Q.10.94 - An Introduction to General, Organic, and Biological Chemistry

Question

Solution X has a pH of 9.0, and solution Y has a pH of 7.0.

a. Which solution is more acidic?

b. What is the $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$ in each?

c. What is the $O{H}^{-}$ in each?

Step-by-Step Solution

Answer

a. none

b. $X=\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]=1\times {10}^{-9}$ and $Y=\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]=1\times {10}^{-7}$

c. $X=\left[O{H}^{-}\right]=1\times {10}^{-5}$ and  $Y=\left[{\mathrm{OH}}^{-}\right]=1\times {10}^{-7}$

Step 1: Given Information (Part a)

As a solution gets more acidic, the pH diminishes. As a solution gets more basic, the pH increases. As the pH of a solution diminishes by one pH unit, the concentration of H+ increases by ten times

Step 2: Explanation Part (a)

As the pH of the solution X is $9$ and the pH of the solution Y is $7$, we conclude that none of them is acidic in nature as they have a pH level greater than or equal to $7$.

For a solution to be acidic the pH should be less than $7$.

Step 3: Explanation Part (b)

We know,

$\mathrm{pH}=-\log \left({\mathrm{H}}_3{\mathrm{O}}^{+}\right)$

Hence,

For Solution X, $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]={10}^{-9}=1\times {10}^{-9}\mathrm{M}$

For solution Y, $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]={10}^{-7}=1\times {10}^{-7}\mathrm{M}$

Step 4: Explanation Part (c)

Using,

$\left[{\mathrm{OH}}^{-}\right]=\frac{{\displaystyle 1\times {10}^{-14}}}{\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]}$

We get,

For solution X, $\left[{\mathrm{OH}}^{-}\right]=\frac{1\times {10}^{-14}}{1\times {10}^{-9}}=1\times {10}^{-5}\mathrm{M}$

For solution Y,$\left[{\mathrm{OH}}^{-}\right]=\frac{1\times {10}^{-14}}{1\times {10}^{-7}}=1\times {10}^{-7}\mathrm{M}$