Pure water dissociates according to the equation shown. H₂O(l) ⇌ H⁺(aq) + OH⁻(aq) The equilibrium constant for this reaction is known as Kʷ, the ionic product of water. Kʷ = [H⁺(aq)] [OH⁻(aq)] At 25°C, Kʷ has a value of 1.00 × 10⁻¹⁴ mol² dm⁻⁶. The pH of pure water at 25°C is 7.00. A student finds the pH of pure water at 35°C is 6.84. The student investigates how temperature affects the pH of pure water and determines a value for the enthalpy change for the dissociation of water, ΔH. The student records the pH of pure water at different temperatures. A line of best fit from the results of the student's investigation is shown in Fig. 2.1. [Figure 2.1]

1. (a)(i)Use Fig. 2.1 to calculate the hydrogen ion concentration of pure water at 45°C. pH = −log [H⁺(aq)] hydrogen ion concentration =[1]
2. (a)(ii)Calculate the value of Kʷ for pure water at 45°C. Kʷ =[1]
3. (a)(iii)State the relationship between Kʷ and temperature.[1]
4. (b)(i)Complete Table 2.1. Record 1/T to three significant figures using standard form. Record log Kʷ to two decimal places. Table 2.1 temperature, T /K | 1/T /K⁻¹ | Kʷ /mol² dm⁻⁶ | log Kʷ ------------------|------------|---------------|---------- 283 | | 2.93 x 10⁻¹⁵ | 293 | | 6.81 x 10⁻¹⁵ | 303 | | 1.47 x 10⁻¹⁴ | 313 | | 2.92 x 10⁻¹⁴ | 323 | | 5.48 x 10⁻¹⁴ | 333 | | 1.09 x 10⁻¹³ | 343 | | 1.45 x 10⁻¹³ |[2]
5. (b)(ii)Plot a graph on the grid to show the relationship between log Kʷ and 1/T. Use a cross (x) to plot each data point. Draw a line of best fit.[2]
6. (b)(iii)Circle the one point on the graph that you consider to be most anomalous.[1]
7. (b)(iv)Suggest one reason to explain the anomalous point you have circled. Assume there was no error in determining Kʷ.[1]
8. (b)(v)Use your graph to determine the gradient of the line of best fit. State the coordinates of both points you used in your calculation. These must be selected from your line of best fit. coordinates 1 coordinates 2 gradient =[2]
9. (b)(vi)The relationship between log Kʷ and 1/T is given by the equation shown. log Kʷ = −ΔH / (2.303 RT) + constant Use the gradient determined in (b)(v) to calculate a value for the enthalpy change, in kJ mol⁻¹, for the dissociation of water, ΔH. If you were unable to determine a value for the gradient in (b)(v), use the value –2550. This is not the correct value. ΔH =[2]

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