The ionization constant for water is 1.14 × 10–15 at 0 °C and 9.6 × 10–14 at 60 °C. — Thermodynamics Chemistry Question
Problem Context
The ionization constant for water is 1.14 × 10–15 at 0 °C and 9.6 × 10–14 at 60 °C.
Write the equation for the ionization of water and determine the pH of water at 60 °C.
Model Answer
H2O → H+ + OH–
H+[ ] = ×9 6 10 14. – = 3.1 × 10–7; pH = 6.51
Calculate each value.
i. ∆Hionization over this temperature range
Model Answer
ln – k
k
H
R T T 2
1 1 2
1 1
=
∆
ln .
. . –
–9 6 10
1 14 10 8 314
1
273
1
333
14
15
× ×
=
−
∆H
ln 84.2 = ( )∆H
8 314 0 003663 0 003003
. . – . ;
4 43 8 314
0 000660
. .
. ( ) = ∆H
∆H = ×5.58 10 J or 55.8 kJ4
ii. ∆G at 60 °C
Model Answer
∆G RT K= = × = ×– ln (– . )( ) ln( . ) .–8 314 333 9 6 10 8 30 1014 4 J
iii. ∆S at 60 °C
Model Answer
∆ ∆ ∆G H T S= – ; ∆S = × − × =8 30 10 5 58 10
333 81 7
4 4. .
– – . J
State the significance of the sign of the sign of ∆S obtained in part 2b.iii, and explain how the process indicated in 2a could lead to this sign.
Model Answer
The negative sign corresponds to an increase in order. An increase in order can result from the H+ and OH– ions structuring the H2O molecules around them.