Question

The value of the Boltzmann constant in $erg{K}^{-1_{}}molecul{e}^{-1}$is :

• A. $1.38\times {10}^{-16}$
• B. $1.38\times {10}^{-23}$
• C. $8.314\times {10}^{-7}$
• D. $6.023\times {10}^{-16}$

Answer 1

The correct option is A

$1.38\times {10}^{-16}$

Step 1: Given

1. Universal gas constant, $R=8.31Jmo{l}^{-1}{K}^{-1}$

2. Avogadro's Number, $N=6.023\times {10}^{23}mo{l}^{-1}$

Step 2: Calculating the value of Boltzmann Constant

Boltzmann constant is given by $k=\frac{R}{N}$ where

1. R is the universal gas constant and

2. N is Avogadro's Number.

Substituting the known values,

$$\begin{gathered} k=\frac{8.31}{6.023\times {10}^{23}} \\ k=1.38\times {10}^{-23}J/K \end{gathered}$$

For converting it to

We have, $1J={10}^{7}ergs$

So, $k=1.38\times {10}^{-23}\times {10}^7$

$k=1.38\times {10}^{-16}erg{K}^{-1}molecul{e}^{-1}$

Thus, the correct option is (A) $1.38\times {10}^{-16}$.