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# pH and pKa

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 Sub Topics All known chemical substances cam be classified as acidic and basic substances. There are various parameters to identify the acidic and basic nature of any substance. The simplest definition of an acidic substance is the tendency of that substance to given hydrogen ions. Similarly a basic substance can give hydroxide ion such as sodium hydroxide is a basic substance whereas hydrogen chloride or acetic acid is acidic in nature. The combination of an acid with base results the formation of a neutral compound which is called as salt. In other words we can say that combination of hydrogen ions from acids and hydroxide ions from base form water and neutralise the effect of acid as well as base. You can find some other acidic and alkaline substances in your surroundings such as battery acid, household drain cleaners, citrus fruits, milk etc.  The neutralisation reaction of acid and base results the formation of salt and water. It can be easily observed in our daily life. For example, acidity in stomach occurs due to presence of excess of gastric juice which contains hydrochloric acid. It can be cured with the help of Milk of magnesia which is magnesium hydroxide. The reaction of magnesium hydroxide with gastric juice neutralises the effect of it. On the basis of concentration of hydrogen ions and hydroxide ions in the solutions, acids and bases can be classified as strong and weak. A strong acid can dissociate completely (100% dissociation) in to hydrogen and respective ions whereas a weak acid shows partial dissociation and un-dissociated molecules remain in the solution.  For example; hydrochloric acid is a strong acid whereas acetic acid is a weak acid.

## pH Definition

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We cannot determine the strength of acid or base by just seeing the solution or molecular structure. There must be some scale to determine the strength of acidic and basic solutions. This scale is called as pH scale. The pH definition states that it is the concentration of hydrogen ions in the solution ranges from 0 to 14.  The pH of 7 shows a neutral solution, while pH less than 7 is acidic, and a pH greater than 7 is basic solution. Two adjacent values of pH are 10 times differed from each other. For example, a pH of 12 is 10 times more basic than a pH of 13 and 100 times more basic than a pH of 14.

## pH Balanced Water :

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The pH of pure water is 7 that mean it is neutral. The pH of pure water is good for health. The addition of any acid or base can alter the pH of water. For example, if we add vinegar (dilute solution of acetic acid) or lemon juice (citric acid) the pH of water reduces from 7. Similarly the addition of alkaline substances such as soaps, detergents increases the pH of pure water. The pH scale is negative logarithm of the concentration of hydrogen ions in the solution. Like pH, for alkaline solutions, we can use pOH which is negative logarithm of concentration of hydroxide ions in the solution.
pH = -$log_10$ [$H^+$]

Due to negative sign, as the concentration of hydrogen ions increases, the pH value reduces. In other words, low value of pH indicates the higher proton concentration. Let’s have a look on the ionization of water. Water molecules ionised to hydrogen ions and hydroxide ions which remain in equilibrium.

$H_2O \to H^+ + OH^-$

The equilibrium constant for this equation can be written as:

$Kw$ = $\frac{[H^+] [OH^-]}{[H_2O]}$

Since water is present in excess, therefore the concentration of water can be ignored. Hence the equation can be re-written as:
$K_w = [H^+][OH^-]$

The concentration of hydrogen ions and hydroxide ions is same in neutral water that is:
$H+ = OH^- = 10^{-7}$

Or   $K_w = [10^{-7}] [10^{-7}] = [10^{-14}]$

Or $pK_w = - log_10 [K_w]$

$pK_w$= 14

When we add acids and bases in water, the equilibrium is shifted in that direction. For example: as we add acid, the concentration of hydrogen ions in water, the equilibrium shifts to the left. Similarly the addition of base or hydroxide ions shifts the equilibrium to left.  It also reduces the hydrogen ions. The product of concentration of hydrogen ions and hydroxide ions is always equal to 10-14.

## pKa Definition

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As we discussed, strong acids are ionised 100% whereas weak acids cannot ionised completely and remain un-dissociate in the molecule. The extent of ionisation of weak acids can be determined with the help of acid dissociation constant (Ka). For example a weak acid AH is dissociated to for m hydrogen ion and A- ion. The dissociation equilibrium equation can be written as:
$AH \leftrightharpoons A^- + H^+$

The equilibrium constant or acid dissociation constant (Ka) can be written as:

$K_a$ = $\frac{[A^-][H^+]}{[AH]}$
Here square brackets indicate the concentration of components.  With the help of this expression, we can determine the concentration of hydrogen ions, released by a certain acidic solution.

## Calculating pH from pKa

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Now we can write the pKa definition.  p$K_a$ is the negative logarithm of $K_a$ value that is acid dissociation constant.  It can be written as:

$pK_a = - log_10 [K_a]$

The common term in both pH and p$K_a$ is the concentration of hydrogen ions. Therefore we can calculate pH of a solution if we know the concentration of hydrogen ions. With the help of concentration of hydrogen ions, we can calculate the value of $K_a$ and p$K_a$ which can further related to pH of the solution.

## pKa and pH

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Let’s identify the relation between p$K_a$ and pH. The $K_a$ value is directly proportional to the concentration of hydrogen ions. In other words, as the concentration of hydrogen ions increases, the value of $K_a$ also increases. Remember the high concentration of hydrogen ions can be indicated with the low value of pH. Since p$K_a$ is negative logarithm of $K_a$, therefore high value of Ka stands for low value of p$K_a$.

## pKa values

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For strong acids, the pH and p$K_a$ values are low as the concentration of hydrogen ions and $K_a$ is high. We can say that we can calculate the p$K_a$ or pH. For example, the value of $K_a$ for weak acids like acetic acid and lactic acids lies between 10-3 to 10-6 which is very low but the p$K_a$ value will be high. Thep$K_a$ value for acetic acid is 4.8 and for lactic acid, it is 3.8. Hence p$K_a$ can express the acidity of weak acids.

