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Some Basic Concepts of Chemistry question

2014 · Shift 1 · Q7
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Some Basic Concepts of Chemistry question

2014 · Shift 1 · Q7

JEE AdvancedChemistrySome Basic Concepts of ChemistryNumerical+3 / −1
If the value of Avogadro number is 6.023 ×\times× 1023 mol-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
Numerical answer
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Correct answer: 4

  1. Use the relation between constants

    The universal gas constant is R=NAkBR = N_A k_BR=NA​kB​ where NA=6.023×1023 mol−1N_A = 6.023 \times 10^{23}\ \text{mol}^{-1}NA​=6.023×1023 mol−1 kB=1.380×10−23 J K−1k_B = 1.380 \times 10^{-23}\ \text{J K}^{-1}kB​=1.380×10−23 J K−1

  2. Calculate RRR

    R=(6.023×1023)(1.380×10−23)R = (6.023 \times 10^{23})(1.380 \times 10^{-23})R=(6.023×1023)(1.380×10−23)

    Combine powers of 10: 1023×10−23=100=110^{23} \times 10^{-23} = 10^0 = 11023×10−23=100=1

    So, R=6.023×1.380R = 6.023 \times 1.380R=6.023×1.380

    Now multiply: 6.023×1.380=8.311746.023 \times 1.380 = 8.311746.023×1.380=8.31174

    Hence, R=8.31174 J mol−1K−1R = 8.31174\ \text{J mol}^{-1}\text{K}^{-1}R=8.31174 J mol−1K−1

  3. Determine the number of significant digits

    In multiplication, the result should have the same number of significant figures as the factor with the least number of significant figures.

    • 6.0236.0236.023 has 4 significant figures
    • 1.3801.3801.380 has 4 significant figures

    Therefore, the calculated value of RRR should be reported with 4 significant figures.

    R=8.312 J mol−1K−1R = 8.312\ \text{J mol}^{-1}\text{K}^{-1}R=8.312 J mol−1K−1

  4. Final answer

    The number of significant digits is: 4\boxed{4}4​

  5. Comparison with stored answer

    Stored correct answer = 4, which matches the derived answer.

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