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QJEEAdv14Chcd33: JEE Advanced 2014 Chemistry - Class 11 JEEAdv14Chcd33 Solution: If the value of Avogadro number is 6.023 × 10 23 mol -1 and the …

If the value of Avogadro number is 6.023 × 1023 mol-1 and the value of Boltzmann constant is 1.380 × 10-23 J K-1, then the number of significant digits in the calculated value of the universal gas constant is

Step-by-Step Verified Solution

The universal gas constant, denoted by R, can be calculated using the Avogadro number (NA) and the Boltzmann constant (kB) by the following relationship:

R=NA×kB

Given that:

NA=6.023×1023 mol−1 kB=1.380×10−23 J K−1

Let's multiply these values to find R:

R=(6.023×1023 mol−1)×(1.380×10−23 J K−1) R=(6.023×1.380)×(1023×10−23) J mol−1K−1 R=8.31174×100 J mol−1K−1

To determine the number of significant digits in the calculated value of R, we must consider the number of significant digits in the given values of NA and kB.

The value for NA has four significant digits (6.023), and the value for kB also has four significant digits (1.380). When multiplying or dividing numbers, the number of significant digits in the result is determined by the number with the smallest amount of significant digits used in the calculation.

In this case, since both constants have four significant digits, the value of R calculated from their multiplication will also contain four significant digits:

R≈8.314 J mol−1K−1

Therefore, the calculated value of the universal gas constant R has four significant digits.

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