# Calculating free energy from Ksp

• elitespart
In summary, the formula for calculating free energy from Ksp is ΔG = -RTlnK, where ΔG is the change in free energy, R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant (Ksp). The units for free energy are typically joules (J) or kilojoules (kJ), while the units for the equilibrium constant (Ksp) vary depending on the specific reaction. The temperature scale used in the formula must be in Kelvin (K) in order to obtain accurate results, as the gas constant (R) is based on the Kelvin scale. A negative value for free energy indicates that the reaction is spontaneous and thermodynamically favorable, while a positive value
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.

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.

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!

## What is the formula for calculating free energy from Ksp?

The formula for calculating free energy from Ksp is ΔG = -RTlnK, where ΔG is the change in free energy, R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant (Ksp).

## How do I determine the units for free energy and equilibrium constant in the formula?

The units for free energy are typically joules (J) or kilojoules (kJ), while the units for the equilibrium constant (Ksp) vary depending on the specific reaction. It is important to ensure that the units for both ΔG and K are consistent in order to obtain an accurate calculation.

## Can I use any temperature scale when calculating free energy from Ksp?

No, the temperature scale used in the formula must be in Kelvin (K) in order to obtain accurate results. This is because the gas constant (R) is based on the Kelvin scale.

## What is the significance of a negative value for free energy?

A negative value for free energy indicates that the reaction is spontaneous and will proceed in the forward direction. This means that the products are more stable than the reactants and the reaction is thermodynamically favorable.

## How can I use the calculated free energy to predict the spontaneity of a reaction?

If the calculated ΔG is negative, the reaction is spontaneous and will proceed in the forward direction. If ΔG is positive, the reaction is non-spontaneous and will not occur without an external driving force. A value of 0 for ΔG indicates that the reaction is at equilibrium.

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