Question 32 of 36intermediate🔧 ApplyNumerical3 marks

Use the data given in the following table to calculate the molar mass of naturally occurring argon isotopes:

Isotope Isotopic molar mass Abundance ³⁶Ar 35.96755 g mol⁻¹ 0.337% ³⁸Ar 37.96272 g mol⁻¹ 0.063% ⁴⁰Ar 39.9624 g mol⁻¹ 99.600%

Correct Answer

The molar mass of naturally occurring argon is 39.95 g mol−139.95 \text{ g mol}^{-1}.

Exercise: EXERCISES | Q: 1.32 | (Page 27)
For More Understanding

Explanation

Naturally occurring elements exist as a mixture of isotopes. The average atomic mass (or molar mass) is computed by taking the sum of the products of each isotope's mass and its fractional relative abundance.

Solution Steps

  1. Step 1: Convert the percentage abundances of the isotopes into fractions by dividing by 100. Fractional abundance of 36Ar=0.337100=0.00337^{36}\text{Ar} = \frac{0.337}{100} = 0.00337 Fractional abundance of 38Ar=0.063100=0.00063^{38}\text{Ar} = \frac{0.063}{100} = 0.00063 Fractional abundance of 40Ar=99.600100=0.99600^{40}\text{Ar} = \frac{99.600}{100} = 0.99600

  2. Step 2: Multiply the isotopic molar mass of each isotope by its respective fractional abundance. For 36Ar:35.96755×0.00337=0.12121 g mol−1^{36}\text{Ar}: 35.96755 \times 0.00337 = 0.12121 \text{ g mol}^{-1} For 38Ar:37.96272×0.00063=0.02392 g mol−1^{38}\text{Ar}: 37.96272 \times 0.00063 = 0.02392 \text{ g mol}^{-1} For 40Ar:39.9624×0.99600=39.80255 g mol−1^{40}\text{Ar}: 39.9624 \times 0.99600 = 39.80255 \text{ g mol}^{-1}

  3. Step 3: Add the calculated values to find the average molar mass of argon. Average molar mass =0.12121+0.02392+39.80255=39.94768 g mol−1= 0.12121 + 0.02392 + 39.80255 = 39.94768 \text{ g mol}^{-1} Rounding to two decimal places, the molar mass of naturally occurring argon is 39.95 g mol−139.95 \text{ g mol}^{-1}.

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