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

JEE Advanced · 2014 · 25 May 2014 · Paper 1 · Some Basic Concepts of Chemistry

If the value of Avogadro number is

6.023 \times 1 0^{23} mol^{- 1}

and the value of Boltzmann constant is

1.380 \times 1 0^{- 23} J K^{- 1}

, then the number of significant digits in the calculated value of the universal gas constant is

Answer: 4

Solution

The universal gas constant

R

is related to Avogadro's number

N_{A}

and Boltzmann constant

k_{B}

by:

R = N_{A} \times k_{B}

Given:
•

N_{A} = 6.023 \times 1 0^{23}

mol⁻¹ (4 significant figures)
•

k_{B} = 1.380 \times 1 0^{- 23}

J K⁻¹ (4 significant figures)

Calculation:

R = (6.023 \times 1 0^{23}) \times (1.380 \times 1 0^{- 23})

R = 6.023 \times 1.380 = 8.31174

R = 8.312 J K^{- 1} mol^{- 1}

In multiplication, the result has the same number of significant figures as the measurement with the fewest significant figures. Both values have 4 significant figures.

Number of significant digits in R: 4

JEE Advanced · 2014 · 25 May 2014 · Paper 1 · Integer answer

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JEE Advanced · 2014 · 25 May 2014 · Paper 1 · Some Basic Concepts of Chemistry

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