Chapter 3, Problem 3.47P

(a)

Interpretation Introduction

Interpretation:

The moles of $\text{O}$ present in $55.4\text{ g}$ of ${\text{M}}_2{\text{O}}_3$ are to be determined.

Concept introduction:

The amount of an element present in a compound is determined from the amount of compound and the molar ratio of that element in one mole of compound. Suppose the compound is ${\text{X}}_2{\text{Y}}_3$ and the amount of ${\text{X}}_2{\text{Y}}_3$ is given, then the formula to calculate the amount of element Y is as follows:

$\text{Amount of Y}\left(\text{mol}\right)=\left({\text{Amount of X}}_2{\text{Y}}_3\left(\text{mol}\right)\right)\left(\frac{3\text{ mol Y}}{1{\text{ mol X}}_2{\text{Y}}_3}\right)$ (1)

(b)

Interpretation Introduction

Interpretation:

The mass of $\text{M}$ present in $55.4\text{ g}$ of ${\text{M}}_2{\text{O}}_3$ is to be determined.

Concept introduction:

Following are the step to calculate the mass of an element present in the compound if the amounts of its constituent elements and the mass of the compound are known.

Step 1: Determine the amount of each element present in the compound and convert moles ot mass by using the following expression,

$\text{Mass}\left(\text{g}\right)=\left(\text{Amount}\left(\text{mol}\right)\right)\left(\frac{\text{No}\text{. of grams}}{\text{ 1 mol}}\right)$ (2)

Step 2: Subtract the known mass of element from the mass of the compound to determine the unknown mass of another element. Suppose the compound is ${\text{XY}}_2$, the mass of  Y and sample are given, then the formula to calculate the mass of element X is as follows:

$\text{Mass of X}=\text{Mass of compound}-\text{Mass of Y}$ (3)

(c)

Interpretation Introduction

Interpretation:

The element represented by the symbol M is to be determined.

Concept introduction:

Molar mass is defined as the mass of $1\text{ mol}$ of a chemical substance in grams. It is the characteristics of an element. The unknown substance is determined by calculating its molar mass. The expression to that relates mass and moles of a substance to its molar mass is as follows:

$\text{Molar mass}=\frac{\text{Mass}\left(\text{g}\right)}{\text{Amount}\left(\text{mol}\right)}$ (4)

The amount of an element present in a compound is determined from the amount of compound and the molar ratio of that element in one mole of compound. Suppose the compound is ${\text{X}}_2{\text{Y}}_3$ and the amount of ${\text{X}}_2{\text{Y}}_3$ is given, then the formula to calculate the amount of element X is as follows:

$\text{Amount of X}\left(\text{mol}\right)=\left({\text{Amount of X}}_2{\text{Y}}_3\left(\text{mol}\right)\right)\left(\frac{2\text{ mol X}}{1{\text{ mol X}}_2{\text{Y}}_3}\right)$ (5)