Chapter 6, Problem 57A

Interpretation Introduction

Interpretation: The number of grams of iron that contain the same number of atoms as 2.24 g of cobalt 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 57A

The mass of iron that contains the same number of atoms as the given weight of cobalt is $2.12\text{ g}$ .

Explanation of Solution

The atomic masses are

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

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

  $\begin{array}{c}\text{Moles of Co =}\frac{\left(\text{2}\text{.24 g}\right)}{\left(\text{58}\text{.933 g}{\text{.mol}}^{-1}\right)}\\ =0.0380\text{ mol}\end{array}$

  $\begin{array}{c}\text{Number of Co atoms in 0}\text{.0380 mol =}\left(0.0380\text{ mol}\right)\times \frac{\left(6.02\times {10}^{23}\text{ atoms}\right)}{\left(1\text{ mol}\right)}\\ =2.2876\times {10}^{22}\text{ atoms}\end{array}$

  $\begin{array}{c}\text{Mass of Fe =}\left(2.2876\times {10}^{22}\text{ atoms}\right)\times \frac{\left(1\text{ mol}\right)}{\left(6.02\times {10}^{23}\text{ atoms}\right)}\times \frac{\left(55.845\text{ g}{\text{.mol}}^{-1}\right)}{\left(\text{1 mol}\right)}\\ =2.12211\text{ g}\\ \approx \text{2}\text{.12 g}\end{array}$

Conclusion

The mass of iron that contains the same number of atoms as the given weight of cobalt is $2.12\text{ g}$ .