IB Chemistry HL 3.1.5 Ion product of water (Kw)

[Maximum number: 6]

Iron rusts in the presence of oxygen and water. Rusting is a redox process involving several steps that produces hydrated iron(III) oxide, $\mathrm{Fe}_{2} \mathrm{O}_{3} \bullet \mathrm{nH}_{2} \mathrm{O}$ , as the final product. The half-equations involved for the first step of rusting are given below.

Half-equation 1: $\quad \mathrm{Fe}(\mathrm{s}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-}$

Half-equation 2: $\quad \mathrm{O}_{2}(\mathrm{aq})+4 \mathrm{e}^{-}+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 4 \mathrm{OH}^{-}(\mathrm{aq})$

(a)

State a chemical equation for the partial dissociation of water into ions, including state symbols.

[ 1 ]

$\quad \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) / 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq})$ ;

⇌ and state symbols are necessary for the mark.

(b)

The dissociation of water into ions is reversible. State the expression for the ionic product constant of water.

[ 1 ]

$K_{\mathrm{w}}=\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right] / K_{\mathrm{w}}=\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{OH}^{-}\right]$ ;

(c)

The ionic product constant of water was measured at three different temperatures.

Table for Question (c) — IB Chemistry HL

Deduce whether the ionization of water is exothermic or endothermic, giving your reason.

[ 2 ]

(d)

Use the data in part (iii) to determine the pH of water at 373 K , correct to two decimal places.

[ 2 ]

$\left.5.13 \times 10^{-13}=\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]^{2} /\left[\mathrm{H}^{+}\right]^{2} /\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] /\left[\mathrm{H}^{+}\right]=7.16 \times 10^{-7}(\mathrm{moldm})^{-3}\right)$ ;
pH=6.14 / 6.15;

Marking guidance:

Award [2] for correct final answer.

IB Chemistry HL 3.1.5 Ion product of water (Kw) Question Bank

Exam points

3.1.5—Ion product of water (Kw) question 1

Question (a)

Question (b)

Question (c)

Question (d)