Questions: Using the table below, calculate the atomic weight of made up element X: Calculate Average Isotopic Mass Isotope Atomic Mass Natural Abundance --------- Xisotope 1 43.687 amu 22.39% Xisotope 1 45.670 amu 18.42% Xisotope 1 46.920 amu 59.19%

Using the table below, calculate the atomic weight of made up element X: Calculate Average Isotopic Mass

Isotope Atomic Mass Natural Abundance
---------
Xisotope 1 43.687 amu 22.39%
Xisotope 1 45.670 amu 18.42%
Xisotope 1 46.920 amu 59.19%

Transcript text: Using the table below, calculate the atomic weight of made up element X : Calculate Average Isotopic Mass Isotope | Atomic Mass | Natural Abundance ---|---|--- Xisotope 1 | 43.687 amu | $22.39 \%$ Xisotope 1 | 45.670 amu | $18.42 \%$ Xisotope 1 | 46.920 amu | $59.19 \%$

Solution

Solution Steps

Step 1: Convert Natural Abundance to Decimal Form

To calculate the average atomic weight, we first need to convert the natural abundance percentages into decimal form. This is done by dividing each percentage by 100.

For Xisotope 1: $22.39\% = \frac{22.39}{100} = 0.2239$
For Xisotope 2: $18.42\% = \frac{18.42}{100} = 0.1842$
For Xisotope 3: $59.19\% = \frac{59.19}{100} = 0.5919$

Step 2: Calculate the Contribution of Each Isotope to the Atomic Weight

Multiply the atomic mass of each isotope by its corresponding decimal abundance to find its contribution to the average atomic weight.

Contribution of Xisotope 1: $43.687 \, \text{amu} \times 0.2239 = 9.7835 \, \text{amu}$
Contribution of Xisotope 2: $45.670 \, \text{amu} \times 0.1842 = 8.4105 \, \text{amu}$
Contribution of Xisotope 3: $46.920 \, \text{amu} \times 0.5919 = 27.7700 \, \text{amu}$

Step 3: Sum the Contributions to Find the Average Atomic Weight

Add the contributions from each isotope to find the average atomic weight of element X.

\[ 9.7835 \, \text{amu} + 8.4105 \, \text{amu} + 27.7700 \, \text{amu} = 45.9640 \, \text{amu} \]