Q26PE - College Physics (Urone)

Question

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

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

 $$\begin{gathered} UnitsofnRT=mol \times \left(J/mol.K\right)\times K \\ =J \end{gathered}$$

Joule is a unit of energy.

(b)

For R=1.99 cal/mol K

Units of nRT

 $$\begin{gathered} UnitsofnRT=mol \times \left(cal/mol.K\right)\times K \\ =cal \end{gathered}$$

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

(c)

For R=0.0821 L atm/mol K

Units of nRT

 $$\begin{gathered} UnitsofnRT=mol \times \left(L·atm/mol.K\right)\times K \\ =L·atm \end{gathered}$$

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.