Q. 10.39 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate the pH of each solution given the follow in:

a. $\left|{\mathrm{H}}_2{\mathrm{O}}^{+}\right|=1\times {10}^4\mathrm{M}$

b. $\left|\mathrm{H},{\mathrm{O}}^{+}\right|=3\times {10}^{-9}\mathrm{M}$

c.$\left[\mathrm{OH}\right]=1\times {10}^{-9}\mathrm{M}$

d. $\lfloor \mathrm{OH}\rfloor =2.5\times {10}^{-11}\mathrm{M}$

e.$\left|\mathrm{H},{\mathrm{O}}^{\text{'}}\right|=6.7\times {10}^{-1}\mathrm{M}$

f. $\left[{\mathrm{OH}}^{-}\right]=8.2\times {10}^{-4}\mathrm{M}$

Step-by-Step Solution

Answer

a) The pH value of the component$\left|{\mathrm{H}}_2{\mathrm{O}}^{+}\right|=1\times {10}^4\mathrm{M}$ is determined as $4$

b) The pH value of the component$\left|\mathrm{H},{\mathrm{O}}^{+}\right|=3\times {10}^{-9}\mathrm{M}$ is determined as $8.5$

c) The pH value of the component $\left[\mathrm{OH}\right]=1\times {10}^{-9}\mathrm{M}$ is determined as $9.0$

d) The pH value of the component $\lfloor \mathrm{OH}\rfloor =2.5\times {10}^{-11}\mathrm{M}$ is determined as$3.40$

e) The pH value of the component$\left|\mathrm{H},{\mathrm{O}}^{\text{'}}\right|=6.7\times {10}^{-1}\mathrm{M}$ is determined as $7.17$

f) The pH value of the component$\left[{\mathrm{OH}}^{-}\right]=8.2\times {10}^{-4}\mathrm{M}$ is determined as $10.92$

Step 1 : Introduction (part a)

The objective is to find the pH values of each solution

Step 2 : Explanation (part a)

By definition, $pH=-\log \left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$

$pOH=-\log \left[O{H}^{-}\right]$

Relation between $P^H$ and $P^{\mathrm{OH}}$

$pH+pOH=14.0\text{ at }25°\mathrm{C}$

(a)

$pH=-\log \left(1\times {10}^{-4}\right)$

$=4$

Step 3 : Introduction (part b)

The objective is to find the pH values of each solution

Step 4 : Explanation (part b)

(b)

$pH=-\log \left(3\times {10}^{-9}\right)$

$=8.52$

$\approx 8.5$

Step 5 : Introduction (part c)

The objective is to find the pH values of each solution

Step 6 : Explanation (part c)

(c) $pOH=-\log \left(1\times {10}^{-5}\right)$

$$\begin{gathered} =5.0 \\ pH=14-pOH \\ =14-5.0 \\ =9.0 \end{gathered}$$

Step 7 : Introduction (part d)

The objective is to find the pH values of each solution

Step 8 : Explanation (part d)

(d) $pOH=-\log \left(2.5\times {10}^{-11}\right)$

$$\begin{gathered} =10.60 \\ pH=14.0-pOH \\ =14.00-10.60 \\ =3.40 \end{gathered}$$

Step 9 : Introduction (part e)

The objective is to find the pH values of each solution

Step 10 : Explanation (part e)

(e)

$pH=-\log \left(6.7\times {10}^{-8}\right)$

$=7.17$

Step 11 : Introduction (part f)

The objective is to find the pH values of each solution

Step 12 : Explanation (part f)

(f) 

$$\begin{gathered} pOH=-\log (8.2 \times {10}^{-4}) \\ = 3.08 \\ pH=14.0-pOH \\ =14.0-3.08 \\ = 10.92 \end{gathered}$$