## Calculate pKa from pH

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Let’s discuss how to calculate p$K_a$ from pH. We can use the Henderson-Hasselbach equation for calculation of pH or p$K_a$.

## pH pKa Equation

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The Henderson-Hasselbach equation or pH, pKa equation is as given below.

$pH$ = $\frac{pK_a + log[A^-]}{[HA]}$

## pH pKa log

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Here in the Henderson-Hasselbach equation;

[$A^-$] = Concentration of deprotonated form

[HA] = Protonated form of acid

If   $\frac{log ([A-]}{[HA])}$ = 0

then $\frac{[A-]}{[HA]}$ = 1

## pH to pKa

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Same equation can be used to calculate the pH of solution with the help of pKa and concentration of anion and un-dissociated acid molecules.

pH = $\frac{pK_a + log [A^-]}{[HA]} ## pKa to pH Back to Top In this case the pH of solution will be equal to the pKa value of the given acid. It makes the concentration of protonated and deprotonated form exactly equal to each other. Another important term is buffer solutions. If we add acid to a solution, it pH value reduces. Similarly the addition of base increases the pH of solution. Overall the pH of solution alters due to addition of acids or bases. The solutions whose pH does not alter due to addition of small quantity of acids or bases are called as buffer solutions. The ability of a solution to maintain its pH is referred as its buffer capacity. Let’s have a look on the relation between pKa and buffer capacity of solution. The Henderson-Hasselbach equation can be re-write as given below:${K_a}{[H^+]} = \frac{[A^-]}{[AH]}$So we can say that pKa and pH are equal when$\frac{[A-]}{[AH]}$= 1. We can say that buffer solution must have some things which can remove any hydrogen ions or hydroxide ions. We add acid or base, it must remove those extra ions to maintain the pH of the solution. Let’s discuss one example of acidic buffer solutions that is mixture of acetic acid and sodium acetate. We know that acetic acid is a weak acid which can ionised partially to form acetate ion with hydrogen ions. The un-dissociate acetic acid molecules remain in the solution. The equilibrium equation can be written as given below.$CH_3COOH_{(aq)} \leftrightharpoons   CH_3COO^-_{(aq)} + H^+_{(aq)}$Now with the addition of sodium acetate to acetic acid increases the concentration of acetate ions to the solution. We know that Le Chatelier's Principle states that reactions will move to reduce the effect of change. Hence the equilibrium will move in left direction to reduce the affect of high concentration of acetate ions. In this condition, there are un-ionised acetic acid molecules, acetate ions from the sodium acetate and hydrogen ions. If we add acid to this buffer solution, these new hydrogen ions will combine with acetate ions to form un-ionised acetic acid molecules. It would prevent the drop in the pH value.$CH_3COO^-_{(aq)} + H^+_{(aq)} \leftrightharpoons     CH3COOH_{(aq)}$Since the concentration of hydrogen ions again balanced, therefore the pH will remain same as before. Similarly by the addition of alkali to same buffer solution, the concentration of hydroxide ions increases which increases the solution. These extra OH- ions react with un-ionised acetic acid molecules to form acetate ions and water. The equilibrium is as given below.$CH_3COOH_{(aq)} + OH^-_{(aq)}   \leftrightharpoons   CH_3COO^-_{(aq)}  + H_2O_{(l)}\$

It decreases the concentration of OH- ions in the solution and control the pH of solution. Some of the OH- ions also react with hydrogen ions which come from acetic acid and form water. High concentration of water increases the ionisation of acetic acid and form more acetate ions in the solution. Water can also re-ionised but up to a small extent to form few hydrogen ions and hydroxide ions. One of the best examples of alkaline buffer solution is mixture of ammonia and ammonium chloride which also show almost constant pH even after the addition of acid or base to the solution.

## How to test soil pH?

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The concentration of hydrogen ions plays an important role in the agriculture and food industries. All plants can grow at certain pH of soil. The pH of soil indicates the acidity or alkanet of the soil. Like the pH of solution, the pH of soil also indicates the strength or concentration of hydrogen ions in it. It is negative logarithm of concentration of hydrogen ions. It also ranges from 0-14.  The pH of soil provides an idea about soil profile and its properties which can be used for the proper growth of plants. Now question comes in your mind how we can test the pH of soil. There are several ways to determine the pH of soil. We can use the pH meter to test the soil pH. It is one of the most accurate methods of the determination of pH. Another method is to use certain indicators or dyes which is less accurate and gives approximate value of the pH of soil. Since many dyes show a certain colour at certain pH therefore any change in the pH of soil shows change in the colour of dyes and provide an approximate idea about pH of soil. For the determination of pH of the soil first the sample of soil is saturated with the dye for a few minutes. Now observe the colour of soil. The colour of sample can be matched with the colour chart and get an idea about the pH of soil. On large scale like on field or lawn, we can collect the soil and repeat same in laboratory.  The addition of acidic or alkaline substances can alter the pH of soil. For example, the pH of soil reduces by

• Lleaching due to rain water as it removes the alkaline ions like Ca2+, Mg2+, Na+ and K+,
• Excess of CO2 which is released due to decomposition of organic matter,
• Formation of weak organic acids like carbonic acid due to combination of carbon dioxide gas with water,
• Formation of strong acids like HNO3, H2SO4 from ammonium and sulphur fertilizers etc.
The acidity of soil can be controlled by the addition of lime which increases the pH of soil as it replaces the hydrogen ions from the soil. Ground limestone and dolomitic limestone can be used as liming materials. Remember the amount of lime must be correct as excess of lime can make the soil alkaline which is again not good for the proper growth of plants.