Question

The equation of state for n moles of an ideal gas is \[pv = nRT\], where R is a constant. The SI unit for R is:
A.\[J{K^{ - 1}}\] per molecule
B.\[J{K^{ - 1}}mo{l^{ - 1}}\]
C.\[JK{g^{ - 1}}{K^{ - 1}}\]
D.\[J{K^{ - 1}}{g^{ - 1}}\]

Answer 1

Hint: We also know that the ideal gas will occupy a negligible space and there is no interaction between the ideal gas, which means, it will not attract or repel each other. Only the elastic collision takes place between the ideal gas. The ideal gas equation can be represented as, \[pv = nRT\]. It expresses the relationship between pressure, volume, number of moles and temperature.

Complete answer:
The SI units of R present in the ideal gas equation is not equal to \[J{K^{ - 1}}\] per molecule. Hence, option (A) is incorrect.
The equation of state for n moles of an ideal gas is \[pv = nRT\], where R is the universal gas constant and it is equal to \[8.314\]. And, p is pressure, v is volume, n is equal to number of moles and T is equal to temperature.
The unit of universal constant can be found by taking the units of pressure, volume, number of moles and temperature.
SI unit of pressure is equal to \[\dfrac{N}{{{m^2}}}\]
SI unit of volume is equal to \[{m^3}\]
SI unit of number of moles equal to mole
SI moles of temperature is equal to K
Hence, SI unit of P and V can be written as, \[\dfrac{N}{{{m^2}}}\,x\,{m^3}\]
\[\dfrac{N}{{{m^2}}}\,x\,{m^3} = nM = Joule\]
By rearranging the ideal gas equation,
\[R = \dfrac{{PV}}{{nT}}\]
Substitute the units of each terms, will get the unit of R
\[R = \dfrac{J}{{molK}}\]
\[R = J{K^{ - 1}}mo{l^{ - 1}}\]
Hence, option (B) is correct.
The SI units of R present in the ideal gas equation are not equal to \[JK{g^{ - 1}}{K^{ - 1}}\]. Hence, option (C) is incorrect.
The SI units of R present in the ideal gas equation are not equal to \[J{K^{ - 1}}{g^{ - 1}}\]. Hence, the option (D) is incorrect.

Note:
We have to know that the ideal gas equation represents the relation between, pressure, temperature, volume, number of moles and universal gas constant. And the unit of universal gas constant will be as, \[J{K^{ - 1}}mo{l^{ - 1}}\]. When dividing the sum of pressure and volume with the number of moles and temperature will always get a constant value.