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Age 16 to 18
Challenge Level


Water naturally dissociates into an equilibrium mixture of $H^+$ and $OH^-$ ions and $H_2O$ molecules
H_2O \rightleftharpoons^{K_W} H^++OH^-\,,
where the concentrations of $H^+$ and $OH^-$ ions, written as $[H^+]$ and $[OH^-]$ are related by the expression
K_W = [H^+][OH^-].
$K_W$ is called the dissociation constant, and depends on the temperature of the water.
The following table of data shows the dissociation constant for water at various temperatures and standard pressure.

Water temperature $\quad K_W\times10^{14}\quad$
$0^\circ$ C 0.1
$10^\circ$ C 0.3
$18^\circ$ C 0.7
$25^\circ$ C 1.2
$30^\circ$ C 1.8
$50^\circ$ C 8.0
$60^\circ$ C 13
$70^\circ$ C 21
$80^\circ$ C 35
$90^\circ$ C 53
$100^\circ$ C 73

From this table, work out an estimate for the temperature at which water has a $pH$ of exactly 7, 6.8 and 7.2. Recall that the $pH$ is defined as $pH=-\log_{10}([H^+])$