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Chapter 2: Problem 50

Hydrogen and chlorine atoms react to form simple diatomic molecules in a 1: 1 ratio, that is, \(\mathrm{HCl}\). The natural abundances of the chlorine isotopes are \(75.77 \%^{35} \mathrm{Cl}\) and \(24.23 \%^{37} \mathrm{Cl} .\) The natural abundances of \(^{2} \mathrm{H}\) and \(^{3} \mathrm{H}\) are \(0.015 \%\) and less than \(0.001 \%,\) respectively. (a) How many different HCl molecules are possible, and what are their mass numbers (that is, the sum of the mass numbers of the H and Cl atoms)? (b) Which is the most abundant of the possible HCl molecules? Which is the second most abundant?

Short Answer

Expert verified
The six different HCl molecules are \(^1\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 36, \(^1\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 38, \(^2\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 37, \(^2\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 39, \(^3\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 38 and \(^3\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 40. The most abundant molecule is \(^1\mathrm{H}\,^{35}\mathrm{Cl}\) and the second most abundant molecule is \(^1\mathrm{H}\,^{37}\mathrm{Cl}\).

Step by step solution

01

Determining Possible Molecules and their Mass Numbers

First, identify the distinct isotopes for both Hydrogen and Chlorine. Hydrogen has two, namely \(^{1}\mathrm{H}\), \(^{2}\mathrm{H}\) and \(^{3}\mathrm{H}\), and Chlorine has two as well, namely \(^{35}\mathrm{Cl}\) and \(^{37}\mathrm{Cl}\). By pairing each Hydrogen isotope with each Chlorine isotope, you will be able to determine the number of different HCl molecules. Using the isotopic mass, sum the mass numbers of the Hydrogen and Chlorine atoms to get the mass number for each molecule.
02

Number of Different Molecules and their Mass Numbers

There are six different molecules possible: \(^1\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 36, \(^1\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 38, \(^2\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 37, \(^2\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 39, \(^3\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 38 and \(^3\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 40.
03

Determining the Most and Second Most Abundant Molecules

Use the natural abundances to determine the most common molecules. Multiply the abundance of each Hydrogen isotope by the abundance of each Chlorine isotope for each possible pair. The molecule whose isotopes have the highest product of abundances is the most abundant, and the molecule with the second highest product is the second most abundant.
04

The Most and Second Most Abundant Molecules

The most abundant HCl molecule is \(^1\mathrm{H}\,^{35}\mathrm{Cl}\) as both the isotopes \(^1\mathrm{H}\) and \(^{35}\mathrm{Cl}\) are the most abundant isotopes of their respective elements. The second most abundant HCl molecule is \(^1\mathrm{H}\,^{37}\mathrm{Cl}\), since \(^1\mathrm{H}\) is the most common isotope of hydrogen and \(^{37}\mathrm{Cl}\) is the second most common isotope of chlorine.

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