Question

A 53.000g sample of silver is found to consist of 27.475g of 107Ag and 25.525g of 109Ag. How would you calculate the average atomic mass of silver?

Answer 1

`"107.96 u"`

Explanation:

The idea here is that you can use the total mass of the sample and the mass of the two isotopes to find their respective abundances.

So, if your smple contains of `"27.475 g"` of silver-107 and `"25.525 g"` of silver-109, it follows that the percent composition of the sample is

`(27.475color(red)(cancel(color(black)("g"))))/(53.000color(red)(cancel(color(black)("g")))) xx 100 = 51.840% -> ""^107"Ag"`

and

`(25.525color(red)(cancel(color(black)("g"))))/(53.000color(red)(cancel(color(black)("g")))) xx 100 = 48.160% -> ""^109"Ag"`

Now, the average atomic mass of silver is calculated by taking the weighted average of the atomic masses of its isotopes.

In other words, each isotope will contribute to the average atomic mass proportionally to its respective percent abundace.

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

In your case, the average atomic mass of silver will be - use decimal abundances, which are simply percent abundances divided by `100`

`"avg. atomic mass " = "107 u" xx 0.51840 + "109 u" xx 0.48160`

`"avg. atomic mass" = color(white)(x)color(green)("107.96 u")`