Question

What is the molar mass of a gas that diffuses three times faster than oxygen under similar conditions

Answer 1

288 g/mol

Step-by-step explanation:

What is diffusion?

• It is a process whereby the random motion of particles move from a region of higher concentration to a region of lower concentration.

Graham's law of diffusion of gas

• states that at constant conditions of temperature and pressure, the rate of diffusion of gases is inversely proportional to the square root of their molar masses

`\boxed{ (Rate_1)/(Rate_2) = \sqrt{ (M_2)/(M_1) } }`

Calculations

Oxygen exist as O₂ at room temperature, thus its molar mass is 2(16)= 32.

Let the rate of O₂ be Rate₁, while the rate and molar mass of the unknown gas be Rate₂ and M₂ respectively.

Since O₂ diffuses 3 times as fast as the unknown gas,

Rate₁= 3(Rate₂)

`(Rate_1)/(Rate_2) = 3`

`3 = \sqrt{ (M_2)/(32) }`

`\sqrt{ (M_2)/(32) } = 3`

Square both sides:

`(M_2)/(32) = 3^(2)`

`(M_2)/(32) = 9`

Multiply both sides by 32:

M₂= 9(32)

M₂= 288