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# pH and Solutions

When we talk about the pH (“potential of hydrogen” or “power of hydrogen”) of a solution, we are basically discussing the measure of hydrogen ion concentration in a solution. pH, in other words, is a scale that is used to specify the acidity or basicity of an aqueous solution. Acidic solutions which contain higher concentrations of H+ ions are generally measured to have lower pH values than basic or alkaline solutions.

If the temperature is 25 °C and the solution has a pH of less than 7, then it is acidic. Likewise, solutions with a pH greater than 7 are basic. If a solution has a pH of 7 at the temperature, they are neutral; for example, pure water, which tends to dissociate slightly into equal concentrations of hydrogen and hydroxyl (OH−) ions. The concentration of the dissociated hydrogen ions in pure water is 10-7 moles per litre. Solutions are categorised as acidic or basic based on their hydrogen ion (H+) concentration compared to pure water.

The pH of an aqueous solution is based on the pH scale, which typically ranges from 0 to 14 in water. In any case, students can keep these points in mind.

• Acidic solutions have lower hydroxide concentrations and high hydronium concentrations. Acidic solutions have a hydrogen ion concentration greater than 10-7 moles per litre.
• Basic solutions have high hydroxide concentrations and lower hydronium concentrations. Alkaline (basic) solution has a lower concentration of H+ ion that is less than 10-7 moles per litre.
• The concentration of hydrogen ions in a solution is expressed in terms of pH.

Additionally, some indicators (universal indicator paper, etc.) may be used to measure pH. It is solely based on the fact that the indicator’s colour changes with pH. A visual comparison of the colour of a test solution with a defined colour chart helps to determine the pH accurately to the nearest whole number. pH can also be measured using an electronic pH metre.

### The Mixture of Two Strong Acids

The strong acids dissociate completely 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 ionisation of acid in the aqueous solution. The greater the number of cations and anions dissociated in the aqueous solution, the stronger the acid is.

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 ions 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 the strength and volume, respectively, of the first strong acid and N2, V2 is the strength and volume, respectively, 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

$$\begin{array}{l}[H^+]=\frac{N1V1+N2V2}{V1+V2}\end{array}$$

The pH of the solution can be calculated using the below formula.

$$\begin{array}{l}pH = -log_{10}\left [ H^{+} \right ]\end{array}$$

### The Mixture of Two Strong Bases

The strong bases are completely ionised 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, respectively, of the first strong base, and N2, V2 of the is the strength and volume, respectively, 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

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

From this, the pH of the solution can be calculated.

Also Read: Study the pH Change

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

On mixing, strong acid and strong base neutralisation (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, respectively, of the strong acid, and N2, V2 is the strength and volume, respectively, of the strong base.

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

### Weak Acid

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

$$\begin{array}{l}HA\rightleftharpoons H^{+}+A^{-}\end{array}$$

Initial concentration, moles/l, C 0 0

At equilibrium, moles /l C(1-α) Cα Cα

So, acid ionisation constant = Ka

$$\begin{array}{l}=\frac{[H+][A-]}{HA}=\frac{(C\alpha +C\alpha)}{c(1-\alpha)}=\frac{c\alpha^{2}}{(1-\alpha)}\end{array}$$

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

$$\begin{array}{l}\therefore Ka=C\alpha^{2\;\;\;\;\;}\alpha = \sqrt{\frac{Ka}{c}}=\sqrt{KaV}\end{array}$$

(ii) Concentration [H+] of ion

$$\begin{array}{l}=C\alpha = \sqrt{CKa}=\sqrt{\frac{Ka}{V}}\end{array}$$

iii)

$$\begin{array}{l}pH=-\log\sqrt{CKa}=\frac{1}{2}(-\log Ka -\log C)\end{array}$$
;

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

### The 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.

The 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 to as levelling effect. If the [H+] is less than 10-6 mole/l, hydrogen ion concentration from water also is to be added.

### The Mixture of Two Weak Monoprotic Acids

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

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

So,

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

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

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

Related Topics

## Frequently Asked Questions – FAQs

Q1

### What is the pH of an acidic solution?

The pH of an acidic solution is less than 7.
Q2

### What is the pH of a basic solution?

The pH of a basic solution is 8-14.
Q3

### Which pH value is considered neutral?

A pH value of 7 is considered neutral.
Q4

### What does the pH value indicate?

The pH value indicates the concentration of hydrogen ions in the solution.
Q5

### How is the pH value related to hydrogen ion concentration?

pH and hydrogen ion concentration are inversely proportional to each other. Lower the concentration of hydrogen ions, the higher the value of pH.
Test Your Knowledge on pH and Solutions