The acid dissociation constant of p‑nitrophenol is K_a = 7.0 × 10^-8 at 25°C. Calculate its pK_a.

The acid dissociation constant of $p$ ‑nitrophenol is $K_{a} = 7.0 \times 1 0^{- 8}$ at $2 5^{\circ} C$ . Calculate its $p K_{a}$ .

medium 2 marks Class 12 · Chemistry · Alcohols Phenols and Ethers

Answer

p K_{a} = 7.15

The correct answer is $p K_{a} = 7.15$ — Thus $p K_{a} \approx 7.15$ .

Recall the definition $p K_{a} = - lo g_{10} K_{a}$ .
Insert the given $K_{a}$ : $p K_{a} = - lo g_{10} (7.0 \times 1 0^{- 8})$ .
Separate the mantissa and exponent: $- lo g_{10} (7.0) - lo g_{10} (1 0^{- 8})$ .
$- lo g_{10} (7.0) \approx - 0.845$ and $- lo g_{10} (1 0^{- 8}) = 8$ .
Add the two values: $p K_{a} = 8 - 0.845 = 7.155$ , round to two decimal places.
Thus $p K_{a} \approx 7.15$ .

Common mistake: Using

lo g

instead of

- lo g

or forgetting to subtract the mantissa.

Concept tested: Acidity of phenols – $pK_a$ calculation