Question

How do you calculate the average atomic mass of copper if 69.2% of copper has a mass of 62.93 amu and 30.8% has a mass of 64.93 amu?

Answer 1

The answer lies in the concept of general chemistry where average atomic mass also called as average atomic weight is calculated using the formula which when the abundance is given in terms of % is Average atomic mass $=\dfrac{{{f}_{1}}{{M}_{1}}+{{f}_{2}}{{M}_{2}}+........+{{f}_{n}}{{M}_{n}}}{100}$

Complete answer:
In the lower classes of chemistry, we have come across the various concepts regarding the basic chemistry which includes the calculation of empirical formula, molecular formula, molecular mass and many other parameters.
Let us now see what does average atomic mass mean and how is it calculated.
- Average atomic mass is usually measured for the isotopes.
- Isotopes are those atoms which have the same atom and atomic number but with different atomic masses. There can be more than a single isotope.
- In the above given question, the copper atom has two isotopes and they are $^{63}Cu$ and $^{65}Cu$.
- Among these two isotopes of copper, $^{63}Cu$ occurs as 69.2% of abundance and that of $^{65}Cu$ occurs as 30.8% abundance.
- The masses of these two isotopes as per the given data are,
$^{63}Cu$=62.93 amu and $^{65}Cu$= 64.93 amu.
Now, the formula used for the calculation of average atomic mass is given by,
Average atomic mass $=\dfrac{{{f}_{1}}{{M}_{1}}+{{f}_{2}}{{M}_{2}}+........+{{f}_{n}}{{M}_{n}}}{100}$
where, ${{f}_{1}},{{f}_{2}}.....{{f}_{n}}$are the fractions or the % abundance of the isotopes
Now, substituting the values in the above given formula, we have
Average atomic mass $=\dfrac{(62.93)\times 69.2+(64.93)\times 30.8}{100}$
Average atomic mass = 63.546 amu
Thus, the average atomic mass of the given isotopes is 63.546 amu.

Note:
Note that relative atomic mass and average atomic mass are the different entities and not to be confused as the relative atomic mass is the ratio of the average mass of one atom to one twelfth the mass of carbon – 12 atom and average atomic mass is the weighted average mass of all the atoms which naturally occurs