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Chapter 10: Problem 75

The wiki-phony site states that the atomic mass of chlorine is \(40 \mathrm{g} / \mathrm{mol} .\) Check this result. Hint: The two, most common stable isotopes of chlorine are: 35 17 (The abundance of \(\mathrm{Cl}-35\) is \(75.8 \%,\) and the abundance of Cl-37 is 24.2\(\%.\))

Short Answer

Expert verified
The atomic mass of chlorine provided by the wiki-phony site is incorrect. The weighted average atomic mass of chlorine, calculated using the given abundances of its common stable isotopes, is approximately 35.484 g/mol.

Step by step solution

01

Convert the percentage abundances into decimals

To find the weighted average, we need to first convert the percentage abundances into decimals. Divide each percentage abundance by 100. Abundance of Cl-35 = 75.8% = \(75.8 \div 100 = 0.758\) Abundance of Cl-37 = 24.2% = \(24.2 \div 100 = 0.242\)
02

Multiply the masses of the isotopes by their respective decimal abundances

Now, multiply the masses of each isotope by their respective decimal abundance: Mass of Cl-35 * Abundance of Cl-35 = \(35 \times 0.758 = 26.53\) Mass of Cl-37 * Abundance of Cl-37 = \(37 \times 0.242 = 8.954\)
03

Calculate the weighted average atomic mass of chlorine

To find the weighted average atomic mass, we will now sum the products obtained in step 2: Weighted average atomic mass of chlorine = mass of Cl-35 * abundance of Cl-35 + mass of Cl-37 * abundance of Cl-37 Weighted average atomic mass of chlorine = \(26.53 + 8.954 = 35.484 \) The weighted average atomic mass of chlorine is 35.484 g/mol.
04

Compare with the given mass on the wiki-phony site

The atomic mass provided by the wiki-phony site is 40 g/mol. Our calculated atomic mass is 35.484 g/mol. Comparing these two values, we can conclude that the wiki-phony site's atomic mass of chlorine is incorrect. The correct atomic mass of chlorine is approximately 35.484 g/mol.

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