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 : 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, = 44 g/mole

Molar mass of oxygen gas, = 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.

or,

where,

= rate of effusion of a carbon dioxide gas

= rate of effusion of oxygen gas

= molar mass of a carbon dioxide gas

= molar mass of oxygen gas  

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

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.