Question

How does $\text{pH}$ relate to $pKa$?

Answer 1

$pH$ denotes potential of hydrogen or power of hydrogen. It is a scale used to specify the acidity or basicity of an aqueous solution. The $pKa$ value is one method used to indicate the strength of an acid. The $pH$ of a solution can be predicted when the analytical concentration and $pKa$ values of all acids and bases are known; conversely, it is possible to calculate the equilibrium concentration of the acid and bases in solution.

Complete step by step answer:
$pKa$ is the negative log of the acid dissociation constant or $Ka$ value. A lower $pKa$ value indicates a stranger acid.
The $pKa$ is the $pH$ value at which a chemical species will accept or donate a proton. The lower the $pKa$ the stronger acid and the greater the ability to denote a proton in aqueous solution.
By Henderson Hasselblad equation $pH$ and $pKa$ can be related as
$pH=pKa+{{\log }_{10}}\left( \dfrac{\text{Base}}{\text{Acid}} \right)$
The Henderson Hasselblad equation relates the $pH$ of a solution containing a mixture of the two components to the acid dissociation constant, $Ka$ and the concentration of the species in solution.
The $pKa$ value is directly proportional to the standard Gibbs free energy charge for the reaction. The quantitative behavior of acids and bases in solution can be understood only if their $pKa$ values are known.
The $pH$ of a solution can be predicted when the analytical concentration and $pKa$ values of all acids and bases are known; conversely, it is possible to calculate the equilibrium concentration of the acid and bases in solution when the $pH$ is known. There are multiple techniques to determine the $pKa$ of a chemical, leading to some discrepancies between different sources. The $pH$ is established by international agreement. Primary $pH$ standard values are determined using a concentration cell with transference, measuring the potential difference between a hydrogen electrode and a standard electrode such as the silver chloride electrode.

Additional Information:
A $pH$ indicator is a weak acids or weak base that changes color in the transition $pH$ range, which is approximately $pKa\pm 1$ The design of a universal indicator requires a mixture of indicator whose adjacent $pKa$ values differ by about two, so that their transition $pH$ ranges just overlap.
At $25{}^\circ \text{C}$ solutions with a $pH$ less than $7$ are basic. Solutions with a $pH$ of $7$ at this temperature are neutral. The $pH$ values can be less than $0$ for a strong acid, or greater than $14$ for very strong bass. $pH$ is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity ${{a}_{H+}}$ in a solution. $pH={{\log }_{10}}({{a}_{H+}})$
The concept of “unified $pH$ scale” has been developed on the basis of the absolute chemical potential of the proton. The model uses the lewis acid-base definition. Pauling’s second rule is that the value of the first $pKa$ for acids of the formula $X{{0}_{m}}{{(04)}_{n}}$ depends primarily on the number of Oxo groups $m$ independent of hydroxyl group $n$

Note: The $pH$ of aqueous solution can be measured with a gas electrode and a $pH$ meter, or a color changing indicator. Any aqueous acid with a $pKa$ value of less than $0$ is almost completely deprotonated and is considered a strong acid. $pKa$ values for strong acids have been estimated by theoretical means. The experimental determination of $pKa$ values is commonly performed by means of titration, in a medium of high ionic strength and at a constant temperature. With organic acids inductive effects the $pKa$ values. Alcohols do not normally behave as acids in water, but the pressure of a double bond adjacent to the $\text{OH}$ groups can substantially keto enol tautomerism.