Calculating free energy from Ksp

[elitespart]

Okay so I'm confused. In my book it says that ksp for Ca(OH)2 = 6.5E-6 and $$\Delta G=-898.5$$ yet when I use the equation $$\Delta G=-RTln(Ksp)$$ the value I get is 29.59KJ/mol. I used R=8.314 and T=298K. What's up with that? Thanks.

 

[lluviata]

Hint: Consider the implications of the solubility constant versus the
\Delta G\
of formation (which is the value you have given), specifically the reactions involved.

 

[Blueshift5]

Hello there,

It's great to see that you are trying to understand the concept of calculating free energy from Ksp. Let me explain what might be causing the discrepancy in your calculations.

Firstly, the value of Ksp for Ca(OH)2 that you have mentioned (6.5E-6) is in mol/L units. However, the value of \Delta G=-898.5 is in J/mol units. This could be why you are getting a different value when using the equation \Delta G=-RTln(Ksp).

To resolve this, you can convert the Ksp value to J/mol units by multiplying it with the molar mass of Ca(OH)2. This will give you a Ksp value of 0.0381 J/mol. Now when you use this value in the equation \Delta G=-RTln(Ksp), you should get a value close to -898.5 J/mol.

Secondly, make sure that you are using the correct value for R in the equation. The value of R can vary depending on the units of the other variables used. In this case, since you are using the Ksp value in J/mol units, you should use the value of R as 8.314 J/mol·K. This could also be a reason for the discrepancy in your calculations.

I hope this helps clarify your confusion. Keep up the good work in understanding scientific concepts!