An Easy Explanation of How to Find Percent Abundance

Percent abundance formula
According to chemistry principles, isotopes have same atomic number but different mass number. Abundance is defined as the amount of isotope contained in its parent element. This Buzzle post tells you how to calculate percent abundance for any element having isotopes.
Note
An element can consist of number of isotopes, and it is necessary to consider all of its isotopes while computing the percent abundance. Consider element carbon (C), it has 15 isotopes, and it is mandatory to consider all of them.
Every element has atoms which consist of protons, electrons, and neutrons. When an element has more than one form having same number of protons but different number of neutrons in the nucleus, they are called isotopes. They either occur naturally or are artificially produced. The element chlorine (Cl) has more than 50 isotopes, of which Cl-35 and Cl-37 are two stable isotopes. They have same atomic number, which is 17; however, their mass number is 35 and 37, respectively.
For any element, abundance is expressed as the percentage of an isotope to the total amount of all isotopes of that element. Note that the sum of the abundance percentages of all the isotopes for any element must equal 100.

Definition of percentage abundance for X in Y can be best explained in two possible ways as follows:

1. how many percent of Y is X.
2. how much of X is in Y

The formula to find the percent abundance of an element with two isotopes is as follows:
Average mass of an element=
(atomic mass of isotope I X percent abundance of isotope I/100) + (atomic mass of isotope II X percent abundance of isotope II/100)


In order to find the abundance of an element, it's necessary to compute the average of atomic masses of its isotopes in the first place. Proceed by substituting either one of the isotopes in terms of the other. Add the similar terms in the equation to get the final answer.
How to Calculate Percent Abundance
Consider that an element has two isotopes. If the atomic masses of these isotopes are given, calculating the percentage abundance of each of the isotopes is possible. Given below is a problem, with its detailed solution explaining how to find the same.

Problem I:

The value of atomic mass of copper is 63.546 ± 0.003 u. 63Cu and 65Cu are two isotopes of copper. The atomic masses of 63Cu and 65 are 62.9296 and 64.9278 amu, respectively. Given their atomic masses, calculate the percentage abundance of 63Cu and 65Cu.

Solution:

Data given:
Atomic mass of copper = 63.54 (Rounded value)
Atomic mass of 63Cu = 62.9296 amu
Atomic mass of 65Cu = 64.9278 amu

Step I: Find the average mass of these two isotopes

Average mass = (% 63Cu /100 * mass 63Cu) + (% 65Cu /100 * mass 65Cu)
Substituting the values of mass in the above equation we get:

Average mass = (% 63Cu /100 * 62.9296) + (% 65Cu /100 * 64.9278)

(% 63Cu /100 * 62.9296) + (% 65Cu /100 * 64.9278) = 63.54 amu ----Equation I

Step II: We know that:

% 63Cu + % 65Cu = 100
% 65Cu = 100 - % 63 Cu ------------------ Equation II

Step III: Substituting Equation II in Equation I, we get,

(% 63Cu /100 * 62.9296) + (% 65Cu /100 * 64.9278) = 63.54

(% 63Cu /100 * 62.9296) + ((100 - % 63Cu) /100) * 64.9278 = 63.54

% 63Cu /100 * 62.9296 + 64.9278 - (% 63Cu /100) * 64.9278 = 63.54

62.9296(% 63Cu) + 64.9278 - 64.9278(% 63Cu) = 63.54

62.9296(% 63Cu) - 64.9278(% 63Cu) = 63.54 - 64.9278

-1.9982(% 63Cu) = -1.3878

Step IV: Eliminating negative sides from both sides we get:

1.9982(% 63Cu) = 1.3878

1.9982(% 63Cu) = 1.3878

% 63Cu = 1.3878/1.9982

% 63Cu = 69.4525

Substituting the value of % 63Cu in equation II, we get:

% 65Cu = 30.5475
Calculation of percent abundance of isotopes is usually done in chemistry worksheets.