Chapter 15, Problem 27CR

Interpretation Introduction

Interpretation:

One equivalent of an acid is to be defined. An equivalent of a base is to be explained. The relation between the equivalent weight of an acid or a base and the substance’s molar mass is to be explained. An example of an acid and a base that have equivalent weights equal to their molar masses is to be stated. An example of an acid and a base that have equivalent weights that are not equal to their molar masses is to be given. The normal solution of an acid or a base is to be defined. The relation between the normality of an acid or a base solution and its molarity is to be explained. An example of a solution that has equal normality and molarity, and an example of a solution that have different normality and molarity is to be stated.

Concept Introduction:

The molarity of a solution is the molar concentration of the solution; it measures the number of moles of solute dissolved in one liter of the solution. The formula for molarity is given as,

$\text{M}=\frac{\text{n}}{\text{V}}$

Where,

• $\text{n}$ represents the number of moles of the solute.
• $\text{V}$ represents the volume of the solution.

The normality of a solution is referred as the gram equivalent weight of a solute dissolved in one liter of the solution. The normality of solution is given as:

$\text{N}=\frac{{\text{n}}_{\text{eq}}}{\text{V}}$

Where,

• ${\text{n}}_{\text{eq}}$ represents the number of equivalents of the solute.
• $\text{V}$ represents the volume of the solution.

Answer to Problem 27CR

One equivalent of an acid is defined as amount of the acid solution that has one mole of ${\text{H}}^{\text{+}}$ ion. An equivalent of a base represents a base solution that has one mole of ${\text{OH}}^{-}$ ions.

The relation between the equivalent weight of an acid or a base and the substance’s molar mass is represented as,

${\text{M}}_{\text{eq}}=\frac{{\text{M}}_{\text{m}}}{\text{n}}$

An acid that has equivalent weights equal to its molar masses is $\text{HCl}$ and a base that has equivalent weights equal to its molar masses is $\text{NaOH}$. An acid that has equivalent weights that are not equal to its molar masses is ${\text{H}}_2{\text{SO}}_4$ and a base that has equivalent weights that are not equal to its molar masses is $\text{Ca}{\left(\text{OH}\right)}_{\text{2}}$. A normal solution of an acid or a base is defined as the solution in which one mole of ${\text{H}}^{\text{+}}$ or ${\text{OH}}^{-}$ ions are dissolved in one liter of the solution.

The relation between the normality of an acid or a base solution and its molarity is given as,

$\text{N}=\text{n}\text{'}\text{M}$

An example of a solution that has equal normality and molarity is $\text{HCl}$, and an example of a solution that has different normality and molarity is ${\text{H}}_2{\text{SO}}_4$.

Explanation of Solution

One equivalent of an acid is defined as amount of the acid solution that has one mole of ${\text{H}}^{\text{+}}$ ion. An equivalent of a base represents a base solution that has one mole of ${\text{OH}}^{-}$ ions.

The relation between the equivalent weight of an acid or a base and the substance’s molar mass is represented as,

${\text{M}}_{\text{eq}}=\frac{{\text{M}}_{\text{m}}}{\text{n}}$    (1)

Where,

• ${\text{M}}_{\text{m}}$ represents the molar mass of the substance.
• $\text{n}$ represents the equivalence factor of the substance.
• ${\text{M}}_{\text{eq}}$ represents the equivalent weight of the substance.

The dissociation reaction of $\text{HCl}$ in water is represented as:

$\text{HCl}\left(\text{a}\text{q}\right)\to {\text{H}}^{+}\left(\text{a}\text{q}\right)+{\text{Cl}}^{-}\left(\text{a}\text{q}\right)$

The number of ${\text{H}}^{+}$ ion released by $\text{HCl}$ is $1$.

Hence the equivalence factor of $\text{HCl}$ is $1\text{eq}\cdot {\text{mol}}^{-1}$.

The molar mass of $\text{HCl}$ is $36.469\text{g}\cdot {\text{mol}}^{-1}$.

Substitute the value of ${\text{M}}_{\text{m}}$ and $\text{n}$ in the equation (1).

$\begin{array}{c}{\text{M}}_{\text{eq}}=\frac{36.469\text{g}\cdot {\text{mol}}^{-1}}{1\text{eq}\cdot {\text{mol}}^{-1}}\\ =36.469\text{g}\cdot {\text{eq}}^{-1}\end{array}$

Therefore, $\text{HCl}$ has equal molar mass and equivalent weight.

The dissociation reaction of $\text{NaOH}$ in water is represented as,

$\text{NaOH}\left(\text{a}\text{q}\right)\to {\text{Na}}^{+}\left(\text{a}\text{q}\right)+{\text{OH}}^{-}\left(\text{a}\text{q}\right)$

The number of ${\text{OH}}^{-}$ ion released by $\text{NaOH}$ is $1$.

Hence the equivalence factor of $\text{NaOH}$ is $1\text{eq}\cdot {\text{mol}}^{-1}$.

The molar mass of $\text{NaOH}$ is $39.9979\text{g}\cdot {\text{mol}}^{-1}$.

Substitute the value of ${\text{M}}_{\text{m}}$ and $\text{n}$ in the equation (1).

