Question

If the value of Avogadro number is $6.022\times {10}^{23}mo{l}^{-1}$ 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

This problem can be solved by using the concept involved in calculation of significant figure.
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, the last digit is increased by 1 if following digits $\ge$ 5 and is left as such if following digits is $\le$ 4.]
Hence, correct integer is (4).