An unknown gas effuses at 0.770 times the effusion rate of nitrogen dioxide (NO2). Estimate the molar mass of the unknown gas. Answer in units of g/mol.

77.58g/mol

Explanation:

Let the rate of effusion of NO2 be R1

The rate of effusion of the unknown gas (R2) = 0.770R1

Molar Mass of NO2 (M1) = 14 + (2x16) = 14 + 32 = 46g/mol

The molar mass of the unknown gas (M2) = ?

R1/R2 = √ (M2/M1)

R1/0.770R1 = √ (M2/46)

1/0.770 = √ (M2/46)

Take the square of both sides

(1/0.770) ^2 = M2/46

Cross multiply to express in linear form

M2 = (1/0.770) ^2 x 46

M2 = 77.58g/mol

The molar mass of the unknown gas is 77.58g/mol