Calculate the average atomic mass of silver. The percentages denote the relative abundances. Isotope 109 Ag 47 107 amu Rel. Abundance Atomic Mass 48.16% 51.84% 108.905 amu 106.905 amu
The Correct Answer and Explanation is :
To calculate the average atomic mass of silver (Ag), we use the formula:
[
\text{Average Atomic Mass} = (\text{mass of isotope}_1 \times \text{relative abundance}_1) + (\text{mass of isotope}_2 \times \text{relative abundance}_2)
]
Given Data:
- Isotope 1: ( ^{107}Ag )
- Mass = 106.905 amu
- Relative Abundance = 51.84% = 0.5184
- Isotope 2: ( ^{109}Ag )
- Mass = 108.905 amu
- Relative Abundance = 48.16% = 0.4816
Calculation:
[
\text{Average Atomic Mass} = (106.905 \times 0.5184) + (108.905 \times 0.4816)
]
[
= 55.456 \, + \, 52.434
]
[
= 107.87 \, \text{amu}
]
Explanation:
The average atomic mass of an element is a weighted average of all its isotopes based on their natural abundances. Silver has two stable isotopes: (^{107}Ag) and (^{109}Ag), which occur in almost equal proportions.
- Why use a weighted average?
- Elements exist as mixtures of isotopes in nature, and their atomic mass depends on the relative proportion of each isotope.
- Importance of Relative Abundance
- If an isotope is more abundant, it contributes more to the average atomic mass. In silver, (^{107}Ag) has a slightly higher abundance (51.84%), so the average mass is closer to its atomic mass (106.905 amu).
- Final Value in Periodic Table
- The calculated 107.87 amu matches the atomic mass of silver in the periodic table.
Thus, the average atomic mass of silver is 107.87 amu.
Now, I will generate an image representing this calculation.
Here is the image illustrating the calculation of the average atomic mass of silver. Let me know if you need any modifications or additional details!
