Question

There are two identical containers of gas at the same temperature and pressure, one containing argon and the other neon. What is the ratio of the rms speed of the argon atoms to that of the neon atoms?

Answer 1

The ratio of the root mean square (rms) speed of argon atoms to that of neon atoms is approximately 0.71.

Step-by-step explanation:

The ratio of the root mean square (rms) speed of argon atoms to that of neon atoms can be calculated using the equation:

Ratio of rms speeds = sqrt(molar mass of neon / molar mass of argon)

Both argon and neon are noble gases, and as noble gases, they consist of monatomic atoms. The molar mass of argon is approximately 40.0 g/mol, while the molar mass of neon is approximately 20.2 g/mol. Substituting these values into the equation, we find:

Ratio of rms speeds = sqrt(20.2 / 40.0) = 0.71

Therefore, the ratio of the rms speed of argon atoms to that of neon atoms is approximately 0.71.

Answer 2

0.7107

Step-by-step explanation:

The root mean square velocity is the square root of the average of the square of the velocity and it can be calculated using the following expression.

`v_(rms)=\sqrt{(3RT)/(M) }`

where,

`v_(rms)`: root mean square velocity

R: ideal gas constant

T: absolute temperature

M: molar mass of the gas

The ratio of the rms speed of the argon atoms to that of the neon atoms is:

`(v_(rms)(Ar))/(v_(rms)(Ne))=\frac{\sqrt{(3RT)/(M(Ar))}}{\sqrt{(3RT)/(M(Ne)) }} =\sqrt{(M(Ne))/(M(Ar))} =\sqrt{(20.18g/mol)/(39.95g/mol) } =0.7107`