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Question: What is the pH of \({10^{ - 8}}\) M HCl?...

What is the pH of 10−8{10^{ - 8}} M HCl?

Explanation

Solution

To answer this question, we first need to understand what pH is. The pH of aqueous or other liquid solutions is a quantitative measure of their acidity or basicity. The term, which is frequently used in chemistry, biology, and agronomy, converts hydrogen ion concentrations—which typically vary from around 1to10−141 to {10^{ - 14}} gram-equivalents per liter—into numbers between 0 and 14.

Complete answer:
As we know that HCl is a strong acid, so its pH will be less than 7.
The concentration of HCl = 10−8{10^{ - 8}}M
Total [H+][{H^ + }] =[H+] = [{H^ + }] obtained from HCL +[H+] + [{H^ + }] obtained from H2O[H+]{H_2}O[{H^ + }]
HCl being a strong acid, it completely ionizes.
[H+]HCl=1.0×10−8[{H^ + }]HCl = 1.0 \times {10^{ - 8}}.
The concentration of H+{H^ + } from ionization is equal to that of OH−O{H^ - } from water, so let us consider it to be XX.
[H+]H2O=[OH−]H2O=X[{H^ + }]{H_2}O = [O{H^ - }]{H_2}O = X.
Total [H+]=X+1.0×10−8[{H^ + }] = X + 1.0 \times {10^{ - 8}}------(1)
But we know
[H+][OH−]=1.0×10−14[{H^ + }][O{H^ - }] = 1.0 \times {10^{ - 14}}
(1.0×10−8 X+ X) (X) = 1.0  ×10−14(1.0 \times {10^{ - 8}}{\text{ X}} + {\text{ X}}){\text{ }}\left( X \right){\text{ }} = {\text{ }}1.0\; \times {10^{ - 14}}
X2+10−8X−10−14=0{X^2} + {10^{ - 8}}X - {10^{ - 14}} = 0
Solving XX, we get
X = 9.5×10−8  {\text{X }} = {\text{ }}9.5 \times {10^{ - 8}}\;
Substituting XX value in equation (1)
Total [H+]=9.5×10−8+1.0×10−8[{H^ + }] = 9.5 \times {10^{ - 8}} + 1.0 \times {10^{ - 8}}
Total [H+]=1.05×10−7[{H^ + }] = 1.05 \times {10^{ - 7}}.
Consider an equation
⇒pH = − log [H+]\Rightarrow pH{\text{ }} = {\text{ }}-{\text{ }}log{\text{ }}[{H^ + }]
⇒pH = − log [1.05×10−7]\Rightarrow pH{\text{ }} = {\text{ }}-{\text{ }}log{\text{ }}[1.05 \times {10^{ - 7}}]
pH = 6.98pH{\text{ }} ={\text{ }}6.98
So, the final pH value is 6.986.98.

Note:
Hydrochloric acid, commonly known as muriatic acid, is a hydrogen chloride aqueous solution. It's a colorless liquid with a strong, pungent odor. It's considered a strong acid. In the digestive processes of most animal species, including humans, it is a component of stomach acid.