A hypothetical element X has only two stable isotopes X1 (34.969 amu) and x2 (36.966 amu). X1 has a natural abundance of 75.77%. Calculate the average atomic mass of the element.

Answer 1

Let's start with the known information:

X1 = 34.969 amu

X2 = 36.966 amu

Natural abundance of X1 = 75.77%

We know total abundance is 100% and we have the abundance of X1 (75.77%), so the abundance of X2 must be:

%abundance of X2 = 100% -% of X1 = 100% - 75.77% = 24.23%

This means that in nature you'd find the X1 isotope 75.77% of the time and the X2 isotope 24.23% of the time.

If we just average the weights together, our average will be off since the X1 isotope appears more frequently than the X2 isotope. We need to use the % abundance to account for higher % X1 in nature. We're going to calculate a weighted average based on these percentages to get the average atomic mass:

Average mass = (X1 weight * % Abundance X1) + (X2 weight * % Abundance X2)

Average mass = (34.969 amu * 0.7577) + (36.966 amu * 0.2423)

Average mass = 26.4960113 amu + 8.9568618 amu

Average mass = 35.4528731 amu

Then to round off based on significant figures, our final answer is 35.45 amu to 4 sig figs.

Hope this helps!