \mathrm{C} = 30.8 + 273.15 = 303.95 \, \mathrm{K} \)
• Final temperature: \( 8.1^\circ \mathrm{C} = 8.1 + 273.15 = 281.25 \, \mathrm{K} \)

Since the average molecular speed is proportional to the square root of the temperature, we can compare the initial and final temperatures to determine the effect on speed:

• Initial speed is proportional to \( \sqrt{303.95} \)
• Final speed is proportional to \( \sqrt{281.25} \)

Since \( 281.25 \, \mathrm{K} < 303.95 \, \mathrm{K} \), the square root of the final temperature will be less than the square root of the initial temperature. Therefore, the average molecular speed will decrease.

Final Answer