Understanding the Logarithm of K in DeltaG

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In summary, the conversation discusses the relationship between Gibbs free energy and the equilibrium constant, and how the log of a non-dimensionless K can be taken. It also mentions the use of the Grand canonical partition function and the Nernst-Planck equation in understanding diffusive processes of charged solutes in solution. The conversation concludes with a reminder to understand this fundamental concept and notes that the K inside the logarithm is divided by a dimensionless K0.
  • #1
aniketp
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Well I read in a book that:
[tex]\Delta[/tex]G= RTln (K) (Where K is the eqm const)
H "K" is not necessarily dimensionless so how can we take a log of "K"?
 
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  • #2
Do you mean Gibbs free energy?

then it's given by:
[tex]\tau log(Z_G)[/tex]
after taking the derivative you can get the difference or differential form of this energy.
Z_G is the Grand canonical partition function, and it's indeed dimensionless.
 
  • #3
The full Nernst-Planck equation is:

[tex]\Delta\mu=RTln(\frac{[x_{i}]}{[x_{o}]})+ZF(\psi_{i}-\psi_{o})[/tex], where

[tex]\Delta\mu[/tex] is the change in chemical potential for a particular species

[tex][x_{i}][/tex] is the concentration of species 'x' on one side of a dividing surface (and [tex][x_{o}][/tex] the concentration on the other side)

[tex]\psi_{i}[/tex] the electrical potential on one side of a dividing surface (and [tex]\psi_{o}[/tex] the potential on the other side)

And R, T, Z, F the usual gas constant, temperature, charge per molecule and Faraday constant.

It's worth understanding this equation- it governs diffusive processes of charged solutes in solution and leads to a remarkable (IMO) result: the membrane potential. There's various simplifications, it looks like you have uncharged solutes (Z = 0), and instead of [tex]\Delta\mu[/tex] you are using [tex]\Delta G[/tex], which also changes the [tex]\frac{[x_{i}]}{[x_{o}]}[/tex] term to the equilibrium constant. But, since it's still dimensionless, there's no problem.

Does that help? This is a really fundamental concept- make sure you understand it.
 
  • #4
It's often ignored, but the K inside the logarithm is divided by K0, which has magnitude of 1 and the same units. The quotient is therefore dimensionless and equal to the magnitude of K.

EDIT: Whoops, Andy got there first with a more complete answer.
 

1. What is the significance of the logarithm of K in the calculation of DeltaG?

The logarithm of K is an important factor in determining the spontaneity of a chemical reaction, as it is directly related to the Gibbs free energy change (DeltaG) of the reaction. It represents the ratio of products to reactants at equilibrium and can provide information about the direction and extent of a reaction.

2. How is the logarithm of K calculated?

The logarithm of K is calculated using the equilibrium constant (K) of a reaction, which is the ratio of the concentrations of products to reactants at equilibrium. The logarithm of K is then determined by taking the base 10 logarithm of this value.

3. What does a positive or negative value for the logarithm of K indicate?

A positive value for the logarithm of K indicates that the reaction favors the products at equilibrium, meaning that the reaction is spontaneous in the forward direction. A negative value indicates that the reaction favors the reactants at equilibrium, and the reaction would be spontaneous in the reverse direction.

4. How does the magnitude of the logarithm of K affect the spontaneity of a reaction?

The magnitude of the logarithm of K is directly related to the spontaneity of a reaction. A larger magnitude (either positive or negative) indicates a greater difference in concentration between products and reactants at equilibrium, and therefore a more spontaneous reaction.

5. Can the logarithm of K be used to predict the rate of a reaction?

No, the logarithm of K is only related to the spontaneity of a reaction and does not provide information about the rate of the reaction. The rate of a reaction is determined by factors such as temperature, concentration, and catalysts.

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