Question

One container is filled with argon gas and the other with krypton gas. If both gases have the same temperature, in which container are the atoms moving faster?

Answer 1

Answer:

Argon

Explanation:

The average kinetic energy of the particles in a gas is given by

$KE=\frac{1}{2}mv^2$

where

m is the mass of the particles

v is their rms speed

The average kinetic energy of the particles in a gas can also be written as

$KE=\frac{3}{2}kT$

where

k is the Boltzmann's constant

T is the absolute temperature of the gas

Combining the two equations,

$\frac{1}{2}mv^2=\frac{3}{2}kT$

We can re-write the equation as

$v=\sqrt{\frac{3kT}{m}}$

We see that:

- The speed is directly proportional to the square root of the temperature

- The speed is inversely proportional to the square root of the mass of the particles

Therefore, if the two gases are at same temperature, the particles will move faster in the gas with lighter particles (smaller mass).

Since Krypton atoms have larger mass than Argon atoms, it means that atoms in Argon move faster than in Krypton.