Chapter 3, Problem 3.15P

(a)

Interpretation Introduction

Interpretation:

The mass of $4.6\times {10}^{21}\text{ molecules}$ of ${\text{NO}}_2$ in $\text{kg}$ 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 number of molecules is given.

Step 1: Determine the amount of substance 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 moleswith the molar mass of the chemical substance to obtain the mass of chemical substance in grams. The mass can be converted to kilogram by using the relation between gram and kilogram. The formula to calculate the mass of a substance in kilogram is as follows:

$\text{Mass }\left(\text{kg }\right)=\left(\text{Amount }\left(\text{mol}\right)\right)\left(\frac{\text{No}\text{. of grams}}{\text{1 mol}}\right)\left(\frac{{10}^{-3}\text{ kg}}{1\text{ g}}\right)$

(b)

Interpretation Introduction

Interpretation:

The amount of chlorine atoms in $0.0615\text{ g}$ of ${\text{C}}_{\text{2}}{\text{H}}_{\text{4}}{\text{Cl}}_{\text{2}}$ in $\text{mol}$ 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 amount of an element in a compound.

Step 1: Convert the mass of the compound to moles by using molar mass of that compound by using the formula as,

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

Step 2: Determine the number of moles of atoms of an element from the molecular formula of the compound. The formula to calculate the moles of an element is as follows:

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

(c)

Interpretation Introduction

Interpretation:

The number of ${\text{H}}^{-}$ ions in $5.82\text{ g}$ of ${\text{SrH}}_2$ 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.

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

Following are the steps to calculate the number of ions in a compound.

Step 1: Convert the mass of the compound to moles by using the molar mass of that compound as follows:

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

Step 2: Determine the number of moles of ions of an element from the molecular formula of the compound. The formula to calculate the moles of ions is as follows:

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

Step 3: Determine the number of ions by multiplying the moles of ions with the Avogadro’s number. The expression to calculate the number of ions of an element is as follows:

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