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,
${\text{V = }}\dfrac{{{\text{nRT}}}}{{\text{P}}}$
Molar volume of gas calculate by putting all values in the above equation and we get,
${\text{V = }}\dfrac{{\left( {{\text{1mol}}} \right)\left( {{\text{0}}{\text{.0821atmLmo}}{{\text{l}}^{{\text{ - 1}}}}{{\text{K}}^{{\text{ - 1}}}}} \right)\left( {{\text{273K}}} \right)}}{{{\text{1atm}}}}$
${\text{V = 22}}{\text{.4L}}$
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.