Question

How many times greater is the rate of effusion of oxygen gas than that of carbon dioxide gas at the same temperature and pressure? (carbon atomic mass = 12.011; oxygen atomic mass = 15.999)
A; 2.173
B; 1.375
C; 1.173
D; 66.33

Answer 1

C.) 1.173. Hope this helps you.

Answer 2

Answer : The correct option is, (C) 1.173

Solution : Given,

Molar mass of carbon = 12.011 g/mole

Molar mass of oxygen = 15.999 g/mole

Molar mass of carbon dioxide gas, $CO_2$ = 44 g/mole

Molar mass of oxygen gas, $O_2$ = 31.998 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 a gas.

$R\propto \sqrt{\frac{1}{M}}$

or,

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

where,

$R_1$ = rate of effusion of a carbon dioxide gas

$R_2$ = rate of effusion of oxygen gas

$M_1$ = molar mass of a carbon dioxide gas

$M_2$ = molar mass of oxygen gas  

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

$\frac{R_1}{R_2}=\sqrt{\frac{31.998}{44}}$

$\frac{R_1}{R_2}=0.85$

${R_2}=1.17\times {R_1}$

Therefore, the 1.17 times greater is the rate of effusion of oxygen gas than that of carbon dioxide gas at the same temperature and pressure.