The pH, a measure of acidity or alkalinity, plays a fundamental role in chemistry. It quantifies the concentration of hydrogen ions (H+) in a solution and is essential for various chemical and biological processes. On the other hand, the acid dissociation constant, Ka, is a crucial parameter used to measure the strength of an acid. It quantifies the extent of acid dissociation in an aqueous solution, distinguishing strong acids from weak ones.

Outline

## Understanding pH and Ka

Ka or acid dissociation constant is the standard used to measure the strength of an acid. It determines the extent of acid dissociation in an aqueous solution. The more the Ka, the more the dissociation, and hence stronger be acid and lower Ka values indicate a weak dissociation that corresponds to weak acid. Thus Ka is used to distinguish a strong acid from a weak one.

Since Ka values are extremely small numbers usually given in scientific notations that are hard to understand, the logarithmic function makes this math easier by changing the Ka values into pKa values.

pKa is the negative base (-10) logarithm of the acid dissociation constant (Ka), thus, the lower the pKa value, the stronger the acid.

## How to calculate pH using Ka?

**Calculating pH for Strong Acids**

Calculating pH for strong acids is straightforward because strong acids are fully dissociated in solution. In this case, the hydrogen ion concentration ([H^{+}]) is equal to the initial acid concentration. Therefore, pH can be calculated directly using the negative logarithm of [H^{+}].

**Calculating pH for Weak Acids**

For weak acids, calculating pH is more complex because the acid is only partially dissociated, leading to an equilibrium. The dissociation reaction can be represented as:

HA ⇌ H^{+} + A^{–}

The equilibrium constant or dissociation constant (Ka) is defined as;

Ka = [H^{+}] [A^{–}] / [HA]

To calculate pH for a weak acid, you need to consider the initial concentration ([HA]), the concentration of dissociated ions ([H^{+}] and [A^{–}]), and Ka. You can then use Ka to find [H^{+}] and subsequently calculate the pH.

The equilibrium constant or the dissociation constant is represented as Ka = [H^{+}] [A^{–}] / [HA]

**Example Calculations**

### 1. Calculating pH from Ka

Consider a 0.04 M benzoic acid (C6H5COOH) solution with a known Ka of 3.3 × 10^-7. To find the pH:

C_{6}H_{5}COOH + H_{2}O **→** H_{3}O^{+} + C_{6}H_{5}COO^{–}

Find the pH knowing that K_{a}= 3.3 × 10^{-7}.

- Let x represent the concentration of H
_{3}O^{+}that dissociates from C_{6}H_{5}COOH, then [C_{6}H_{5}COOH]- = C – x, where C is the initial concentration.

- Benzoic acid dissociates one H
^{+}ion for every C_{6}H_{5}COO^{–}ion, they are equimolar, so [H^{+}] = [C_{6}H_{5}COO^{–}]= x

Using the Ka rule:

Ka = [H_{3}O^{+}] [C_{6}H_{5}COO^{–}]/ [C_{6}H_{5}COOH]

3.3 × 10 ^{-7} = X^{2} / (0.04 – X)

but Ka is small; 0.04 -x ≈ 0.04

3.3 × 10 ^{-7} = X^{2} / 0.04

X^{2 }= 1.32× 10 ^{-8} ; x = 1.15× 10 ^{-4}

X = [ H3O^{+}] = 1.15× 10 ^{-4} M

pH = – log [H3O+]

= – log (1.15× 10 ^{-4} )

pH = 3.9 (approx).

**2. Calculating Ka from pKa**

To calculate Ka from pKa, use the equation: Ka = 10^(-pKa). The pKa is the negative base-10 logarithm of the acid dissociation constant (Ka).

**3. Calculating Percent Ionization from Ka**

The percent ionization of a weak acid is calculated using the formula:

% HA dissociation = [H3O^{+}] / [HA] Initial

Once you know the concentration of [H3O^{+}], you can determine the extent of ionization.

## Concepts Berg

**How to calculate the pH of a weak Acid?**

The pH equation is still the same (pH = -log[H^{+}]), but you need to use the acid dissociation constant (K_{a}) to find [H^{+}]. after writing the table of variation at equilibrium and considering [H^{+}]=x, ka is used to solve x and finally calculate pH.

**How can we calculate the Ka value from pKa?**

pKa is the negative base -10 logarithm of the acid dissociation constant (Ka).

pKa = -log_{10}Ka

Ka= 10^{-pka}

**How to calculate percent ionization from Ka?**

The equation of dissociation of a weak acid is HA+ H_{2}O **→** H_{3}O^{+ }+ A^{– }^{ }

Ka = [H_{3}O^{+}] [A^{–}] / [HA]

Once we know the [H_{3}O^{+}] we can calculate the percent ionization using this rule:

% HA dissociation = [H_{3}O^{+}] / [HA] _{Initial}