Chapter 2, Problem 2.21QP

Interpretation Introduction

Interpretation: The comparison of average atomic mass between magnesium on Earth $\left(24.31\text{amu}\right)$ and on Mars is to be stated.

Concept introduction: The exact mass of an element from its compound is calculated by subtracting the exact mass of given element from exact mass of total compound.

To determine: The comparison of average atomic mass between magnesium on Earth $\left(24.31\text{amu}\right)$ and on Mars.

Answer to Problem 2.21QP

Solution

The average atomic masses of magnesium on Earth $\left(24.31\text{amu}\right)$ and on Mars are equal.

Explanation of Solution

Explanation

In the question isotopic composition the exact mass $\text{MgO}$ is shown with different isotopes of magnesium is given. There is only oxygen- $16$ $\left(15.9948\text{amu}\right)$ isotope in the given isotopic composition.

The exact mass of magnesium isotopes from its compound is calculated by subtracting the exact mass of oxygen- $16$ $\left(15.9948\text{amu}\right)$ from exact mass of $\text{MgO}$.

The exact mass of magnesium isotope from $\text{MgO}$ $\left(39.9872\text{amu}\right)$.

Hence, the exact mass of magnesium isotopes is calculated in Table $1$.

Exact mass of $\text{MgO}\text{(amu)}$	Exact mass of ${}^{16}\text{O}$ isotope in $\text{amu}$	Exact mass of $\text{Mg}$ isotopes $\left(\text{m}\right)$ in $\text{amu}$ $=$ $\left(\text{Exact}\text{mass}\text{of}\text{MgO}-{\text{Exact mass of isotope }}^{\text{16}}\text{O}\right)$
$39.9872$	$15.9948$	$39.9872-15.9948=23.9924$
$40.9886$	$15.9948$	$40.9886-15.9948=24.9938$
$41.9846$	$15.9948$	$41.9846-15.9948=25.9891$

Table $1$

The natural abundance of magnesium isotopes in decimals is calculated by dividing the natural abundance $(\%)$ with $100$ is given in Table $2$.

Natural abundance $(\%)$ of $\text{Mg}$ isotopes	Natural abundance of $\text{Mg}$ isotopes in decimals $\left(x\right)$
$78.70$	$\frac{78.70}{100}=0.7870$
$10.13$	$\frac{10.13}{100}=0.1013$
$11.17$	$\frac{11.17}{100}=0.1117$

Table $2$

The weighted atomic mass of magnesium is calculated by the multiplication of exact mass of magnesium isotopes $\left(\text{m}\right)$ with natural abundance $\left(x\right)$ of magnesium isotopes in decimals. This is shown in Table $3$.

Exact mass of $\text{Mg}$ isotopes $\left(\text{m}\right)$ in $\text{amu}$	Natural abundance of $\text{Mg}$ isotopes in decimals $\left(x\right)$	Weighted atomic mass $\left(\text{m}\times x\right)$
$23.9924$	$0.7870$	$23.9924\times 0.7870=18.882$
$24.9938$	$0.1013$	$24.9938\times 0.1013=2.5318$
$25.9891$	$0.1117$	$25.9891\times 0.1117=2.9029$

Table $3$

The values of Table $1$, Table $2$, and Table $3$ are summarized in Table $4$.

Exact mass of $\text{MgO}\text{(amu)}$	Exact mass of ${}^{16}\text{O}$ isotope in $\text{amu}$	Exact mass of $\text{Mg}$ isotopes $\left(\text{m}\right)$ in $\text{amu}$	Natural abundance $(\%)$ of $\text{Mg}$ isotopes	Natural abundance of $\text{Mg}$ isotopes in decimals $\left(x\right)$	Weighted atomic mass $\left(\text{m}\times x\right)$
$39.9872$	$15.9948$	$23.9924$	$78.70$	$0.7870$	$18.882$
$40.9886$	$15.9948$	$24.9938$	$10.13$	$0.1013$	$2.5318$
$41.9846$	$15.9948$	$25.9891$	$11.17$	$0.1117$	$2.9029$

Table $4$

The average atomic mass is the summation of weighted atomic mass. So,

$\begin{array}{c}\text{Average}\text{atomic}\text{mass}=18.882\text{amu}+2.5318\text{amu}+2.9029\text{amu}\\ =24.3167\text{amu}\end{array}$

The average atomic mass of magnesium on Earth is also $24.31\text{amu}$. Hence, the average atomic masses of magnesium on Earth $\left(24.31\text{amu}\right)$ and on Mars are equal.

Conclusion

The average atomic masses of magnesium on Earth $\left(24.31\text{amu}\right)$ and on Mars are equal