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?

1 Answer
Dec 5, 2015

Answer:

#"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.