Ch.2 - Atoms, Molecules & Ions

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.2 - Atoms, Molecules & Ions

Problem 121

Chapter 2, Problem 121

A sample of naturally occurring silicon consists of 28^Si (27.9769), 29^Si (28.9765), and 30^Si (29.9738). If the atomic weight of silicon is 28.0855 and the natural abundance of 29^Si is 4.68%, what are the natural abundances of 28^Si and 30^Si?

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Identify the given values: atomic weight of silicon (28.0855), natural abundance of 29^Si (4.68%), and the atomic masses of 28^Si (27.9769), 29^Si (28.9765), and 30^Si (29.9738).

Let the natural abundance of 28^Si be x and the natural abundance of 30^Si be y. Since the total natural abundance must sum to 100%, set up the equation x + 4.68% + y = 100%.

Use the average atomic mass formula for silicon, which is the sum of the products of each isotope's mass and its abundance: (27.9769 \(\times\) x) + (28.9765 \(\times\) 4.68\%) + (29.9738 \(\times\) y) = 28.0855.

Solve the system of equations from steps 2 and 3 to find the values of x and y. This involves substituting the value of y from the first equation into the second equation and solving for x.

Once x is found, substitute it back into the equation from step 2 to find y, completing the determination of the natural abundances of 28^Si and 30^Si.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Weight and Isotopes

Atomic weight is the weighted average mass of an element's isotopes based on their natural abundances. Isotopes are variants of an element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. Understanding how to calculate the atomic weight using the masses and abundances of isotopes is crucial for solving problems related to elemental composition.

Natural Abundance

Natural abundance refers to the relative proportion of each isotope of an element found in nature. It is usually expressed as a percentage and is essential for calculating the average atomic weight of an element. In this problem, knowing the natural abundance of one isotope allows for the calculation of the abundances of the other isotopes by using the total atomic weight.

Weighted Average Calculation

The weighted average calculation involves multiplying each value by its corresponding weight (or abundance) and then summing these products. This method is used to find the average atomic weight of an element based on its isotopes. In this context, the equation must be set up to include the known abundance of one isotope and solve for the unknown abundances of the others, ensuring that the total adds up to 100%.

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