Chapter 4, Problem 28QP

Calculate the molar mass of each of the following compounds.

$\begin{array}{l}\left(\text{a}\right){\text{K}}_{\text{2}}{\text{SO}}_{\text{4}}\\ \left(\text{b}\right){\text{NiCl}}_{\text{2}}\cdot {\text{6H}}_{\text{2}}\text{O}\\ \left(\text{c}\right){\text{C}}_{\text{2}}{\text{H}}_{\text{4}}{\text{Cl}}_{\text{2}}\\ \left(\text{d}\right)\text{Mg}{\left({\text{NO}}_{\text{3}}\right)}_{\text{2}}\end{array}$

Interpretation Introduction

Interpretation:

The molar mass of the compound given is to be calculated.

Explanation of Solution

The given compound is ${\text{K}}_2{\text{SO}}_4$ . Molar mass can be determined by adding the masses of the component’s elements which are present in a chemical formula. Molar mass of ${\text{K}}_2{\text{SO}}_4$ is calculated as follows:

The mass of potassium from the periodic table is $39.01\text{ g/mole}$ . For $2\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{K}}=2\text{ mole}\times \text{39}\text{.10 g/mole}\\ =\text{78}\text{.20 g}\end{array}$

The mass of sulfur from the periodic table is $32.06\text{ g/mole}$ . For $1\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{S}}=1\text{ mole}\times \text{32}\text{.06 g/mole}\\ =\text{32}\text{.06 g}\end{array}$

The mass of oxygen from the periodic table is $16.00\text{ g/mole}$ . For $4\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{O}}=4\text{ mole}\times \text{16}\text{.00 g/mole}\\ =\text{64}\text{.00 g}\end{array}$

Therefore, the mass for $1\text{ mole}$ of ${\text{K}}_2{\text{SO}}_4$ is:

$\begin{array}{c}mas{s}_{{\text{K}}_2{\text{SO}}_4}=78.20\text{ g}+32.06\text{ g}+64.00\text{ g}\\ =174.26\text{ g}\end{array}$

Hence, the molar mass of ${\text{K}}_2{\text{SO}}_4$ is $\text{174}\text{.26 g/mole}$ .

Interpretation Introduction

Interpretation:

The molar mass of the substance is to be calculated.

Explanation of Solution

The given compound is ${\text{NiCl}}_2.6{\text{H}}_2\text{O}$ . Molar mass can be determined by adding the masses of the component’s elements which are present in a chemical formula. Molar mass of ${\text{NiCl}}_2.6{\text{H}}_2\text{O}$ is calculated as follows:

The mass of nickel from the periodic table is $58.69\text{ g/mole}$ . For $1\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{Ni}}=1\text{ mole}\times \text{58}\text{.69 g/mole}\\ =\text{58}\text{.69 g}\end{array}$

The mass of chlorine from the periodic table is $35.45\text{ g/mole}$ . For $2\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{Cl}}=2\text{ mole}\times \text{35}\text{.45 g/mole}\\ =\text{70}\text{.90 g}\end{array}$

The mass of $1{\text{ mole H}}_2\text{O}$ is $18.016\text{ g/mole}$ . For $6\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{{\text{H}}_2\text{O}}=6\text{ mole}\times \text{18}\text{.016 g/mole}\\ =\text{108}\text{.096 g}\end{array}$

Therefore, the mass for $1\text{ mole}$ of ${\text{NiCl}}_2.6{\text{H}}_2\text{O}$ is:

$\begin{array}{c}mas{s}_{{\text{NiCl}}_2.6{\text{H}}_2\text{O}}=58.69\text{ g}+72.90\text{ g}+108.096\text{ g}\\ =237.69\text{ g}\end{array}$

Hence, the molar mass of ${\text{NiCl}}_2.6{\text{H}}_2\text{O}$ is $237.69\text{ g/mol}$ .

Interpretation Introduction

Interpretation:

The molar mass of the substance is to be calculated.

Explanation of Solution

The given compound is ${\text{C}}_2{\text{H}}_4{\text{Cl}}_2$ . Molar mass can be determined by adding the masses of the component’s elements which are present in a chemical formula. Molar mass of ${\text{C}}_2{\text{H}}_4{\text{Cl}}_2$ is calculated as follows:

The mass of carbon from the periodic table is $12.01\text{ g/mole}$ . For $2\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{C}}=2\text{ mole}\times \text{12}\text{.01 g/mole}\\ =\text{24}\text{.02 g}\end{array}$

The mass of hydrogen from the periodic table is $1.008\text{ g/mole}$ . For $4\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{H}}=4\text{ mole}\times \text{1}\text{.008 g/mole}\\ =\text{4}\text{.032 g}\end{array}$

The mass of Chlorine from the periodic table is $35.45\text{ g/mole}$ . For $2\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{Cl}}=2\text{ mole}\times \text{35}\text{.45 g/mole}\\ =\text{70}\text{.90 g}\end{array}$

Therefore, the mass for $1\text{ mole}$ of ${\text{C}}_2{\text{H}}_4{\text{Cl}}_2$ is:

$\begin{array}{c}mas{s}_{{\text{C}}_2{\text{H}}_4{\text{Cl}}_2}=24.02\text{ g}+4.032\text{ g}+70.90\text{ g}\\ =98.95\text{ g}\end{array}$

Hence, the molar mass of ${\text{C}}_2{\text{H}}_4{\text{Cl}}_2$ is $\text{98}\text{.95 g/mole}$ .

Interpretation Introduction

Interpretation:

The molar mass of the substance is to be determined.

Explanation of Solution

The given compound is $\text{Mg}{\left({\text{NO}}_3\right)}_2$ . Molar mass can be determined by adding the masses of the component’s elements which are present in a chemical formula. Molar mass of $\text{Mg}{\left({\text{NO}}_3\right)}_2$ is calculated as follows:

The mass of magnesium from the periodic table is $24.31\text{ g/mole}$ . For $1\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{Mg}}=1\text{ mole}\times \text{24}\text{.31 g/mole}\\ =\text{24}\text{.31 g}\end{array}$

The mass of nitrogen from the periodic table is $14.01\text{ g/mole}$ . For $2\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{N}}=2\text{ mole}\times \text{14}\text{.01 g/mole}\\ =\text{28}\text{.02 g}\end{array}$

The mass of oxygen from the periodic table is $16.00\text{ g/mole}$ . For $6\text{ mole}$ , the mass is:

$\begin{array}{c}mas{s}_{\text{O}}=6\text{ mole}\times \text{16}\text{.00 g/mole}\\ =\text{96}\text{.00 g}\end{array}$

Therefore, the mass for $1\text{ mole}$ of $\text{Mg}{\left({\text{NO}}_3\right)}_2$ is:

$\begin{array}{c}mas{s}_{\text{Mg}{\left({\text{NO}}_3\right)}_2}=24.31\text{ g}+28.02\text{ g}+96.00\text{ g}\\ =148.33\text{ g}\end{array}$

Hence, the molar mass of $\text{Mg}{\left({\text{NO}}_3\right)}_2$ is $148.33\text{ g/mol}$ .