Chapter 9, Problem 9.77P

Calculate the value of ${\text{[OH}}^{\text{-}}\text{]}$ from the given ${\text{[HO}}^{\text{-}}\text{]}$ and label the solution as acidic or basic.
a. ${\text{10}}^{-2}\text{ M}$
b. $\text{4}{\text{.0 × 10}}^{\text{-8}}\text{ M}$
c. $\text{6}{\text{.2 × 10}}^{\text{-7}}\text{ M}$
d. $\text{8}{\text{.5 × 10}}^{\text{-13}}\text{ M}$

Interpretation Introduction

(a)

Interpretation:

The value of ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ for the given solution with ${\text{10}}^{\text{-2}}$ M of ${\text{[OH}}^{\text{-}}]$ ions needs to be determined. The given 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 whereas 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 9.77P

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] =1}{\text{.0 × 10}}^{\text{-12}}\text{ M}$

Since the concentration of ${\text{[OH}}^{\text{-}}]$ is more than ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ , therefore, the solution must be basic.

Explanation of Solution

Given Information:

  ${\text{[OH}}^{\text{-}}]$ ions = ${\text{10}}^{\text{-2}}$ M

Calculation:

Calculate ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ with the help of ${\text{K}}_{\text{w}}$ expression:

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ \text{ 1}{\text{.0 × 10}}^{\text{-14}}{\text{= [10}}^{\text{-2}}{\text{M] [H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ {\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] =}\frac{\text{1}{\text{.0 × 10}}^{\text{-14}}}{{\text{10}}^{\text{-2}}}\\ {\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] =1}{\text{.0 × 10}}^{\text{-12}}\text{ M}\end{array}$

Since the concentration of ${\text{[OH}}^{\text{-}}]$ is more than ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ , therefore, the solution must be basic.

Interpretation Introduction

(b)

Interpretation:

The value of ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ for the given solution with $\text{4}\text{.0 }\times {\text{ 10}}^{\text{-8}}$ M of ${\text{[OH}}^{\text{-}}]$ 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 whereas 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 9.77P

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] =2}{\text{.5 × 10}}^{\text{-7}}\text{ M}$

Since the concentration of is ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ more than ${\text{[OH}}^{\text{-}}]$ , therefore, the solution must be acidic.

Explanation of Solution

Given Information:

  ${\text{[OH}}^{\text{-}}]$ ions = $\text{4}\text{.0 }\times {\text{ 10}}^{\text{-8}}$ M

Calculation:

Calculate ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ with the help of ${\text{K}}_{\text{w}}$ expression:

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ \text{ 1}{\text{.0 × 10}}^{\text{-14}}\text{= [4}\text{.0 }\times {\text{ 10}}^{\text{-8}}{\text{M] [H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ {\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] =}\frac{\text{1}{\text{.0 × 10}}^{\text{-14}}}{\text{4}\text{.0 }\times {\text{ 10}}^{\text{-8}}}\\ {\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] =2}{\text{.5 × 10}}^{\text{-7}}\text{ M}\end{array}$

Since the concentration of is ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ more than ${\text{[OH}}^{\text{-}}]$ , therefore, the solution must be acidic.

Interpretation Introduction

(c)

Interpretation:

The value of ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ for the given solution with $\text{6}\text{.2 }\times {\text{ 10}}^{\text{-7}}$ M of ${\text{[OH}}^{\text{-}}]$ ions needs to be determined. The solution should be labeled as acidic or basic.

Concept Introduction:

A base is defined as the substance that can give ${\text{[OH}}^{-}\text{]}$ in its solution whereas 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 9.77P

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] = 1}{\text{.6 × 10}}^{\text{-8}}\text{ M}$

Since the concentration of is ${\text{[OH}}^{\text{-}}]$ more than ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ , therefore, the solution must be basic.

Explanation of Solution

Given Information:

  ${\text{[OH}}^{\text{-}}]$ ions = $\text{6}\text{.2 }\times {\text{ 10}}^{\text{-7}}$ M

Calculation:

Calculate ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{]}$ with the help of ${\text{K}}_{\text{w}}$ expression:

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ \text{ 1}{\text{.0 × 10}}^{\text{-14}}\text{= [6}\text{.2 }\times {\text{ 10}}^{\text{-7}}{\text{M] [H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ {\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] =}\frac{\text{1}{\text{.0 × 10}}^{\text{-14}}}{\text{6}\text{.2 }\times {\text{ 10}}^{\text{-7}}}\\ {\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] = 1}{\text{.6 × 10}}^{\text{-8}}\text{ M}\end{array}$

Since the concentration of is ${\text{[OH}}^{\text{-}}]$ more than ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ , therefore, the solution must be basic.

Interpretation Introduction

(d)

Interpretation:

The value of ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ for the given solution with $\text{8}\text{.5 }\times {\text{ 10}}^{\text{-13}}$ M of ${\text{[OH}}^{\text{-}}]$ ions needs to be determined. The solution should be labeled as acidic or basic.

Concept Introduction:

A base is defined as the substance that can give ${\text{[OH}}^{-}\text{]}$ in its solution whereas 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 9.77P

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] = 1}{\text{.2 × 10}}^{\text{-2}}\text{ M}$

Since the concentration of is ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ more than ${\text{[OH}}^{\text{-}}]$ , therefore, the solution must be acidic.

Explanation of Solution

Given Information:

  ${\text{[OH}}^{\text{-}}]$ ions = $\text{8}\text{.5 }\times {\text{ 10}}^{\text{-13}}$ M

Calculation:

Calculate ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{]}$ with the help of ${\text{K}}_{\text{w}}$ expression:

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ \text{ 1}{\text{.0 × 10}}^{\text{-14}}\text{= [8}\text{.5 }\times {\text{ 10}}^{\text{-13}}{\text{M] [H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }\\ {\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] =}\frac{\text{1}{\text{.0 × 10}}^{\text{-14}}}{\text{8}\text{.5 }\times {\text{ 10}}^{\text{-13}}}\\ {\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] = 1}{\text{.2 × 10}}^{\text{-2}}\text{ M}\end{array}$

Since the concentration of is ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$ more than ${\text{[OH}}^{\text{-}}]$ , therefore, the solution must be acidic.