Chapter 16, Problem 10STP

Interpretation Introduction

Interpretation:

The number of moles in $\text{4}\text{.30}\times {\text{10}}^{\text{2}}\text{g}$ of calcium phosphate $\left({\text{Ca}}_{\text{3}}{\left({\text{PO}}_{\text{4}}\right)}_{\text{2}}\right)$ needs to be determined.

Concept introduction:

Molar mass is the grams per mole of a certain molecule.

$\text{Molar}\text{mass}\text{=}\frac{\text{Mass}}{\text{Number}\text{of}\text{moles}}$ …… (1)

Answer to Problem 10STP

B. 1.39 moles

Explanation of Solution

From the formula (1) of molar mass,

$\text{Mass}\text{=}\text{Molar mass×Number}\text{of}\text{moles}$ …… (2)

$\frac{\text{Mass}}{\text{Molar mass}}\text{=}\frac{\text{Molar mass}}{\text{Molar mass}}\text{×Number}\text{of}\text{moles}$

(Multiply both sides by number of moles)

$\text{Number}\text{of}\text{moles}\text{=}\frac{\text{Mass}}{\text{Molar mass}}$ …… (3)

Molar mass of calcium is $\text{310}\text{.18}\text{g}/\text{mol}$. Given mass is $\text{4}\text{.30}\times {\text{10}}^{\text{2}}\text{g}$

Put these values in equation (3) is as follows:

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{=}\frac{\text{4}\text{.30}\times {\text{10}}^{\text{2}}\cancel{\text{g}}}{\text{310}\text{.18}\cancel{\text{g}}/\text{mol}}\\ =1.386\text{mol}\\ \approx 1.39\text{mol}\end{array}$

Thus the moles are in $\text{4}\text{.30}\times {\text{10}}^{\text{2}}\text{g}$ of calcium phosphate $\left({\text{Ca}}_{\text{3}}{\left({\text{PO}}_{\text{4}}\right)}_{\text{2}}\right)$ is 1.39 moles. The correct option is B.

Conclusion

The incorrect options are as follows:

A. 0.721 moles

The formula of molar mass is as follows:

$\text{Mass}\text{=}\text{Molar mass×Number}\text{of}\text{moles}$

C. 1.54 moles

The formula of molar mass is as follows:

$\text{Mass}\text{=}\text{Molar mass×Number}\text{of}\text{moles}$

D. 3.18 moles

The formula of molar mass is as follows:

$\text{Mass}\text{=}\text{Molar mass×Number}\text{of}\text{moles}$