$6-11.$ The equilibrium constant for the reaction of $N{H}_3(aq)+$

$H_{2}ON{H}_4^{+}+O{H}^{-}$is $K_b=1\mathrm{.}479{10}^{-5}$ at $5C$ and $1\mathrm{.}570{10}^{-5}$

at $10C.$

$($a$)$ Assuming $H$ and $S$ are constant in the interval $5-10C$

$($probably a good assumption for small $T),$ use Equation $6-8$ to find

$H$ for the reaction in this temperature range.

Other Information

$K=e^{-G\frac{}{R}T}=e^{-\frac{H-TS}{R}T}=e^{(-H\frac{}{R}T+S\frac{}{R})}$

$=e^{-H\frac{}{R}T}*e^{S\frac{}{R}}$

The term $e^{S\frac{}{R}}$ is independent of $T($at least over a limited temperature range in which $S$

is constant$).$ The term $e^{-H\frac{}{R}T}$ increases with increasing temperature if $H$ is positive and

decreases if $H$ is negative. Therefore,

The answer is $7\mathrm{.}82k\frac{J}{m}ol$