States of Matter - Result Question 65
65. If the value of Avogadro number is $6.023 \times 10^{23} \mathrm{~mol}^{-1}$ and the value of Boltzmann constant is $1.380 \times 10^{-23} \mathrm{JK}^{-1}$, then the number of significant digits in the calculated value of the universal gas constant is
(2014 Adv.)
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Answer:
Correct Answer: 65. (4)
Solution:
This problem can be solved by using the concept involved in calculation of significant figure.
Universal gas constant, $R=k N_A$
where, $\quad k=$ Boltzmann constant
and $\quad N_A=$ Avogadro’s number
$$ \begin{aligned} \therefore \quad R & =1.380 \times 10^{-23} \times 6.023 \times 10^{23} \mathrm{~J} / \mathrm{Kmol} \\ & =8.31174 \cong 8.312 \end{aligned} $$
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 $\geq 5$ and is left as such if following digits is $\leq 4$.] Hence, correct integer is (4).
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