Answer:
288 g/mol
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
[tex]\boxed{ \frac{Rate_1}{Rate_2} = \sqrt{ \frac{M_2}{M_1} } } [/tex]
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)
[tex]\frac{Rate_1}{Rate_2} = 3 [/tex]
[tex] 3 = \sqrt{ \frac{M_2}{32} } [/tex]
[tex] \sqrt{ \frac{M_2}{32} } = 3[/tex]
Square both sides:
[tex] \frac{M_2}{32} = 3^{2} [/tex]
[tex] \frac{M_2}{32} = 9[/tex]
Multiply both sides by 32:
M₂= 9(32)
M₂= 288
