Q26PE - College Physics (Urone)

Question

Confirm that the units of nRT are those of energy for each value of R : (a) 8.31 J/mol K, (b) 1.99 cal/mol K, and (c) 0.0821 L atm/mol K.

Step-by-Step Solution

Answer

All units of nRT are confirmed to be those of energy.

Step 1: Introduction

We find the unit of nRT for different values of R.

Step 2: Different values of R and ideal gas equation

(a)

The unit of n will be mol and that of temperature will be kelvin.

For R=8.31 J/mol K

 $\mathbf{Units}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{nRT}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{mol}\mathbf{ }\mathbf{\times }\left(J/\mathrm{mol}-K\right)\mathbf{\times }\mathbf{K}$

Joule is a unit of energy.

(b)

For R=1.99 cal/mol K

Units of nRT

 $\begin{array}{rcl}\mathbf{Units}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{nRT}\mathbf{ }& \mathbf{=}& \mathbf{ }\mathbf{mol}\mathbf{ }\mathbf{\times }\left(\mathrm{cal}/\mathrm{mol}-K\right)\mathbf{\times }\mathbf{K}\\ & \mathbf{=}& \mathbf{cal}\end{array}$

Calorie is a unit of energy.(1 cal = 4.2 J).

(c)

For R=0.0821 L atm/mol K

Units of nRT

 $\begin{array}{rcl}\mathbf{Units}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{nRT}\mathbf{ }& \mathbf{=}& \mathbf{ }\mathbf{mol}\mathbf{ }\mathbf{\times }\left(L-\mathrm{atm}/\mathrm{mol}.K\right)\mathbf{\times }\mathbf{K}\\ & \mathbf{=}& \mathbf{L}\mathbf{.}\mathbf{atm}\end{array}$

Litre atm is again a unit of energy (1 L atm = 101.33 J)

Therefore, the unit of nRT comes out to be that of energy for different values of R.