Chlorine exists as one of two isotopes with atomic masses of 34.969 amu (35Cl) and 36.966 amu (37Cl) . Calculate the relative abundance of 35Cl and 37Cl based on the average atomic mass of 35.453 amu.

Ch. 2 - General Chemistry Translated: Finding the Electrons

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Ch. 2 - General Chemistry Translated: Finding the Electrons

문제 8

1장, 문제 8

Chlorine exists as one of two isotopes with atomic masses of 34.969 amu (³⁵Cl) and 36.966 amu (³⁷Cl) . Calculate the relative abundance of ³⁵Cl and ³⁷Cl based on the average atomic mass of 35.453 amu.

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Define the variables: Let the relative abundance of ³⁵Cl be x, and the relative abundance of ³⁷Cl be (1 - x), since the total abundance must equal 1.

Write the equation for the average atomic mass of chlorine:

35.453 = (34.969 × x) + (36.966 × (1 - x))

Distribute the terms in the equation:

35.453 = 34.969x + 36.966(1 - x)

, which expands to

35.453 = 34.969x + 36.966 - 36.966x

Combine like terms: Simplify the equation to

35.453 = 36.966 - 1.997x

Rearrange the equation to solve for x: Subtract 36.966 from both sides, then divide by -1.997 to isolate x. The value of x represents the relative abundance of ³⁵Cl, and (1 - x) gives the relative abundance of ³⁷Cl.

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Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For chlorine, the isotopes ³⁵Cl and ³⁷Cl have atomic masses of 34.969 amu and 36.966 amu, respectively. Understanding isotopes is crucial for calculations involving average atomic mass and relative abundance.

Average Atomic Mass

The average atomic mass of an element is a weighted average of the masses of its isotopes, taking into account their relative abundances. In this case, the average atomic mass of chlorine is given as 35.453 amu. This value is essential for determining the proportions of each isotope present in a sample.

Relative Abundance

Relative abundance refers to the proportion of each isotope of an element present in a sample, usually expressed as a percentage. To calculate the relative abundance of ³⁵Cl and ³⁷Cl, one can set up equations based on the average atomic mass and the known masses of the isotopes. This concept is fundamental for understanding how isotopes contribute to the overall atomic mass of an element.