# Homework Help: Estimate molarity from enthalpy, gibbs energy and entropy of formation

1. Dec 24, 2012

### Telemachus

Hi there, I have to solve this problem:

Use the following data to estimate the molarity of a saturated aqueous solution of $Sr(IO_3)_2$

So, I think I should use the Van't Hoff equation in some way, but I don't know how.
I also have:

$\Delta_r G=\Delta G^o+RT\ln K$

$K$ is the equilibrium constant, and $\Delta G^o$ is the Gibbs energy of formation.

In equilibrium $\Delta_r G=0$ and the equation can be managed to get the Van't Hoff equation, which is:

$\ln K_1-\ln K_2=-\displaystyle\frac{\Delta H^o}{R} \left( \displaystyle\frac{1}{T_2}-\displaystyle\frac{1}{T_1} \right)$

I think that I should handle this equations to get the equilibrium constant in some way, and then the molarity. Another equation that may be useful is the definition of the Gibbs energy:

$\Delta G^o=\Delta H^o-T\Delta S^o$

The chemical equation involved I think should be:
$Sr(IO_3)_2(s)+H_2O(l) \rightleftharpoons Sr^{2+}(aq)+2IO_3^{-}$

And from it: $K'=\displaystyle\frac{[Sr^{2+}][IO_3^{-}]^2}{[Sr(IO_3)_2]}$

The solid concentration remains constant, and then: $K=[Sr^{2+}][IO_3^{-}]^2$

Can anybody help me to work this out?

Thanks.

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Last edited: Dec 24, 2012
2. Dec 25, 2012

### Telemachus

Ok. The chemical equation I set before was wrong. I wrote it hurried, because of christmass I had to dinner with my family and all that stuff.

Here is the correct chemical equation as I think it should be:
$Sr(IO_3)_2(s) \rightleftharpoons Sr^{2+}(aq)+2IO_3^{-}(aq)$

Alright, so I tried to solve this in the following manner. I am trying to find the equilibrium constant, I think that if I find it, then I will find the asked molarity.

So I thought of using that at equilibrium:
$K_c=e^{\displaystyle\frac{\Delta G^o}{RT}}$

So, I have to find the temperature at first. And for that I thought of using

$\Delta G=\Delta H-T\Delta S\rightarrow T=\displaystyle\frac{\Delta H-\Delta G}{\Delta S}$ (1)

And then for the reaction I have:

$\Delta S=\sum \nu S^o(products)-\sum \nu S^o (reactants)$

nu stands for the stoichiometric coefficients. From the data in the table I get:

$\Delta S=-0.0.0298\frac{kJ}{mol K}$

Similarly: $\Delta G=\sum \nu \Delta G_f^o(products)-\sum \nu \Delta G_f^o (reactants)=-0.4\frac{kJ}{mol}$

And: $\Delta H=\sum \nu \Delta H_f^o(products)-\sum \nu \Delta H_f^o (reactants)=30.8\frac{kJ}{mol}$

Then, back to (1) I get:

$T=\frac{252.1-127.6}{-0.1482}K=-1020.13K$

And there is the problem, I'm getting a negative temperature. I don't know what I did wrong. Besides, at first I found a negative entropy, which implies not spontaneous reaction. And the enthalpy is positive, with means endothermic reaction, I think that is consistent. But I don't know why I get this negative temperature, which is obviously wrong.