Question

choose the gas that has the greatest average molecular speed at 25°c. cl₂ xe ne ar he

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, and \(M\) is the molar mass of the gas. At a given temperature (\(T = 25^{\circ}C=298\space K\) here), since \(R\) and \(T\) are constant, \(v_{avg}\) is inversely proportional to the square - root of the molar mass (\(M\)) of the gas (\(v_{avg}\propto\frac{1}{\sqrt{M}}\)).

Step2: Calculate the molar masses of the given gases

• For \(Cl_2\): \(M = 2\times35.45\space g/mol=70.90\space g/mol\)
• For \(Xe\): \(M = 131.29\space g/mol\)
• For \(Ne\): \(M = 20.18\space g/mol\)
• For \(Ar\): \(M = 39.95\space g/mol\)
• For \(He\): \(M = 4.00\space g/mol\)

Step3: Compare the molar masses

Since \(v_{avg}\propto\frac{1}{\sqrt{M}}\), the gas with the smallest molar mass will have the greatest average molecular speed. Among the given gases, \(He\) has the smallest molar mass (\(M = 4.00\space g/mol\)).

Answer:

He