# Finding the temperature at which the system reaches equilibrium

I’m really stuck on this problem. This involves dissolving Borax: $$\ce{Na2B4O7•10H2O(s)<=>2Na^+(aq) + B4O7^2-(aq) + 10H2O}$$

\begin{align}\Delta H&=\pu{109 kJ/mol} \\ \Delta S&= \pu{340 J/mol\:K} \\ K_\mathrm{c} &=0.047 \;@ \; \pu{25 ^\circ C} \end{align}

1. If the starting concentration of $$\ce{B4O7}$$ is $$\pu{0.17 M}$$ and the sodium ions are $$\pu{0.34 M}$$ at $$\pu{25^\circ C}$$, which direction will the reaction proceed? I said forward because Q < K

2. At what temperature would a mixture of these same starting concentrations be a saturation solution (i.e. be at equilibrium) And that’s where I’m stuck

3. At what temperature would a mixture under standard conditions ($$[\ce{B4O7}]=\pu{1M}$$, $$[\ce{Na}]=\pu{1 M}$$) be a saturation solution (i.e. be at equilibrium) And I’m stuck here again

I understand that crossover temperature plays a role ($$T_c=\Delta H/\Delta S$$) but I don’t understand how to work with given concentrations.

• Hint: Use vant Hoff equation. $\ln(keq(T2)/keq(T1))= ∆H/R [\frac{1}{T1}-\frac{1}{T2}]$ and the equation you got. – user600016 Jun 23 at 9:21