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?

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

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BarrettArcher BarrettArcher · Answer 2 · 2019-01-30T17:41:23+01:00

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 :

[tex]\frac{R_1}{R_2}=\sqrt{\frac{M_2}{M_1}}[/tex]

where,

[tex]R_1[/tex] = diffusion rate of neon gas

[tex]R_2[/tex] = diffusion rate of unknown gas

[tex]M_1[/tex] = molar mass of neon gas

[tex]M_2[/tex] = molar mass of unknown gas

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

[tex]\frac{7cm/s}{4.9cm/s}=\sqrt{\frac{M_2}{20g/mole}}[/tex]

[tex]M_2=40.81g/mole=41g/mole[/tex]

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