Question

If the value of Avogadro number is $6.023\times {10}^{23}mo{l}^{-1}$ and the value of Boltzmann constant is $1.380\times {10}^{-23}J{K}^{-1}$, then the number of significant digits in the calculated value of the universal gas constant is :

• A. 4
• B. 3
• C. 5
• D. 2

Answer 1

Answer: (A)

The relation between Boltzmann constant ($k$) and universal gas constant ($R$) is as follows:

$k=\frac{R}{N_A}$

$R=k{N}_A$

$=1.380\times {10}^{-23}\times 6.023\times {10}^{23}$

$=8.31174$

In these operations, the result must be reported with no more significant figures as are there in the measurement with the few significant figures. Hence, the answer is $8.312$, reported to $4$ significant numbers as in the number with least significant numbers.
So, number of significant number in 8.312 is 4.

Hence, the correct option is A.