Question

Explain molar volume of a gas at STP using the ideal gas equation?

Answer 1

Hint: Here STP stands for standard temperature and pressure, so we have to calculate the molar volume of gas at 1 atmospheric pressure and $273$ Kelvin ($\text{K}$) of temperature because they are the standard values.

Complete answer:
For getting of molar volume of a gas we have to use that equation in which volume term occurs and that equation is ideal gas equation, which is written as:
$\text{PV = nRT}$………. (i)
Where, $\text{P}$ = Pressure of gas,
$\text{V}$ = Volume of gas,
$\text{R}$ = Gas constant,
$\text{T}$ = Temperature of gas,
And $\text{n}$ = No. of moles.
As it is given in question that we have to calculate molar volume of gas at standard pressure it means-
At temperature = $\text{273K}$, pressure = $\text{1atm}$and for one mole of gas i.e. $\text{n = 1mol}$ and value of $\text{R = 0}\text{.0821atmLmo}{\text{l}}^{\text{ - 1}}{\text{K}}^{\text{ - 1}}$.
On rearranging the equation (i) we get,
$\text{V = }{\displaystyle \frac{\text{nRT}}{\text{P}}}$
Molar volume of gas calculate by putting all values in the above equation and we get,
$\text{V = }{\displaystyle \frac{\left(\text{1mol}\right)\left(\text{0}\text{.0821atmLmo}{\text{l}}^{\text{ - 1}}{\text{K}}^{\text{ - 1}}\right)\left(\text{273K}\right)}{\text{1atm}}}$
$\text{V = 22}\text{.4L}$
The molar volume of a gas at STP is $\text{22}\text{.4L}$.

Note:
Here some of you may do the calculation wrong by putting the wrong value of gas constant ($\text{R}$) because in chemistry many values of gas constant are present on the basis of different units of pressure, temperature, volume and moles of gas. Like value of $\text{R}$ is also given by $\text{8}\text{.314Jmo}{\text{l}}^{\text{ - 1}}{\text{K}}^{\text{ - 1}}$but if you put this value then you never get correct answer.