QuestionFind the atomic weight of an element with isotopes: $120.9038 \mathrm{amu}$ (57.25\% abundance) and $122.8831 \mathrm{amu}$ .

Studdy Solution

STEP 1

Assumptions1. The atomic weight of the first isotope is $120.9038 \, \mathrm{amu}$ and its abundance is $57.25 \%$ . . The atomic weight of the second isotope is $122.8831 \, \mathrm{amu}$ .
3. The abundance of the second isotope is $100\% -57.25\% =42.75\%$ , since the total abundance of all isotopes of an element must add up to $100\%$ .
4. The atomic weight of the element is the weighted average of the atomic weights of its isotopes, where the weights are the abundances of the isotopes.

STEP 2

First, we need to calculate the contribution of each isotope to the atomic weight of the element. This is done by multiplying the atomic weight of each isotope by its abundance.
$\text{Contribution of first isotope} = \text{Atomic weight of first isotope} \times \text{Abundance of first isotope}$ $\text{Contribution of second isotope} = \text{Atomic weight of second isotope} \times \text{Abundance of second isotope}$

STEP 3

Now, plug in the given values for the atomic weights and abundances to calculate the contributions.
$\text{Contribution of first isotope} =120.9038 \, \mathrm{amu} \times57.25\%$ $\text{Contribution of second isotope} =122.8831 \, \mathrm{amu} \times42.75\%$

STEP 4

Convert the percentages to decimal values.
$57.25\% =0.572$ $42.75\% =0.427$ Then, calculate the contributions.
$\text{Contribution of first isotope} =120.9038 \, \mathrm{amu} \times0.572$ $\text{Contribution of second isotope} =122.8831 \, \mathrm{amu} \times0.427$

STEP 5

Calculate the contributions.
$\text{Contribution of first isotope} =120.9038 \, \mathrm{amu} \times0.5725 =69.228 \, \mathrm{amu}$ $\text{Contribution of second isotope} =122.8831 \, \mathrm{amu} \times0.4275 =52.563 \, \mathrm{amu}$

STEP 6

Now that we have the contributions of each isotope, we can find the atomic weight of the element by adding these contributions.
$\text{Atomic weight of element} = \text{Contribution of first isotope} + \text{Contribution of second isotope}$

STEP 7

Plug in the values for the contributions to calculate the atomic weight of the element.
$\text{Atomic weight of element} =69.228 \, \mathrm{amu} +52.563 \, \mathrm{amu}$

STEP 8

Calculate the atomic weight of the element.
$\text{Atomic weight of element} =69.228 \, \mathrm{amu} +52.563 \, \mathrm{amu} =121.791 \, \mathrm{amu}$ The atomic weight of the element is $121.791 \, \mathrm{amu}$ , which is closest to option1 $121.75 \, \mathrm{amu}$ .

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