Most students grasp the concept of isotopes atoms of the same element that differ in mass number because of a different number of neutrons in the nucleus What students tend to have a hard time with is how to calculate isotopic mass given percent abundance or vice versa The following tutorial hopes to explain this concept in detail Calculating average isotopic mass requires a strong understanding of how averages work Consider the following Here we have ten coins Some have a value of 5 units and some have a value of 10 units If we wanted to calculate the average value of all the coins above we would add up all of their individual values 65 and divide by the total number of coins 10 The average value of the coins is 6 5 units But what if we had hundreds of thousands of coins How would we calculate the average then Technically we could add up all of their values and divide the total by the number of coins we had But there s a better way and that s to use a representative sample Suppose that the coins above are a representative sample a sample that exhibits the same proportion of components as the total of the hundreds of thousands of coins we want to find an average for We can use the percent abundance of each coin and each coin s individual value to find the overall average What percentage of the coins have a value of 5 units What percentage of the coins have a value of 10 units We can calculate the average value of all all of the coins by multiplying each percentage in decimal form by its respective value and then adding the two numbers together As you can see the averages are the same using both methods The second method however is how we calculate the average atomic masses that you see on the periodic table Speaking of let s do some examples that are actually related to chemistry Average Atomic Mass m m Calculating Average Atomic Mass Given Percent Abundance Example 1 There are two known naturally occurring isotopes of copper copper 62 and copper 64 Given that the percent abundance of Cu 62 is 24 3 calculate the average atomic mass in amu of copper The equation above includes the ellipses to show that you could have more than two naturally occurring isotopes for an element and that it too would have to be included in the average mass But in this example we only have two so let s write what we know and then substitute the information into the equation Example 2 What is the average atomic mass in amu of silicon if the only known isotopes are Si 26 24 9 Si 28 49 7 and Si 30 25 4 Calculating Percent Abundance Given Average Atomic Mass In the previous examples we were given the identity of the isotopes and their individual atomic masses and asked to calculate the average atomic mass for the element In the following example we will work out problems in which we calculate the percent abundance of each isotope given the average atomic mass These problems will test your algebra skills so pay close attention to how each value is substituted into the formula Example 3 The average atomic mass of iodine is 126 90 amu The two naturally occurring isotopes of iodine are I 126 and I 128 Calculate the percent abundance of each isotopic species We will use the same equation from before but with a slight modification The x in this equation represents the unknown abundance of the first isotope in decimal form The 1 x represents the percent abundance of the second isotope in relation to the first We subtract from 1 because 1 is the decimal form of 100 And now to work out our example Average Atomic Mass x m 1 x m
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