Chapter 3, Problem 3.27P

(a)

Interpretation Introduction

Interpretation:

The moles of rust $\left({\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{4H}}_{\text{2}}\text{O}\right)$ in $45.2{\text{ kg Fe}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{4H}}_{\text{2}}\text{O}$ are to be calculated.

Concept introduction:

Molar mass is defined as the mass of $1\text{ mol}$ of a chemical substance in grams. The molar mass of a compound is calculated by the addition of the molar mass of each element multiplied by its number of atoms present in the chemical formula.

The SI unit for amount of substance is $\text{mol}$. The mass and molar mass of a substance are used to calculate the amount of substance. The formula to calculate moles from the mass is as follows:

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

(b)

Interpretation Introduction

Interpretation:

The moles of ${\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}$ in $45.2\text{ kg}$ of rust $\left({\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{4H}}_{\text{2}}\text{O}\right)$ are to be calculated.

Concept introduction:

One mole is defined as the amount of substance that contains the same number of entities such as molecules, ions, atoms as the number of atoms in $12\text{ g}$ of $\text{C-12}$. The SI unit for amount of substance is $\text{mol}$.

The formula to calculate the moles of chemical substance in a compound is as follows:

$\text{Amount of A}\left(\text{mol}\right)=\left(\begin{array}{l}\text{amount of}\\ \text{compound}\\ \left(\text{mol}\right)\end{array}\right)\left(\frac{\begin{array}{l}\text{moles of A in}\\ \text{molecular formula}\end{array}}{1\text{ mol compound}}\right)$ (3)

(c)

Interpretation Introduction

Interpretation:

The mass $\left(\text{g}\right)$ of $\text{Fe}$ in $45.2\text{ kg}$ of rust $\left({\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{4H}}_{\text{2}}\text{O}\right)$ is to be calculated.

Concept introduction:

Molar mass is defined as the mass of $1\text{ mol}$ of a chemical substance in grams. The molar mass of a compound is calculated by the addition of the molar mass of each element multiplied by its number of atoms present in the chemical formula.

The molecular formula of a compound tells the number of atoms of each element present in the compound.

Following are the steps to calculate the mass of an element when the amount of compound is given.

Step 1: Determine the number of moles of atoms of an element A from the molecular formula of the compound. The formula to calculate the moles of element A is as follows:

$\text{Amount of element A}\left(\text{mol}\right)=\left(\begin{array}{l}\text{amount of}\\ \text{compound}\\ \left(\text{mol}\right)\end{array}\right)\left(\frac{\begin{array}{l}\text{moles of element A in}\\ \text{molecular formula}\end{array}}{1\text{ mol compound}}\right)$ (4)

Step 2: Multiply the calculated moles of A with its molar mass to obtain the mass. The formula to calculate the mass of an element is as follows:

$\text{Mass of element A}\left(\text{g}\right)=\left(\text{Amount of element A}\left(\text{mol}\right)\right)\left(\frac{\text{No}\text{. of grams}}{1\text{ mol}}\right)$ (5)