Question

How would 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

`"63.546 u"`

Explanation:

The average atomic mass of an element is calculated by taking the weighted average of the atomic masses of its naturally-occurring isotopes.

Simply put, each isotope will contribute to the average atomic mass of the element proportionally to its percent abundance.

`color(blue)("avg. atomic mass" = sum_i ("isotope"_i xx "abundance"_i)`

As far as the actual calculations go, you will use decimal abundances, which are simply percent abundances divided by `100`.

So, you know that the atomic masses of these two copper isotopes are `"62.93 u"` and `"64.93 u"`, respectively. Their decimal abundances will be `0.692` and `0.308`, respectively.

The average atomic mass of copper will thus be

`"avg. atomic mass" = overbrace("62.93 u" xx 0.692)^(color(red)(1^"st" "isotope")) + overbrace("64.93 u" xx 0.308)^(color(red)(2^"nd" "isotope"))`

`"avg. atomic mass " = color(green)(" 63.546 u")`

I'll leave the answer is rounded to four sig figs, despite the fact that the values you have for the percent abundances justify only three sig figs.