Indian Forest Service (Mains), Chemistry optional · 2022 · Paper I

Q1(d). Neutral pH at body temperature

Question

What is the pH of pure water at 37 °C? (Given: ΔᵣH° (enthalpy of ionization) at 25 °C is 55.82 kJ mol⁻¹.)

Using K_w(298.15 K) = 10⁻¹⁴ and constant ionisation enthalpy, the neutral pH at 37 °C is approximately 6.81.

Apply the integrated van’t Hoff equation: ln(K_w,2/K_w,1) = −(ΔᵣH°/R)(1/T₂ − 1/T₁).
With T₁ = 298.15 K and T₂ = 310.15 K, ln(K_w,2/10⁻¹⁴) = 0.8713; K_w,2 ≈ 2.39 × 10⁻¹⁴ and pK_w ≈ 13.622.
In pure water a(H⁺) = a(OH⁻) ≈ √K_w = 1.55 × 10⁻⁷, so pH = pK_w/2 = 6.811.
Ionisation is endothermic, so warming increases K_w; the water remains neutral because hydrogen and hydroxide activities are equal.

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

Coversionic product of watervan't Hoff equationpH of water at 37 °CKw temperature dependenceneutral pH