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{(1)/(M)}`

or,

`(R_1)/(R_2)=\sqrt{(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.

`(R_1)/(R_2)=\sqrt{(31.998)/(44)}`

`(R_1)/(R_2)=0.85`

`{R_2}=1.17* {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.