Chapter 11, Problem 12STP

Interpretation Introduction

Interpretation:

The number of moles in 7.13 g of cobalt(III) titanate, ${\text{Co}}_{\text{2}}{\text{TiO}}_{\text{4}}$ should be calculated.

Concept introduction:

The ratio of mass of substance to its molar mass is said to be number of moles of that substance.

Answer to Problem 12STP

The correct option is (b), $\text{3}\text{.1}\times {\text{10}}^{-2}\text{ mol}$.

Explanation of Solution

The number of moles of cobalt(III) titanate, ${\text{Co}}_{\text{2}}{\text{TiO}}_{\text{4}}$ is calculated as shown:

The molar mass is sum of the atomic mass of all the elements present in the compound so, the molar mass of cobalt(III) titanate, ${\text{Co}}_{\text{2}}{\text{TiO}}_{\text{4}}$ is:

${\text{Molar mass of Co}}_{\text{2}}{\text{TiO}}_{\text{4}}\text{ = Atomic mass of }\left[\text{2Co + Ti + 4(O)}\right]$

Substituting the values:

$\begin{array}{l}{\text{Molar mass of Co}}_{\text{2}}{\text{TiO}}_{\text{4}}\text{ = }\left[\text{2(58}\text{.933) + 47}\text{.87 + 4(15}\text{.999)}\right]\text{ g/mol}\\ {\text{Molar mass of Co}}_{\text{2}}{\text{TiO}}_{\text{4}}\text{ = 229}\text{.73 g/mol}\end{array}$

The given mass of ${\text{Co}}_{\text{2}}{\text{TiO}}_{\text{4}}$ is 7.13 g so,

$\begin{array}{l}\text{Number of moles}=\frac{\text{Mass}}{\text{Molar mass}}\\ \text{Number of moles}=\frac{\text{7}\text{.3 g}}{\text{229}\text{.73 g/mol}}\\ \text{Number of moles}=\text{ 0}\text{.03177 mol }\simeq \text{ 3}\text{.1}\times {\text{10}}^{-2}\text{ mol}\end{array}$

Hence, the number of moles in 7.13 g of cobalt(III) titanate, ${\text{Co}}_{\text{2}}{\text{TiO}}_{\text{4}}$ is $\text{3}\text{.1}\times {\text{10}}^{-2}\text{ mol}$.