Calculate the average atomic mass of silver using the following isotopes: Isotope Abundance Mass Ag 51.84% 106.905 amu Ag 48.16% 107.9048 amu O 0.91% 106.91 amu O 0.87% 107.87 amu O 0.00% 108.00 amu O 0.90% 107.90 amu O 0.90% 108.90 amu
The Correct Answer and Explanation is:
To calculate the average atomic mass of silver, we need to account for the isotopes and their relative abundances. The average atomic mass is a weighted average, which takes into account the mass of each isotope and its percentage abundance.
We have the following data:
- Isotope 1: Ag with mass 106.905 amu and abundance 51.84%
- Isotope 2: Ag with mass 107.9048 amu and abundance 48.16%
Note: The extra isotopes listed, such as O with their corresponding masses, seem to be an error. I will ignore those and focus on the two relevant silver isotopes.
The formula for calculating the average atomic mass is:Average Atomic Mass=(Abundance of Isotope 1×Mass of Isotope 1100)+(Abundance of Isotope 2×Mass of Isotope 2100)\text{Average Atomic Mass} = \left( \frac{ \text{Abundance of Isotope 1} \times \text{Mass of Isotope 1} }{100} \right) + \left( \frac{ \text{Abundance of Isotope 2} \times \text{Mass of Isotope 2} }{100} \right)Average Atomic Mass=(100Abundance of Isotope 1×Mass of Isotope 1)+(100Abundance of Isotope 2×Mass of Isotope 2)
Now, plugging in the values:Average Atomic Mass=(51.84×106.905100)+(48.16×107.9048100)\text{Average Atomic Mass} = \left( \frac{51.84 \times 106.905}{100} \right) + \left( \frac{48.16 \times 107.9048}{100} \right)Average Atomic Mass=(10051.84×106.905)+(10048.16×107.9048)Average Atomic Mass=(55.3624)+(51.9681)\text{Average Atomic Mass} = (55.3624) + (51.9681)Average Atomic Mass=(55.3624)+(51.9681)Average Atomic Mass=107.3305 amu\text{Average Atomic Mass} = 107.3305 \, \text{amu}Average Atomic Mass=107.3305amu
So, the average atomic mass of silver is approximately 107.33 amu.
This value represents the weighted average of the isotopes based on their abundance. The isotopes of silver are close in mass, so the average mass is slightly higher than the mass of the lighter isotope (106.905 amu). This is because the second isotope (107.9048 amu) is more abundant, thus pulling the average atomic mass toward its value.
