Chapter 9, Problem 128A

Interpretation Introduction

Interpretation:

The average atomic mass of chromium needs to be determined.

Concept introduction:

Isotopes are those elements which have an equal number of protons that means atomic number but different neutrons number. Neutron numbers are unequal so, the isotopes of elements have different mass number.

Answer to Problem 128A

Atomic mass of chromium is $51.996\text{amu}$.

Explanation of Solution

The data of percent abundances and masses of the natural isotopes of chromium are given in the table.

Isotope	Percent Abundance	Mass (amu)
$\text{Cr}-\text{5}0$	$\text{4}.\text{35}\%$	$\text{49}.\text{946}$
$\text{Cr}-\text{52}$	$\text{83}.\text{79}\%$	$\text{51}.\text{941}$
$\text{Cr}-\text{53}$	$\text{9}.\text{5}0\%$	$\text{52}.\text{941}$
$\text{Cr}-\text{54}$	$\text{2}.\text{36}\%$	$\text{53}.\text{939}$

To calculate the average atomic mass, calculate the weighted average of the four isotopes by multiplying the percent abundances by corresponding masses.

$\begin{array}{c}\text{Average of Cr isotopes }=\frac{\left(4.35\right)}{100}\left(49.946\right)+\frac{\left(83.79\right)}{100}\left(51.941\right)+\frac{\left(9.50\right)}{100}\left(52.941\right)+\frac{\left(2.36\right)}{100}\left(53.939\right)\\ =\left(0.0435\right)\left(49.946\right)+\left(0.8379\right)\left(51.941\right)+\left(0.095\right)\left(52.941\right)+\left(0.0236\right)\left(53.939\right)\\ \approx 51.996\text{amu}\end{array}$

$\text{Average of the four isotopes}\approx 51.996\text{amu}$

Conclusion

Thus, the tomic mass of chromium is $51.996\text{amu}$.