Question

In a gas equation \[PV = nRT\], the value of universal gas constant depends upon:
A. the nature of the gas
B. the pressure of the gas
C. the temperature of the gas
D. the units of measurement

Answer 1

Hint: We know that the gas constant is a fixed quantity. It does not vary with surrounding conditions for any ideal gas and we take it \[8.314\;{\rm{J}}/{\rm{Kmol}}\] at STP. It is fixed for all ideally behaving gases and is useful to calculate any unknown variable in the ideal gas equation that is \[PV = nRT\].

Complete step by step answer:
As we know the ideal gas equation is written as \[PV = nRT\]. We can rearrange this equation to write the value of gas constant \[R\] as, \[R = \dfrac{{nRT}}{P}\]. Thus it is clear that it is the ratio of two quantities \[nRT\] and \[P\]. This ratio is always fixed. But when we measure temperature, pressure or volume in different units, the gas constant comes out different.
For e.g, the value of gas constant is \[8.314\;{\rm{J}}/{\rm{Kmol,}}\;0.082\;{\rm{L - atm}}/{\rm{K - mol}}\] or \[82.06\;{\rm{c}}{{\rm{m}}^3} - {\rm{atm}}/{\rm{K - mol}}\]. So, it is clear that gas constant depends on units of measurement.

So, the correct answer is “Option D”.

Note:
We know that all ideally behaving gases follow the ideal gas equation and this equation contains the term \[R\] or gas constant. As we know it is the ratio of \[\dfrac{{nRT}}{P}\], it will have different values according to measurement units of pressure, temperature and volume.