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What is the formula for finding abundance?

How do you calculate the percentage of abundance based on mass? Calculate the average atomic mass using the atomic masses of each isotope and their percent abundances. Divide each percent abundance by 100 to convert it to decimal form. Multiply this value by the isotope's atomic mass.

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How to find Percent Abundance?

What is Relative Abundance?

Isotopes are atoms that have the same number of protons but different numbers of neutrons. The atomic masses of isotopes differ. The percentage of atoms with a specific atomic mass found in a naturally occurring sample of an element is known as its relative abundance. Mass spectrometry can be used to determine the relative abundance of each isotope. Since different isotopes have different relative abundances, some are more naturally abundant on Earth than others. Relative abundances are usually expressed as percentages, which means that the relative abundances of all of an element’s stable isotopes always add up to 100 percent. The average atomic mass of an element is a weighted average of these values.

Table of Contents

Steps to find Percent Abundance

A given problem will ask for the relative abundance or mass of a specific isotope in order to solve isotopic abundance problems.

Step 1: Calculate the Average Atomic Mass

Determine the element’s atomic mass from your isotopic abundance problem on the periodic table.

Step 2: Set up the Relative Abundance Problem

Use the following formula:

(M1)(x) + (M2)(1-x) = M(E)

M1 denotes the mass of one isotope’

x denotes its relative abundance.

The mass of the second isotope is denoted by M2.

M(E) denotes the periodic table element’s atomic mass.

Note: The sum of these two isotopes equals 100% of all the elements found in nature. The equation can be written in either percentage or decimal form. Step 3: Determine the Relative Abundance of the Unknown Isotope by solving for x.

Calculate x using algebra.

To begin, implement the distributive property:

Now, combine similar terms.

Determine x.

Step 4: Determine the percentage of abundance

Since x and (1-x) are numbers, multiply them by 100 to get the percentage of one isotope.

Solved Examples

Example 1: Determine the relative abundance of the isotopes if the masses of one isotope of nitrogen, nitrogen-14, are 14.003 amu and another isotope, nitrogen-15, are 15.000 amu.

Solution:

The average atomic mass of Nitrogen is 14.007 amu.

Applying the formula (M1)(x) + (M2)(1-x) = M(E),

M1 = 14.003 amu

x = unknown relative abundance

M2 = 15 amu

M (E) = 14.007 amu

14.003(x) + 15 (1 – x) = 14.007

14.003x + 15.000 – 15.000x = 14.007

-0.997x = -0.993

x = 0.993/0.997

x = 0.996 amu

Therefore, percent abundance for x = 99.6% and (1 – x) = 0.004 = 0.4%. The abundance of the nitrogen-14 isotope is 99.6%, while the abundance of the nitrogen-15 isotope is 0.4%. Example 2: Determine the percent abundance of chlorine isotopes,35Cl and 37Cl given that chlorine’s average atomic mass is 35.45 amu.

Solution:

The average atomic mass of Chlorine is 35.45 amu.

Applying the formula (M1)(x) + (M2)(1-x) = M(E),

M1 = 35 amu

x = unknown relative abundance

M2 = 37 amu

M (E) = 35.45 amu

35(x) + 37 (1 – x) = 35.45

35x + 37 – 37x = 35.45

–2 x = – 1.55

x = 1.55/2

x = 0.775

Therefore, percent abundance for x = 77.5% and (1 – x) = 0.225 = 22.5%. The abundance of the Chlorine-35 isotope is 77.5%, while the abundance of the Chlorine- 37 isotope is 22.5%.

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