XII. HEAT OF DISSOCIATION OF WATER. 19s
For water, which contains 55*5 gram-molecules in a litre, wo have —
K X 55 '5(1 — a) = (55oa)^
or, since the degree of dissociation, a, is small in comparison with 1—
rf In a = Jd In K,
Therefore, if we know fi, i.e. the heat which is absorbed when a gram-molecule of water dissociates into hydrogen and hydroxyl ions, we can calculate the change of a with temperature. In order to find /i we make the following consideration. Suppose we have 1 gram-molecule of hydro- chloric acid and 1 gram-molecule of sodium hydroxide each in such dilution that we may assume without appreciable error that they are completely dissociated. Leaving the
water out of account, these solutions contain 1 gram-equiva-
+ -
lent of each of the ions H (1 gram) and CI (35'45 grams),
+ -
and of the ions Na (23 grams) and OH (17 grams) respectively.
When these two solutions are mixed, sodium chloride in
+ - the dissociated condition, i.e. Xa -I- CI, and water are formed
according to the equation —
H -I- Ci + Na -I- OH + a!Z = Na -I- Ci + HaO-f- aq
where aq denotes the water present in the system in large
quantity. The only change, therefore, w^hich has actually
+ taken place is the union of a gram-ion of H with a gram-ion
of OH to form a gram-molecule of water. The heat
developed was determined by Thomsen to be 14,247 caL at
10-14° and 13,627 cal. at 24*6°. Evidently this is the same
quantity of heat (ji) which would be absorbed when a gram-
+ -
molecule of water dissociates into H and OH. Kohlrausch
was then able to calculate the change of JT and a with
temperature after I had pointed out the meaning of the heat
of neutralisation. The agreement between the calculated
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