Chapter 6, Problem 61A

Interpretation Introduction

Interpretation: The number of grams of cobalt that contain the same number of atoms as 2.24 g of iron needs to be determined.

Concept Introduction:A mole of a substance is defined as the mass in grams of the substance that contains $6.02\times {10}^{23}$ units (atoms, molecules or ions of the substance). This mass is equal to the molar mass of the compound expressed in g.mol-1.

Answer to Problem 61A

The mass of cobalt that contains the same number of atoms as in the given weight of iron is $2.36\text{ g}$ .

Explanation of Solution

The atomic masses are

Co: $\text{58}\text{.933 g}{\text{.mol}}^{-1}$

Fe: $\text{55}\text{.845 g}{\text{.mol}}^{-1}$

  $\begin{array}{c}\text{Moles of Fe =}\frac{\left(\text{2}\text{.24 g}\right)}{\left(\text{55}\text{.845 g}{\text{.mol}}^{-1}\right)}\\ =0.04011\text{ mol}\end{array}$

  $\begin{array}{c}\text{Number of Fe atoms in 0}\text{.04011 mol =}\left(0.04011\text{ mol}\right)\times \frac{\left(6.02\times {10}^{23}\text{ atoms}\right)}{\left(1\text{ mol}\right)}\\ =2.4146\times {10}^{22}\text{ atoms}\end{array}$

  $\begin{array}{c}\text{Mass of Co =}\left(2.4146\times {10}^{22}\text{ atoms}\right)\times \frac{\left(1\text{ mol}\right)}{\left(6.02\times {10}^{23}\text{ atoms}\right)}\times \frac{\left(58.933\text{ g}{\text{.mol}}^{-1}\right)}{\left(\text{1 mol}\right)}\\ =2.3638\text{ g}\\ \approx \text{2}\text{.36 g}\end{array}$

Conclusion

The mass of cobalt that contains the same number of atoms as contained in the given weight of iron is $2.36\text{ g}$ .