Confused about Free Energy relation to Pressure & Concentration

[breez]

I'm not sure whether this belongs in the chemistry section, but since it concerns free energy, I decided to post it here.

My chemistry text, Zumdhal, says (without proof, I am self-studying a first year college-level chem course) that $$\Delta G = \Delta G^{\circ} + RTln(Q)$$, where Q is the reaction quotient in terms of partial pressures.

Later, when deriving the Nernst Equation, the text uses this previous identity, but in further example problems, partial pressures are not used for the reaction quotient, but rather concentrations.

I am extremely confused on this respect since $$K_p = K_c(RT)^{\Delta n}$$, where n is the difference in coefficients of reactants from products in the balanced reaction.

So how can

$$\Delta G^{\circ} + RTln(Q_p)$$ = $$\Delta G^{\circ} + RTln(Q_c)$$ ??

 

[breez]

I guess I answered my own question: http://www.nyu.edu/classes/tuckerman/honors.chem/lectures/lecture_19/lecture_19.html

That took me a while to dig up, and its explanations mathematically show, using reference points in the mass-action expression, that this same general relationship holds for the free energy identity posted above.

Also, this means that one can use either partial pressures or concentrations in the Nernst equation.

 

[charng]

First of all, it is completely understandable that you are confused about the relationship between free energy, pressure, and concentration. These concepts can be quite complex and it is important to understand them thoroughly in order to fully grasp their relationship.

To start, it is important to understand that free energy (represented by \Delta G) is a measure of the energy available to do work in a system. It is influenced by various factors, including temperature, pressure, and concentration.

In the equation \Delta G = \Delta G^{\circ} + RTln(Q), Q represents the reaction quotient, which is a measure of the relative amounts of reactants and products in a chemical reaction at a given point in time. Q can be expressed in terms of either partial pressures (Q_p) or concentrations (Q_c).

The reason why the Nernst Equation uses the same identity as the one in your chemistry text is because the Nernst Equation is derived from the same principles. In both cases, the equation is used to calculate the free energy change for a reaction at non-standard conditions, where the concentrations or partial pressures of the reactants and products are not at their standard state.

The difference between using Q_p and Q_c lies in the units. Q_p is expressed in terms of partial pressures, which are typically measured in atmospheres (atm), while Q_c is expressed in terms of concentrations, which are typically measured in moles per liter (mol/L). This is why the Nernst Equation includes the gas constant R, as it is necessary to convert between these different units.

In terms of the relationship between K_p and K_c, it is important to remember that these equilibrium constants are calculated at standard conditions, where the partial pressures and concentrations are at their standard states. This is why the equation K_p = K_c(RT)^{\Delta n} includes the gas constant R as well, to account for the conversion between partial pressures and concentrations.

In summary, the equation \Delta G = \Delta G^{\circ} + RTln(Q) can be used with both partial pressures and concentrations, as they are simply different ways of expressing the same reaction quotient. The Nernst Equation and the relationship between K_p and K_c are derived from the same principles, but they are used for different purposes and at different conditions. I hope this helps to clarify your confusion.