Question

an error has been detected in your answer. check for typos, miscalculations etc before submitting your answer.
match the gas sample on the left with a description on the right.
you may use the same answer more than once.
0.219 moles of he in a
5.17 l container at a
temperature of 425k
0.703 moles of he in a
5.20 l container at a
temperature of 302k
0.476 moles of he in a
2.31 l container at a
temperature of 374k
0.564 moles of he in a
1.00 l container at a
temperature of 425k
has the highest average
molecular speed
has the lowest average
molecular speed
has an average
molecular speed
between the highest
and the lowest
clear all

Explanation:

Step1: Recall the formula for average molecular speed

The formula for the average molecular speed of a gas is \(v_{avg}=\sqrt{\frac{8RT}{\pi M}}\), where \(R\) is the gas constant, \(T\) is the temperature, and \(M\) is the molar mass. For a given gas (\(M\) is constant for \(He\)), \(v_{avg}\propto\sqrt{T}\).

Step2: Compare the temperatures

We have four temperature values: \(T_1 = 302K\), \(T_2=374K\), \(T_3 = 425K\), \(T_4 = 425K\).

• For the highest average molecular speed: we look for the highest temperature. The highest temperature among the given data is \(425K\). There are two samples with \(T = 425K\).
• For the lowest average molecular speed: we look for the lowest temperature. The lowest temperature is \(302K\).
• For the average (in - between) molecular speed: the remaining temperature is \(374K\).

Answer:

• Has the highest average molecular speed: \(0.219\) moles of \(He\) in a \(5.17L\) container at a temperature of \(425K\) and \(0.703\) moles of \(He\) in a \(5.20L\) container at a temperature of \(425K\)
• Has the lowest average molecular speed: \(0.476\) moles of \(He\) in a \(2.31L\) container at a temperature of \(302K\)
• Has an average molecular speed (between the highest and the lowest): \(0.564\) moles of \(He\) in a \(1.00L\) container at a temperature of \(374K\)