Question

if the molecules in 1.0 l of each of the gases, ne, cl₂, nh₃ and hcl are all moving with the same average velocity, which gas sample is at the highest temperature, or is the temperature the same in all of the gas samples if they are all moving with the same average velocity?
ocl₂
one
othe temperature is the same in all of the gas samples
ohcl
onh₃

Explanation:

Step1: Recall the formula for average velocity of gas molecules

The formula for the average velocity of gas molecules 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. Rearranging for \(T\) gives \(T = \frac{v_{avg}^2\pi M}{8R}\).

Step2: Compare molar masses of the given gases

• Molar mass of \(Ne\): \(M_{Ne}=20.18\space g/mol\)
• Molar mass of \(Cl_{2}\): \(M_{Cl_{2}} = 70.90\space g/mol\)
• Molar mass of \(NH_{3}\): \(M_{NH_{3}}=17.03\space g/mol\)
• Molar mass of \(HCl\): \(M_{HCl}=36.46\space g/mol\)

Since \(v_{avg}\) is the same for all gases (given in the problem), and \(R\) and \(\pi\) are constants, \(T\propto M\) (temperature is directly proportional to molar mass).

Answer:

A. \(Cl_{2}\)