Chapter 4, Problem 104A

Interpretation Introduction

Interpretation:

The atomic mass of titanium needs to be calculated.

Concept introduction:

Atomic mass of an atomis calculated by calculating the average atomic mass of all the isotopes of that individual atom.

Answer to Problem 104A

The average atomic mass of titanium comes out to be $47.923u$.

Explanation of Solution

The average atomic mass of titanium is calculated by taking the average mass of all the stable isotopes that constitutes titanium.

Each isotope will contribute to the average atomic mass of the element in proportion to its decimal abundance, calculated by dividing percentage abundance with $100$.

$\mathrm{avg}.atomicMass={\displaystyle \sum _i^{}{m}_{a,i}}\times abundanceOf-i$

The relative decimal abundances of the five isotopes given are:

$Ti=\frac{8.0}{100}=0.080$

$Ti=\frac{7.8}{100}=0.078$

$Ti=\frac{73.4}{100}=0.734$

$Ti=\frac{5.5}{100}=0.055$

$Ti=\frac{5.3}{100}=0.053$

The average atomic mass of titanium is

$=46u\times 0.080+47u\times 0.078+0.734+49u\times 0.055+50u\times 0.053=47.923u$

Conclusion

The average atomic mass of titanium comes out to be $47.923u$ by adding the atomic masses of each individual isotopes.