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Chapter 3: Problem 44

The element silver (Ag) has two naturally occurring isotopes: 109 \(\mathrm{Ag}\) and \(^{107} \mathrm{Ag}\) with a mass of 106.905 \(\mathrm{u} .\) Silver consists of 51.82\(\%\) of Ag and has an average atomic mass of 107.868 u. Calculate the mass of \(^{109} \mathrm{Ag}\) .

Short Answer

Expert verified
The mass of the isotope $^{109}\mathrm{Ag}$ is approximately \(109.30\,\text{u}\).

Step by step solution

01

Calculate the percentage of 109 Ag

First, we find the percentage of the isotope 109 Ag by subtracting the given percentage of the isotope 107 Ag from 100%. Percentage of 109 Ag = 100% - 51.82% = 48.18%
02

Rearrange the average atomic mass formula

Next, we arrange the formula for average atomic mass as follows to find the mass of the isotope 109 Ag: Mass of 109 Ag = [(Average atomic mass × 100) - (% of 107 Ag × mass of 107 Ag)] / % of 109 Ag
03

Calculate the mass of 109 Ag

Now, we plug in the given and calculated values into the rearranged formula: Mass of 109 Ag = [(107.868 u × 100) - (51.82% × 106.905 u)] / 48.18% Mass of 109 Ag = [(10786.8 u) - (5541.51 u)] / 48.18% Mass of 109 Ag = 5265.29 u / 48.18% Mass of 109 Ag ≈ 109.30 u So, the mass of the isotope 109 Ag is approximately 109.30 u.

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