Chapter 6, Problem 10A

Interpretation Introduction

Interpretation: The mass of calcium metal containing the same number of atoms as in 12.16 g of magnesium needs to be determined. Also, the mass of calcium metal containing the same number of atoms as in 24.31 g of Mg needs to be determined.

Concept Introduction: The molecular mass of compound is the sum of atomic mass of all the atoms present in the given chemical compound. Mole concept is used to calculate the moles, mass, number of atoms and moles of a compound. The relation between these values can be shown as:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ {\text{1 mole = N}}_{\text{a}}\text{ atoms}\\ {\text{N}}_{\text{a}}\text{ = 6}\text{.022 }\times {\text{ 10}}^{\text{23}}\end{array}$

Answer to Problem 10A

Mass of Ca = 20.0 g

Mass of Ca = 40.0 g

Explanation of Solution

Molar mass of Mg = 24.3 g/mol Molar mass of Ca = 40.1 g/mol

Mass of Mg metal = 12.16 g

Calculate moles of 12.16 g of Mg-

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{12}\text{.16 g}}{\text{24}\text{.3 g/mol }}\text{=0}\text{.500 moles}\end{array}$

Moles of Ca = moles of Mg

Calculate mass of Ca:

  $\begin{array}{l}\text{mass = moles }\times \text{ molar mass }\\ \text{mass = 0}\text{.500 moles }\times \text{ 40}\text{.1 g/mol }\\ \text{mass = 20}\text{.0 g}\end{array}$

Calculate moles of 24.31 g of Mg-

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{24}\text{.31 g}}{\text{24}\text{.3 g/mol }}\text{= 1}\text{.00 moles}\end{array}$

Moles of Ca = moles of Mg

Calculate mass of Ca:

  $\begin{array}{l}\text{mass = moles }\times \text{ molar mass }\\ \text{mass = 1}\text{.00 moles }\times \text{ 40}\text{.1 g/mol }\\ \text{mass = 40}\text{.1 g}\end{array}$

Conclusion

If two metals have same number of atoms, it means they will have same number of moles also.