Chapter 10.2, Problem 26LC

Interpretation Introduction

Interpretation: The mass in grams for $5.66\text{ mol}$ of ${\text{CaCO}}_{\text{3}}$ should be calculated.

Concept Introduction: The mass in grams of one mole of the compound is said to be its molar mass.

Answer to Problem 26LC

The mass in grams for $5.66\text{ mol}$ of ${\text{CaCO}}_{\text{3}}$ is $\text{566 g}$ .

Explanation of Solution

To determine the mass of $5.66\text{ mol}$ of ${\text{CaCO}}_{\text{3}}$ the molar mass of ${\text{CaCO}}_{\text{3}}$ is calculated first. The molar mass is calculated by adding up the sum of the masses of Ca, C and O elements.

The moles of Ca, C and O are converted to grams of Ca, C and O as:

  $\begin{array}{l}\text{1 mol Ca }\times \frac{40.0\text{ g Ca}}{1\text{ mol Ca}}\text{ = 40}\text{.0 g Ca}\\ \text{1 mol C }\times \frac{\text{12}\text{.0 g C}}{1\text{ mol C}}\text{ = 12}\text{.0 g C}\\ \text{3 mol O }\times \frac{\text{16}\text{.0 g O}}{1\text{ mol O}}\text{ = 48}\text{.0 g O}\end{array}$

The mass of 1 mol of ${\text{CaCO}}_{\text{3}}$ is:

  $\begin{array}{l}{\text{mass of 1 mol of CaCO}}_{\text{3}}\text{ = 40}\text{.0 g Ca + 12}\text{.0 g C + 48}\text{.0 g O}=\text{ 100}\text{.0 g}\\ {\text{molar mass of CaCO}}_{\text{3}}=10\text{0}\text{.0 g/mol}\end{array}$

Thus, the molar mass of ${\text{CaCO}}_{\text{3}}$ is $\text{100}\text{.0 g/mol}$ .

Now, the mass in grams for $5.66\text{ mol}$ of ${\text{CaCO}}_{\text{3}}$ is:

  $5.66\text{ mol}\times \frac{\text{100}\text{.0 g}}{1\text{ mol}}\text{ = 566 g}$

Hence, the mass in grams for $5.66\text{ mol}$ of ${\text{CaCO}}_{\text{3}}$ is $\text{566 g}$ .