Question

Under certain conditions, neon (Ne) gas diffuses at a rate of 7.0 centimeters per second. Under the same conditions, an unknown gas diffuses at a rate of 4.9 centimeters per second. What is the approximate molar mass of the unknown gas?

Answer 1

Graham's law of effusion states that the rate of effusion of two substances is equal to the square root of the reciprocal of their molar masses. Hence the equation becomes 7 / 4.9  = square root of x/ 20.18 wher e x is the molar mass of the unknown gas. The molar mass is equal to 41. 18 g/mol

Answer 2

Answer : The molar mass of unknown gas is, 41 g/mole

Solution : Given,

Diffusion rate of neon gas = 7 cm/s

Diffusion rate of unknown gas = 4.9 cm/s

Molar mass of neon gas = 20 g/mole

According to the Graham's law, the rate of effusion of a gas is inversely proportional to the square root of the molar mass of the gas.

Formula used :

$\frac{R_1}{R_2}=\sqrt{\frac{M_2}{M_1}}$

where,

$R_1$ = diffusion rate of neon gas

$R_2$ = diffusion rate of unknown gas

$M_1$ = molar mass of neon gas

$M_2$ = molar mass of unknown gas

Now put all the given values in the above formula, we get the molar mass of unknown gas.

$\frac{7cm/s}{4.9cm/s}=\sqrt{\frac{M_2}{20g/mole}}$

$M_2=40.81g/mole=41g/mole$

Therefore, the molar mass of unknown gas is, 41 g/mole