Question

How many moles of helium gas will occupy $22.4{\text{ L}}$ volume at ${0^ \circ }{\text{C}}$ and at $1{\text{ atm}}$ pressure?

Answer 1

Hint: To solve this we must know the ideal gas law. The ideal gas law states for a given mass of an ideal gas and a constant volume of an ideal gas, the pressure exerted by the molecules of an ideal gas is directly proportional to its absolute temperature.

Formula Used: $PV = nRT$

Complete step-by-step solution:
We know that the expression for the ideal gas law is as follows:
$PV = nRT$
Where, $P$ is the pressure of the gas,
$V$ is the volume of the gas,
$n$ is the number of moles of gas,
$R$ is the universal gas constant,
$T$ is the temperature of the gas.
Rearrange the equation for the number of moles as follows:
$n = \dfrac{{PV}}{{RT}}$
Now, calculate the number of moles of helium gas using the ideal gas equation as follows:
Substitute $1{\text{ atm}}$ for the pressure, $22.4{\text{ L}}$ for the volume of gas, $0.082{\text{ L atm/K mol}}$ for the universal gas constant, ${0^ \circ }{\text{C}} = 273{\text{ K}}$ for the temperature and solve for the number of moles of helium gas. Thus,
$n = \dfrac{{1{\text{ atm}} \times 22.4{\text{ L}}}}{{0.082{\text{ L atm/K mol}} \times 273{\text{ K}}}}$
$n = 1{\text{ mol}}$

Thus, the number of moles of helium gas at $22.4{\text{ L}}$ volume, ${0^ \circ }{\text{C}}$ and $1{\text{ atm}}$ pressure is $1{\text{ mol}}$.

Note:One mole of an ideal gas at standard temperature and pressure occupies $22.4{\text{ L}}$ of volume. This suggests that at the temperature $273{\text{ K}}$ and the pressure $1{\text{ atm}}$ one mole of an ideal gas occupies $22.4{\text{ L}}$ of volume. This is known as ideal gas law. From the statement of ideal gas law we can directly say that $22.4{\text{ L}}$ volume of helium gas at ${0^ \circ }{\text{C}}$ and at $1{\text{ atm}}$ pressure contains $1{\text{ mol}}$ of helium gas.