# 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?

##### 1 Answer

#### 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

#(27.475color(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

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

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