Estimate molarity from enthelpy, gibbs energy and entropy of formation

In summary, the person is trying to estimate the molarity of a saturated aqueous solution of ##Sr(IO_3)_2## using the Van't Hoff equation and other relevant equations. They are attempting to find the equilibrium constant and then use it to calculate the molarity. However, they encounter some errors in their calculations and ask for help in solving the problem.
  • #1
Telemachus
835
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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##

attachment.php?attachmentid=54225&stc=1&d=1356393140.png


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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  • #2
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.

Thanks for your attention :)
 
Last edited:

1. How do I calculate molarity from enthalpy, Gibbs energy, and entropy of formation?

To calculate molarity, or the concentration of a solution, using these parameters, you will need to use the following equation: Molarity = (ΔG° + RTlnK) / ΔH° where R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant. This equation is known as the van 't Hoff equation. By plugging in the values for ΔG°, ΔH°, and ΔS° (calculated from the enthalpy, Gibbs energy, and entropy of formation), you can solve for the molarity of the solution.

2. Can I use any units for enthalpy, Gibbs energy, and entropy of formation to calculate molarity?

It is important to use consistent units when using the van 't Hoff equation to calculate molarity. The standard units for enthalpy and Gibbs energy are kilojoules per mole (kJ/mol), while the standard unit for entropy is joules per mole Kelvin (J/mol*K). Make sure to convert all values to these units before plugging them into the equation.

3. What is the significance of using enthalpy, Gibbs energy, and entropy of formation in calculating molarity?

Enthalpy, Gibbs energy, and entropy of formation are thermodynamic parameters that describe the energy and stability of a chemical system. By using these values in the van 't Hoff equation, you can determine the molarity of a solution at a given temperature and equilibrium constant, providing insight into the chemical equilibrium of the system.

4. Is it possible to calculate molarity from enthalpy, Gibbs energy, and entropy of formation without knowing the equilibrium constant?

Unfortunately, the van 't Hoff equation requires knowledge of the equilibrium constant to calculate molarity. However, if you have experimental data for the concentrations of the reactants and products at equilibrium, you can use the equilibrium constant expression (K = [products]/[reactants]) to solve for the equilibrium constant and then use it in the van 't Hoff equation to calculate molarity.

5. Can molarity be calculated using only enthalpy and entropy of formation?

No, the van 't Hoff equation requires the additional parameter of Gibbs energy to accurately calculate molarity. This is because Gibbs energy takes into account both the enthalpy and entropy of a system, providing a more comprehensive understanding of the thermodynamics of the system. Without this parameter, the calculation would not be accurate.

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