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Chapter 7: Problem 42

Naturally occurring silver is composed of two isotopes: Ag 107 is 51.35\(\%\) with a mass of 106.905092 amu, and the rest is \(\mathrm{Ag}-109\) with a mass of 108.9044757 amu. Calculate the average atomic mass of silver.

Short Answer

Expert verified
The average atomic mass of naturally occurring silver is approximately 107.8681 amu.

Step by step solution

01

Analyze the data

Firstly, identify and note down the information given in the question. The two isotopes are Ag 107 and Ag 109, with the former having a mass of 106.905092 amu and a relative abundance of 51.35 percent, whereas, Ag 109 has a mass of 108.9044757 amu with a relative abundance of (100-51.35) percent, since the total abundance must sum to 100 percent.
02

Convert the relative abundances

Convert the given relative abundances from percentages to fractions by dividing the percentage values by 100. Hence, the fractional abundance of Ag 107 is 0.5135 and that of Ag 109 is 0.4865.
03

Calculate the weighted mass

Now, use the formula for the average atomic mass, which is the sum of the product of each isotope's mass and its relative fraction. This yields the equation (0.5135*106.905092) + (0.4865*108.9044757).
04

Compute the average atomic mass

Perform the calculation set up in the previous step. Multiplying each isotope's mass by its relative abundance and adding the two results gives an average atomic mass of 107.8681 amu.

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