Chapter 9, Problem 9.75P

Calculate the value of ${\text{[OH}}^{\text{-}}\text{]}$ from the given and label the solution as acidic or basic.
a. ${\text{10}}^{\text{-8}}\text{ M}$
b. ${\text{10}}^{\text{-10}}\text{ M}$
c. $\text{3}{\text{.0 × 10}}^{\text{-4}}\text{ M}$
d. $\text{2}{\text{.5 × 10}}^{\text{-11}}\text{ M}$

Interpretation Introduction

(a)

Interpretation:

The value of ${\text{[OH}}^{\text{-}}]$ for the given solution which has ${\text{10}}^{\text{-8}}$ M of ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions needs to be determined. The solution needs to be labeled as acidic or basic.

Concept Introduction:

A base is defined as the substance that can give ${\text{[OH}}^{-}\text{]}$ in its solution where as an acid can give ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ in its solution. General equation for acid and base can be written as:

  ${\text{HA}}_{\text{(l)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ A}}^{\text{-}}{}_{\text{(aq)}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}$

  ${\text{BOH}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ OH}}^{\text{-}}{}_{\text{(aq)}}{\text{ + B}}^{\text{+}}{}_{\text{(aq)}}$

The ionic product of water can be used to calculate the concentration of ${\text{[OH}}^{-}\text{]}$ and ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions in the given solution.

  ${\text{ K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$

Experimentally proved that at $\text{25}°\text{C}$ , the concentration of ${\text{OH}}^{\text{-}}$ and ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is same and that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-7}}$ . Thus, the value of ${\text{K}}_{\text{w}}$ stands for ion product constant for water that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-14}}\text{ at 25}°\text{C}$ . If the concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions is more than ${\text{OH}}^{\text{-}}$ ions it is said to be acidic whereas the solution with more ${\text{OH}}^{\text{-}}$ ions than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Answer to Problem 9.75P

  ${\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =2}{\text{.0 × 10}}^{\text{-8}}\text{ M}$

Since, the concentration of ${\text{OH}}^{\text{-}}$ ions is more than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Explanation of Solution

Given Information:

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ = ${\text{10}}^{\text{-8}}$ M

Calculation:

Calculate ${\text{[OH}}^{\text{-}}]$ with the help of ${\text{K}}_{\text{w}}$ expression:

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ \text{ 1}{\text{.0 × 10}}^{\text{-14}}{\text{= [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{] [10}}^{\text{-8}}\text{] }\\ {\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =}\frac{\text{1}{\text{.0 × 10}}^{\text{-14}}}{{\text{10}}^{\text{-8}}}\\ {\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =1}{\text{.0 × 10}}^{\text{-6}}\text{ M}\end{array}$

Since the concentration of ${\text{OH}}^{\text{-}}$ ions is more than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Interpretation Introduction

(b)

Interpretation:

The value of ${\text{[OH}}^{\text{-}}]$ for the given solution which has $1{\text{0}}^{\text{-10}}$ M of ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions needs to be determined. The solution needs to be labeled as acidic or basic.

Concept Introduction:

A base is defined as the substance that can give ${\text{[OH}}^{-}\text{]}$ in its solution where as an acid can give ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ in its solution. General equation for acid and base can be written as:

  ${\text{HA}}_{\text{(l)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ A}}^{\text{-}}{}_{\text{(aq)}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}$

  ${\text{BOH}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ OH}}^{\text{-}}{}_{\text{(aq)}}{\text{ + B}}^{\text{+}}{}_{\text{(aq)}}$

The ionic product of water can be used to calculate the concentration of ${\text{[OH}}^{-}\text{]}$ and ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions in the given solution.

  ${\text{ K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$

Experimentally proved that at $\text{25}°\text{C}$ , the concentration of ${\text{OH}}^{\text{-}}$ and ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is same and that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-7}}$ . Thus, the value of ${\text{K}}_{\text{w}}$ stands for ion product constant for water that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-14}}\text{ at 25}°\text{C}$ . If the concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions is more than ${\text{OH}}^{\text{-}}$ ions it is said to be acidic whereas the solution with more ${\text{OH}}^{\text{-}}$ ions than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Answer to Problem 9.75P

  ${\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =1}{\text{.0 × 10}}^{\text{-4}}\text{ M}$

Since the concentration of ${\text{OH}}^{\text{-}}$ ions is more than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Explanation of Solution

Given Information:

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ = $1{\text{0}}^{\text{-10}}$ M

Calculation:

Calculate ${\text{[OH}}^{\text{-}}]$ with the help of ${\text{K}}_{\text{w}}$ expression:

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ \text{ 1}{\text{.0 × 10}}^{\text{-14}}{\text{= [OH}}^{\text{-}}{}_{\text{(aq)}}\text{] [}1{\text{0}}^{\text{-10}}\text{M] }\\ {\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =}\frac{\text{1}{\text{.0 × 10}}^{\text{-14}}}{{\text{10}}^{\text{-10}}}\\ {\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =1}{\text{.0 × 10}}^{\text{-4}}\text{ M}\end{array}$

Since the concentration of ${\text{OH}}^{\text{-}}$ ions is more than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Interpretation Introduction

(c)

Interpretation:

The value of ${\text{[OH}}^{\text{-}}]$ for the given solution which has $3.0\times 1{\text{0}}^{\text{-4}}$ M of ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions needs to be determined. The solution needs to be labeled as acidic or basic.

