Question

match the gas sample on the left with a description on the right.
you may use the same answer more than once.
clear all
0.278 moles of so₂ in
a 5.95 l container at a
temperature of 443k
has the highest average
molecular speed
0.794 moles of so₂ in
a 5.62 l container at a
temperature of 308k
has the lowest average
molecular speed
0.371 moles of so₂ in
a 4.38 l container at a
temperature of 374k
has an average
molecular speed
between the highest
and the lowest
0.745 moles of so₂ in
a 2.32 l container at a
temperature of 443k

Explanation:

Step1: Recall the formula for average molecular speed

The formula for the average molecular speed (\(v_{avg}\)) of a gas is \(v_{avg}=\sqrt{\frac{8RT}{\pi M}}\), where \(R\) is the gas constant, \(T\) is the temperature in Kelvin, and \(M\) is the molar mass of the gas. Since all the samples are of \(SO_{2}\) (so \(M\) is constant), \(v_{avg}\) depends only on \(T\). Higher \(T\) means higher \(v_{avg}\).

Step2: Compare the temperatures of the gas samples

The temperatures of the gas samples are:

• First sample: \(T = 443K\)
• Second sample: \(T = 308K\)
• Third sample: \(T = 374K\)
• Fourth sample: \(T = 443K\)

The highest temperature is \(443K\) (first and fourth samples). The lowest temperature is \(308K\) (second sample). The temperature \(374K\) (third sample) is between \(308K\) and \(443K\).

Answer:

• \(0.278\) moles of \(SO_{2}\) in a \(5.95\) L container at a temperature of \(443K\): has the highest average molecular speed
• \(0.794\) moles of \(SO_{2}\) in a \(5.62\) L container at a temperature of \(308K\): has the lowest average molecular speed
• \(0.371\) moles of \(SO_{2}\) in a \(4.38\) L container at a temperature of \(374K\): has an average molecular speed between the highest and the lowest
• \(0.745\) moles of \(SO_{2}\) in a \(2.32\) L container at a temperature of \(443K\): has the highest average molecular speed