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 ___

Answer 1

We have,
Universal gas constant, $R=k{N}_A$
where, k = Boltzmann constant
and $N_A$=Avogadro's number
$\therefore R=1.380\times {10}^{-23}\times 6.023\times {10}^{23}J/Kmol$
= 8.31174 $\cong$ 8.312
Since, k and $N_A$ both have four significant figures, so the value of R is also rounded off upto 4 significant figures.

When number is rounded off, the number of significant figure is reduced.

So, the number of significant figure is 4.