Chapter 3, Problem 3.19P

(a)

Interpretation Introduction

Interpretation:

The mass $\left(\text{g}\right)$ of $\text{8}\text{.42 mol}$ of $\text{chromium}\left(\text{III}\right)\text{sulfate decahydrate}$ 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.

(b)

Interpretation Introduction

Interpretation:

The mass $\left(\text{g}\right)$ of $\text{1}\text{.83}\times {\text{10}}^{\text{24}}\text{ molecules}$ of dichlorine heptoxide is 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 $\text{C-12}$. This number is called Avogadro’s number. The value of Avogadro’s number is $\text{6}\text{.022}\times {\text{10}}^{23}\left(\text{entitites/mol}\right)$.

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.

Following are the steps to calculate the mass of a chemical substance when a number of molecules are given.

Step 1: Determine the amount of substance in moles by using Avogadro’s number. The expression to calculate the moles of a chemical substance is as follows:

$\text{Amount }\left(\text{mol }\right)=\left(\text{Given molecules}\right)\left(\frac{1\text{ mol}}{6.022\times {10}^{23}\text{ molecules}}\right)$

Step 2: Multiply the moles with the molar mass of the chemical substance to obtain the mass of chemical substance in grams. The formula to calculate the mass of a substance in grams is as follows:

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

(c)

Interpretation Introduction

Interpretation:

The number of moles and formula units in $6.2\text{ g}$ of lithium sulfate is 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 $\text{C-12}$. This number is called Avogadro’s number. The value of Avogadro’s number is $\text{6}\text{.022}\times {\text{10}}^{23}\left(\text{entitites/mol}\right)$.

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.

A formula unit is used for the ionic compound to represent their empirical formula. The steps to determine the formula unit of an ionic compound from the given mass are as follows:

Step 1: Divide the given mass of the ionic compound with the molar mass to calculate the moles. The expression to calculate the moles of an ionic compound when the mass is given is as follows:

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

Step 2: Multiply the calculated moles with the Avogadro’s number to determine the formula units of an ionic compound. The expression to determine the formula unit is as follows:

$\text{Number of formula units}=\left(\text{Amount }\left(\text{mol}\right)\right)\left(\frac{6.022\times {10}^{23}\text{ formula units}}{1\text{ mol}}\right)$

(d)

Interpretation Introduction

Interpretation:

The number of lithium ions, sulfate ions, sulfur atoms and oxygen atoms in the mass of the compound ${\text{Li}}_{\text{2}}{\text{SO}}_{\text{4}}$ is to be calculated.

Concept introduction:

A formula unit is used for the ionic compound to represent their empirical formula. The molecular formula of a compound tells the number of atoms/ions of each element present in the compound.

A number of ions in a chemical compound is directly linked to the formula unit of the compound.