Concept Introduction:

A base is defined as the substance that can give ${\text{[OH}}^{-}\text{]}$ in its solution where as an acid can give ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ in its solution. General equation for acid and base can be written as:

  ${\text{HA}}_{\text{(l)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ A}}^{\text{-}}{}_{\text{(aq)}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}$

  ${\text{BOH}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ OH}}^{\text{-}}{}_{\text{(aq)}}{\text{ + B}}^{\text{+}}{}_{\text{(aq)}}$

The ionic product of water can be used to calculate the concentration of ${\text{[OH}}^{-}\text{]}$ and ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions in the given solution.

  ${\text{ K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$

Experimentally proved that at $\text{25}°\text{C}$ , the concentration of ${\text{OH}}^{\text{-}}$ and ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is same and that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-7}}$ . Thus, the value of ${\text{K}}_{\text{w}}$ stands for ion product constant for water that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-14}}\text{ at 25}°\text{C}$ . If the concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions is more than ${\text{OH}}^{\text{-}}$ ions it is said to be acidic whereas the solution with more ${\text{OH}}^{\text{-}}$ ions than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Answer to Problem 9.75P

  ${\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =3}{\text{.3 × 10}}^{\text{-11}}\text{ M}$

Since, the concentration of ${\text{OH}}^{\text{-}}$ ions is lesser than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be acidic solution.

Explanation of Solution

Given Information:

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ = $3.0\times 1{\text{0}}^{\text{-4}}$ M

Calculation:

Calculate ${\text{[OH}}^{\text{-}}]$ with the help of ${\text{K}}_{\text{w}}$ expression:

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ \text{ 1}{\text{.0 × 10}}^{\text{-14}}{\text{= [OH}}^{\text{-}}{}_{\text{(aq)}}\text{] [}3.0\times 1{\text{0}}^{\text{-4}}\text{M] }\\ {\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =}\frac{\text{1}{\text{.0 × 10}}^{\text{-14}}}{3.0\times 1{\text{0}}^{\text{-4}}}\\ {\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =3}{\text{.3 × 10}}^{\text{-11}}\text{ M}\end{array}$

Since the concentration of ${\text{OH}}^{\text{-}}$ ions is lesser than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be acidic solution.

Interpretation Introduction

(d)

Interpretation:

The value of ${\text{[OH}}^{\text{-}}]$ for the given solution which has $2.5\times 1{\text{0}}^{\text{-11}}$ M of ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions needs to be determined. The solution needs to be labeled as acidic or basic.

Concept Introduction:

A base is defined as the substance that can give ${\text{[OH}}^{-}\text{]}$ in its solution where as an acid can give ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ in its solution. General equation for acid and base can be written as:

  ${\text{HA}}_{\text{(l)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ A}}^{\text{-}}{}_{\text{(aq)}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}$

  ${\text{BOH}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ OH}}^{\text{-}}{}_{\text{(aq)}}{\text{ + B}}^{\text{+}}{}_{\text{(aq)}}$

The ionic product of water can be used to calculate the concentration of ${\text{[OH}}^{-}\text{]}$ and ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions in the given solution.

  ${\text{ K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$

Experimentally proved that at $\text{25}°\text{C}$ , the concentration of ${\text{OH}}^{\text{-}}$ and ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is same and that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-7}}$ . Thus, the value of ${\text{K}}_{\text{w}}$ stands for ion product constant for water that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-14}}\text{ at 25}°\text{C}$ . If the concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions is more than ${\text{OH}}^{\text{-}}$ ions it is said to be acidic whereas the solution with more ${\text{OH}}^{\text{-}}$ ions than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Answer to Problem 9.75P

  ${\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =4}{\text{.0 × 10}}^{\text{-4}}\text{ M}$

Since, the concentration of ${\text{OH}}^{\text{-}}$ ions is more than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.

Explanation of Solution

Given Information:

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ = $2.5\times 1{\text{0}}^{\text{-11}}$ M

Calculation:

Calculate ${\text{[OH}}^{\text{-}}]$ with the help of ${\text{K}}_{\text{w}}$ expression:

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ \text{ 1}{\text{.0 × 10}}^{\text{-14}}{\text{= [OH}}^{\text{-}}{}_{\text{(aq)}}\text{] [}2.5\times 1{\text{0}}^{\text{-11}}\text{M] }\\ {\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =}\frac{\text{1}{\text{.0 × 10}}^{\text{-14}}}{2.5\times 1{\text{0}}^{\text{-11}}}\\ {\text{[OH}}^{\text{-}}{}_{\text{(aq)}}\text{] =4}{\text{.0 × 10}}^{\text{-4}}\text{ M}\end{array}$

Since the concentration of ${\text{OH}}^{\text{-}}$ ions is more than ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions it is said to be basic solution.