Question

1. verify that the atomic mass of magnesium is 24.31 amu, given the following information:

²⁴mg, mass = 23.985042 amu; percent abundance = 78.99%
²⁵mg, mass = 24.985837 amu; percent abundance = 10.00%
²⁶mg, mass = 25.982593 amu; percent abundance = 11.01%

Explanation:

Step1: Calculate the contribution of \(^{24}\text{Mg}\)

Multiply the mass of \(^{24}\text{Mg}\) by its percent abundance.

$$23.985042\times\frac{78.99}{100}=23.985042\times0.7899 = 18.955784$$

Step2: Calculate the contribution of \(^{25}\text{Mg}\)

Multiply the mass of \(^{25}\text{Mg}\) by its percent abundance.

$$24.985837\times\frac{10.00}{100}=24.985837\times0.10 = 2.4985837$$

Step3: Calculate the contribution of \(^{26}\text{Mg}\)

Multiply the mass of \(^{26}\text{Mg}\) by its percent abundance.

$$25.982593\times\frac{11.01}{100}=25.982593\times0.1101=2.8606835$$

Step4: Sum up the contributions

Add the contributions of all three isotopes.

$$18.955784 + 2.4985837+2.8606835=24.315051\approx24.31$$

Answer:

The calculated atomic mass of magnesium is approximately \(24.31\) amu, which verifies the given atomic mass.