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The term pH is an abbreviation for 鈥減ower of hydrogen,鈥� where p stands for the German word for 鈥減ower鈥� and H is the element symbol for hydrogen. The logarithm inverse of H⁺ concentration is pH. The pH value of a system is a type of scale that shows acidity or basicity. When a pH value is high, it is referred to as a basic system. When a system鈥檚 pH value is low, it is considered acidic. In order to indicate that there is no acidity or basicity present, the pH value of 7 is considered a neutral pH.

For example, to calculate the pH of an aqueous solution, you need to know the concentration of hydronium ion in moles per liter. So, the pH can be calculated as:

$pH=鈭�\log \left[H_3{O}^{+}\right]$-----------equation (1)

The exact strength of a given acid HA in water solution is described using the acidity constant () for the acid-dissociation equilibrium.

Example:

$\begin{array}{l}{\text{HA+H}}_2\text{O}鈬�{\text{A}}^{鈭�}{\text{+H}}_{\text{3}}{\text{O}}^{鈭�}\\ K_a\underset{}{}\text{=}\underset{}{}\frac{{\text{[H}}_{\text{3}}{\text{O}}^{+}{\text{][A}}^{鈭�}\text{]}}{\left[HA\right]}\end{array}$

Acid strengths are normally using values rather than values, where the is the negative common logarithm of:

$\text{p}K\text{a=-log}{K}_a$------------equation (2)

The $\text{p}K\text{a}$value of formic acid (HCOOH) is 3.75

So, we can calculate the acid dissociation constant from equation (2)

$\begin{array}{l}p{K}_a=鈭�\log K_a\\ 鈭�p{K}_a=\log K_a\\ \text{鈥夆赌夆赌夆赌夆赌�}{K}_a={10}^{鈭�3.75}\\ Hence\\ \text{鈥夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆��}=1.8脳{10}^{鈭�4}\end{array}$

The acid dissociation constant of formic acid is $1.8脳{10}^{鈭�4}$.

-$\begin{array}{l}Formic\text{鈥�}acid\left(HCOOH\right)\underset{}{}+\underset{}{}{H}_{2}O\underset{}{}\stackrel{K_a}{鈬�}\underset{}{}Formalat{e}^{-}\left(HCO{O}^{鈭�}\right)\underset{}{}+\underset{}{}{H}_3{O}^{+}\\ \text{鈥夆赌夆赌夆赌夆赌�}\left[0.050\text{鈥�}M\right]\text{鈥夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌�}\left[x\right]\text{鈥夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌�}\left[x\right]\end{array}$--------equation (3)

The concentration of formic acid (HCOOH) is 0.050 M.

Let x represent the concentration of H⁺ that dissociates from HCOOH (formic acid), then [HCOOH] = 0.050 鈥� x.

$K_a\underset{}{}\text{=}\underset{}{}\frac{{\text{[H}}_{\text{3}}{\text{O}}^{+}{\text{][HCOO}}^{鈭�}\text{]}}{\left[HCOOH\right]}$

$K_a=1.8脳{10}^{鈭�4}=\frac{x^2}{0.050鈭�x}$

Let 0.050-x = 0.050

$\begin{array}{l}{x}^2=1.8脳{10}^{-4}脳0.050\\ x^2=9脳{10}^{-6}\\ x=3脳{10}^{-3}\end{array}$

From equation (2), we have

$pH=-log\left[H_3{O}^{+}\right]$

From equation (3),

So,

$\begin{array}{l}pH=鈭�\log \left[x\right]\\ pH=鈭�\log \left[3.0脳{10}^{鈭�3}\right]\\ pH=鈭�\left(鈭�2.52\right)\\ Thus\\ pH=2.52\end{array}$

The pH of a 0.050 M formic acid solution is 2.52.