Chapter 3, Problem 82RE

Solution

a.

To find: The hydrogen-ion concentrations of sea water and magnesia

The hydrogen-ion concentration of the seawater is $2.51\times {10}^{-8}$ mol/L.

The hydrogen-ion concentration of the milk of magnesia is $3.16\times {10}^{-11}$ mol/L.

Given information:

The pH of seawater is 7.6 and the pH of milk of magnesia is 10.5.

Concept used:

  $\text{pH }=-\text{ log }[{\text{H}}^{+}]$ , where $[{\text{H}}^{+}]$ is the hydrogen-ion concentration in mol/L. $\dots \left(i\right)$

Calculation:

Substitute $\text{pH}=7.6$ and solve for $[{\text{H}}^{+}]$ .

  $\begin{array}{c}\text{7}\text{.6 }=-\text{ log }[{\text{H}}^{+}]\\ [{\text{H}}^{+}]={10}^{-7.6}\text{ [}y=\log x\Rightarrow {10}^y=x\text{]}\\ =2.51\times {10}^{-8}\end{array}$

The hydrogen-ion concentration of the seawater is $2.51\times {10}^{-8}$ mol/L.

Now Substitute $\text{pH}=10.5$ in (i) and solve for $[{\text{H}}^{+}]$ .

  $\begin{array}{c}\text{10}\text{.5 }=-\text{ log }[{\text{H}}^{+}]\\ [{\text{H}}^{+}]={10}^{-10.5}\text{ [}y=\log x\Rightarrow {10}^y=x\text{]}\\ =3.16\times {10}^{-11}\end{array}$

The hydrogen-ion concentration of the milk of magnesia is $3.16\times {10}^{-11}$ mol/L.

b.

To find: The number of times the hydrogen concentration of the seawater is greater than that of milk of magnesia.

The hydrogen-ion concentration of the seawater is 794.33 times greater than that of milk of magnesia.

Given information:

The pH of seawater is 7.6 and the pH of milk of magnesia is 10.5.

Explanation:

Divide the hydrogen-ion concentration of the seawater by that of milk of magnesia.

  $\begin{array}{c}\frac{2.51\times {10}^{-8}}{3.16\times {10}^{-11}}=\frac{2.51}{3.16}\times {10}^{-8+11}\\ =0.79433\times {10}^3\\ =794.33\end{array}$

Hence, the hydrogen-ion concentration of the seawater is 794.33 times greater than that of milk of magnesia.

c.

To find: The time when the school will close.

The concentrations differ by approximately 3 orders of magnitude.

Given information:

The pH of seawater is 7.6 and the pH of milk of magnesia is 10.5.

Explanation:

The hydrogen-ion concentration of the seawater is 794.33 times greater than that of milk of magnesia.

  $794.33=\mathrm{0.794.33}\times {10}^3$

Thus, the concentrations differ by approximately 3 orders of magnitude.