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Chapter 2: Problem 43

There are three naturally occurring isotopes of magnesium. Their masses and percent natural abundances are \(23.985042 \mathrm{u}, 78.99 \% ; 24.985837 \mathrm{u}, 10.00 \% ;\) and \(25.982593 \mathrm{u}, 11.01 \% .\) Calculate the weighted-average atomic mass of magnesium.

Short Answer

Expert verified
The weighted-average atomic mass of magnesium is the sum of the weighted masses for all isotopes, calculated by multiplying each isotope's atomic mass by its relative abundance.

Step by step solution

01

Determine the weighted mass of each isotope

For each isotope, multiply the given atomic mass by its relative natural abundance (expressed as a decimal). For example, for the first isotope with atomic mass 23.985042 u and abundance 78.99%, the weighted mass is \(23.985042 \times \frac{78.99}{100}\). Repeat this for the other two isotopes.
02

Calculate the sum of all weighted masses

Sum the weighted masses calculated in Step 1. This gives the total weighted mass for all isotopes of magnesium.
03

Find the Weighted Average

Since the percentages of all isotopes add up to 100%, the sum of the weighted masses is the weighted-average atomic mass of magnesium.

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