 # pH and Solutions

Table of Content:

## pH and Solutions

Water is autoionized to give equal quantities of hydroxide ion(OHand hydrogen ion (H+). The concentration of the dissociated hydrogen ions in pure water is 10-7 moles per litre.  Solutions are categorized as acidic or basic based on their hydrogen ion (H+) concentration compared to pure water. Acidic solutions have a hydrogen ion concentration greater than the 10-7 moles per litre, while the alkaline (Basic) solution has a lower concentration of H+ ion that is less than 10-7 moles per litre. The concentration of hydrogen ions of a solution is expressed in terms of pH.

### Mixture of Two Strong Acids

The strong acids completely dissociate in the given solvent. The strength of an acid and the concentration of acid are two different terms.

Acid strength: It measures the degree of ionization of acid in the aqueous solution. The greater the number of cations and anions are dissociated in the aqueous solution then acid is strong.

Acid concentration: It measures the number of available acid ions when it is dissolved in a solvent. The concentration is ratio of solute to the solvent content in the solution. So the concentration of hydrogen ion is the same as that of the acid concentration. The concentration of the hydrogen ion in the mixture is the sum of the acid concentration divided by the total volume.

Consider a mixture of two strong acids

Say N1, V1 is strength and volume of the first strong acid and N2, V2 is the strength and volume of the second acid.

The concentration of the hydrogen ion in acid 1 is N1V1 and in acid 2 is N2V2

Total hydrogen concentration = N1V1 + N2V2

Total volume of solution = V1 + V2

[H+] = $=\frac{N1V1+N2V2}{V1+V2}$

From which pH of the solution can be calculated using the formula

$pH = -log_{10}\left [ H^{+} \right ]$.

### Mixture of Two Strong Bases

The strong bases are completely ionized in the given solution. So the concentration of the hydroxide ion is the same as that of the base concentration. The concentration of the hydroxide ion in the mixture is the sum of the base concentration divided by the total volume.

consider a mixture of two strong bases,

Say, N1, V1 is the strength and volume of the first strong base and N2, V2 of the is the strength and volume of the second base.

The concentration of the hydroxide ion in the first strong base is N1V1 and in the second base is N2V2

Total hydroxide ion concentration = N1V1 + N2V2

The total volume of the solution = V1 +V2

[OH] = $=\frac{N1V1+N2V2}{V1+V2}$ [H+] = $=\frac{10^{-14}}{[OH^{-}]}$

From which pH of the solution can be calculated

### Mixture of a Strong Acid and a Strong Base

On mixing a strong acid and strong base neutralization (pH = 7) takes place. The resulting solution may be an acid or base depending on the Concentration.

Say, N1, V1 is the strength and volume of the strong acid and N2, V2 is the strength and volume of the strong base.

• If, N1V1> N2V2, resulting solution will be acidic, with [H+] = $=\frac{N1V1-N2V2}{V1+V2}$
•  If, N1V1˂ N2V2, resulting solution will be basic, with [OH] = $=\frac{N2V2-N1V1}{V1+V2}$

### Weak Acid

Weak acids ionize partly, and Ostwald’s dilution Law can be applied to calculate pH.

$HA\rightleftharpoons H^{+}+A^{-}$

Initial concentration, moles/l, C 0 0

At equilibrium, moles /l C(1-α) Cα Cα

So, Acid Ionization constant = $Ka=\frac{[H+][A-]}{HA}=\frac{(C\alpha +C\alpha)}{c(1-\alpha)}=\frac{c\alpha^{2}}{(1-\alpha)}$

(i) For very weak electrolytes, since α <<< 1, (1 – α ) = 1

.·. $Ka=C\alpha^{2\;\;\;\;\;}\alpha = \sqrt{\frac{Ka}{c}}=\sqrt{KaV}$

(ii) Concentration [H+] of ion = $C\alpha = \sqrt{CKa}=\sqrt{\frac{Ka}{V}}$

iii) $pH=-\log\sqrt{CKa}=\frac{1}{2}(-\log Ka -\log C)$ ;

$pH=\frac{1}{2}(pKa -\log C)$ Increasing dilution, increases ionization and pH

### Mixture of strong acid and weak monoprotic acid

Let C1 and C2 be the concentrations of the strong and weak acids. If α is the degree of dissociation in the mixture, then the hydrogen ion concentration = [H+] = C1+ C2*α.

Degree of dissociation of the weak acid will be less than the pure acid because of the higher [H+] from the strong acid. This is referred as levelling effect. If the [H+] is less than 10-6 mole/l, hydrogen ion concentration from water also is to be added.

### Mixture of two Weak Monoprotic Acids

Say the two weak acid HA1 and HA2, have concentrations C1, C2 and degree of ionization α1 and α2. Initial concentration, moles/l

At equilibrium, moles /l C1(1- α1) C1α1+ C2α2 C1α1 C2(1- α2) C1α1+ C2α2 C2α2

So, $Ka=\frac{[H+][A-]}{[HA]}\;\;\;\;\;\;\;\;Ka1=\frac{c1\alpha 1(c1\alpha 1+c2\alpha 2)}{C1(1-\alpha)}\;\;\; Ka2=\frac{C2\alpha 2(1\alpha 1+C2\alpha 2)}{C2(1-\alpha2)}$

Since α is small, Ka1 = (C1α1+ C2α2) α1 Ka2 = (C1α1+ C2α22

$\alpha 1 = \frac{Ka1}{(C1\alpha 1+C2\alpha 2)}\;\;\;\;\alpha2=\frac{Ka2}{(C1\alpha1+C2\alpha2)}$ [H+] = C1α1+ C2α2 = $=\sqrt{C1 Ka1+ C2 Ka2}$

Also Read: Study The pH Change