Question

What is the ratio of the average kinetic energy of a so2 molecule to that of an o2 molecule in a mixture of two gases? what is the ratio of the root mean square speeds, urms, of the two gases?

Answer 1

1. The kinetic energy of a system is a factor of temperature only. So, since there is no mention of temperatures in the problem, we can safely assume that they have the same temperature. So, that means the ratio would be 1.

2. The formula for rms is

rms=√3RT/M
So, the ratio would be:
ratio = √M of O₂ / M of SO₂, where M is molar mass
Ratio = √32/√64 = 0.71

Answer 2

Ratio of average kinetic energy will be 1:1.

Ratio of root mean square speeds of gases:
`\sqrt{(1)/(2)}`

Step-by-step explanation:

Given the mixture of two gases ,at same temperature T.

Gas A = Sulfur oxide =
`SO_2`

Molar mass of sulfur oxide ,M= 0.064 kg/mol

Gas B = Oxygen gas =
`O_2`

Molar mass of oxygen gas ,M'= 0.032 kg/mo

Average kinetic energy of a molecule of a gas is given as:

`K=(3)/(2)kT`

K = Boltzmann constant

T = temperature of the gas

`K_A=(3)/(2)kT`..(1)

`K_B=(3)/(2)kT`..(2)

Ratio of average kinetic energy will be:

`(K_A)/(K_B)=((3)/(2)kT)/((3)/(2)kT)=(1)/(1)`

Root mean square speeds of the gas particles:

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

M = molar mass of the gas

`u_(rms,SO_2)=\sqrt{(3RT)/(0.064 kg/mol)}`..(3)

`u_(rms,O_2)=\sqrt{(3RT)/(0.032 kg/mol)}`..(4)

Ratio of root mean square speeds of gases:

`(u_(rms,SO_2))/(u_(rms,O_2))=\sqrt{((3RT)/(0.064 kg/mol))/((3RT)/(0.032 kg/mol))}=\sqrt{(1)/(2)}`

Ratio of average kinetic energy will be 1:1.

Ratio of root mean square speeds of gases:
`\sqrt{(1)/(2)}`