$\begin{array}{c}{\text{M}}_{\text{eq}}=\frac{39.9979\text{g}\cdot {\text{mol}}^{-1}}{1\text{eq}\cdot {\text{mol}}^{-1}}\\ =39.9979\text{g}\cdot {\text{eq}}^{-1}\end{array}$

Therefore, $\text{NaOH}$ has equal molar mass and equivalent weight.

The dissociation reaction of ${\text{H}}_2{\text{SO}}_4$ in water is represented as,

${\text{H}}_2{\text{SO}}_4\left(\text{a}\text{q}\right)\to 2{\text{H}}^{+}\left(\text{a}\text{q}\right)+{\text{SO}}_4^{2-}\left(\text{a}\text{q}\right)$

The number of ${\text{H}}^{+}$ ion released by ${\text{H}}_2{\text{SO}}_4$ is $2$.

Hence the equivalence factor of ${\text{H}}_2{\text{SO}}_4$ is $2\text{eq}\cdot {\text{mol}}^{-1}$.

The molar mass of ${\text{H}}_2{\text{SO}}_4$ is $98.079\text{g}\cdot {\text{mol}}^{-1}$.

Substitute the value of ${\text{M}}_{\text{m}}$ and $\text{n}$ in the equation (1).

$\begin{array}{c}{\text{M}}_{\text{eq}}=\frac{98.079\text{g}\cdot {\text{mol}}^{-1}}{2\text{eq}\cdot {\text{mol}}^{-1}}\\ =49.0395\text{g}\cdot {\text{eq}}^{-1}\end{array}$

Therefore, ${\text{H}}_2{\text{SO}}_4$ has different molar mass and equivalent weight.

The dissociation reaction of $\text{Ca}{\left(\text{OH}\right)}_{\text{2}}$ in water is represented as,

$\text{Ca}{\left(\text{OH}\right)}_{\text{2}}\left(\text{a}\text{q}\right)\to 2{\text{OH}}^{-}\left(\text{a}\text{q}\right)+{\text{Ca}}^{2+}\left(\text{a}\text{q}\right)$

The number of ${\text{OH}}^{-}$ ion released by $\text{Ca}{\left(\text{OH}\right)}_{\text{2}}$ is $2$.

Hence the equivalence factor of $\text{Ca}{\left(\text{OH}\right)}_{\text{2}}$ is $2\text{eq}\cdot {\text{mol}}^{-1}$.

The molar mass of $\text{Ca}{\left(\text{OH}\right)}_{\text{2}}$ is $74.093\text{g}\cdot {\text{mol}}^{-1}$.

Substitute the value of ${\text{M}}_{\text{m}}$ and $\text{n}$ in the equation (1).

$\begin{array}{c}{\text{M}}_{\text{eq}}=\frac{74.093\text{g}\cdot {\text{mol}}^{-1}}{2\text{eq}\cdot {\text{mol}}^{-1}}\\ =37.0465\text{g}\cdot {\text{eq}}^{-1}\end{array}$

Therefore, $\text{Ca}{\left(\text{OH}\right)}_{\text{2}}$ has different molar mass and equivalent weight.

The relationship between the molarity and normality of a solution is given as,

$\text{N}=\text{n}\text{'}\text{M}$

Where,

• $\text{N}$ represents the normality of the solution.
• $\text{M}$ represents the molarity of the solution.
• $\text{n}\text{'}$ represents the equivalence factor of the solute.

The equivalence factor of $\text{HCl}$ is one therefore, $\text{HCl}$ has equal normality and molarity.

The equivalence factor of ${\text{H}}_2{\text{SO}}_4$ is not equal to one therefore, ${\text{H}}_2{\text{SO}}_4$ has different normality and molarity.

Conclusion

One equivalent of an acid is defined as the quantity of the acid solution that has one mole of ${\text{H}}^{\text{+}}$ ion. An equivalent of a base represents a base solution that has one mole of ${\text{OH}}^{-}$ ions.

The relation between the equivalent weight of an acid or a base and the substance’s molar mass is represented as,

${\text{M}}_{\text{eq}}=\frac{{\text{M}}_{\text{m}}}{\text{n}}$

Where,

• ${\text{M}}_{\text{m}}$ represents the molar mass of the substance.
• $\text{n}$ represents the equivalence factor of the substance.
• ${\text{M}}_{\text{eq}}$ represents the equivalent weight of the substance.

An example of an acid that has equivalent weights equal to its molar masses is $\text{HCl}$ and an example of a base that has equivalent weights equal to its molar masses is $\text{NaOH}$. An example of an acid that has equivalent weights that are not equal to its molar masses is ${\text{H}}_2{\text{SO}}_4$ and an example of a base that has equivalent weights that are not equal to its molar masses is $\text{Ca}{\left(\text{OH}\right)}_{\text{2}}$. A normal solution of an acid or a base is defined as the solution in which one mole of ${\text{H}}^{\text{+}}$ or ${\text{OH}}^{-}$ ions are dissolved in one liter of the solution.

The relation between the normality of an acid or a base solution and its molarity is given as,

$\text{N}=\text{n}\text{'}\text{M}$

Where,

• $\text{N}$ represents the normality of the solution.
• $\text{M}$ represents the molarity of the solution.
• $\text{n}\text{'}$ represents the equivalence factor of the solute.

The $\text{HCl}$ solution has equal normality and molarity, and the ${\text{H}}_2{\text{SO}}_4$ solution has different normality and molarity.