* 2

We have derived the above formula from experimental evidence that takes into the account for the the spontaneity of a chemical reaction (∆G) that is not at standard conditions.

∆G° = the free energy calculated chemical or physical process at standard thermodynamic conditions (°).

Standard Thermodynamic Conditions:  THESE ARE THE CONDITIONS IN THE TABLATURE

                                                          1.  298 K and 1 atm atmospheric pressure AND

                                                          2.  1 M concentration for (aq) solutions and

                                                          3.  1 atm partial pressures for gases         

Example: [Na⁺] =  1 molar concentration of Na⁺ ions

*(H₂)  = 1 atm of H₂ gas or [H₂]=  1 atm of H₂ gas in a liter                                                                

                                                          *gases can have a concentration [molarity] or a (partial pressure)

So if we are not at the conditions above, we cannot calculate the ∆Gº and thus cannot evaluate the spontaneity of the reaction UNLESS we use the NON-STANDARD ∆G (there is not a º symbol!) formula that we derived.

You should recognize that we only consider the (aq) or (g) phases for chemicals as they relate to how they change the ∆G of the process or chemical reaction BECAUSE ONLY (aq) or (g) can have a change of concentration as chemical reactions or physical changes proceed. This was evident in derivation.

When a (aq) is diluted its entropy increases and when a gas is diluted its concentration or partial pressure is decreased its entropy decreases.  You see we can track the how the spontaneity, Free energy (∆G), or ∆S_univ changes as a chemical reaction or physical change proceeds WHEN WE ARE NOT AT STANDARD CONDITIONS!  That is the power of the reaction Quotient!!!  As it changes it changes the value of the ∆G (nonstandard).  As chemists we want to keep our chemical reactions as spontaneous as possible so that a pathway for our chemical reaction remains open as possible. 

REMEMBER That 99.99999 percent of the time chemical reactions or physical changes ARE NOT occurring at standard conditions!!!!  But we still need ∆Gº as a reference point in the equation.

                                                                ∆G = ∆Gº + RT ln Q

     *Also notice we are using the Universal Gas Constant (R) that is in JOULES (8.31 J mol ^-1 K ^-1 ) 

We know that reactions die or stop because we either run out of the limiting reagent OR the ∆G of the reaction has changed so that it becomes ZERO! We should remember this from our voltaic cells (batteries)!

Because there is no preferred pathway in a reversible chemical reaction (non-completion reactions) at equilibrium ∆G = zero and the forward reaction (and the reverse) is essentially dead BECAUSE NO WORK IS BEING DONE if there is no preferred pathway.

When we are at equilibrium the reaction quotient (Q) represents the amount of products or reactants that are favored when the forward reaction reached equilibrium. Even though we are at equilibrium the Universe will decide whether the forward reaction or the reverse reaction is favored.  This is a special case of Q that we call K_eq (equilibrium constant).  It’s formula is the same as Q  but its value tells up the position that reactions work toward and whether the reactants or products are favored when equilibrium is reached.

So lets Derive how Keq relates with ∆G:

                                                     ∆G   =   ∆G° +   RT ln Q

AT equilibrium                                                0      =   ∆G°  +  RT ln K_eq

                                  Remember that Non standard ∆G will become 0 at equilibrium and Q becomes Keq

                                                                           Rearrange and solve for ∆Gº 

                                                                        ∆G°  =  – RT ln K_eq                                                           

                   So this formula tells us that when there are more products than reactants at equilibrium Keq >1

                                     and when there are more reactants than products at equilibrium Keq < 1

*Notice when Keq is large the ln (or the exponent of a number greater than 1) = positive number.

   ∆G°  =  – RT (Positive Number)    =   – ∆G°  =  spontaneous (forward reaction)

This means that chemical reactions that reach equilibrium and favor the formation of the products HAVE A GREATER Pathway in the forward reaction! Combustion reactions have Keq values that approximate infinity because the ∆G is Incredible LARGE AND NEGATIVE!

*Notice when Keq is small the ln (or the exponent of the a number less than 1) = negative number

 ∆G°  =  – RT (Negative Number)    =   +∆G°  =  spontaneous (reverse reaction)                                                                              but non spontaneous in the forward.

This means that chemical reactions that reach equilibrium and favor the formation of the reactants HAVE A GREATER Pathway in the Reverse reaction! Ionization reactions that are generally insoluble favor formation of the insoluble solid salt (precipitation reactions )and have Keq (Ksp) values that are VERY SMALL because ∆G is Incredible LARGE AND Positive!

We now can use Q, Keq, and ∆G to understand how reactions change their spontaneity as they change their reactants and products (concentrations or partial pressures) or in the case of manipulation in Le Chatelier’s Principle.

Lets look at a U diagam with a very small equilibrium constant : K_{eq = Very Small}

(figure 1)

Chemical reactions will always move toward Keq UNTIL ∆G  is Zero and there will always will be a one thermodynamically pathway that is favored over another. Keq almost never equals 1 because then that could refute the Second Law of Thermodynamics, which requires chemical or physical changes to have a decrease in Free Energy (- ∆G).  Because spontaneous processes must move toward a decrease in Free Energy the more Spontaneous Reaction reaches ZERO at a position that favors the forward or reverse reaction.  In the case of figure one, the formation of the reactants is favored and thus the Keq < 1 and the reverse reaction is more spontaneous (more favored thermodynamically) than the forward. 

What this all means is that chemical reactions are constantly changing their Q (reaction quotient) as the chemical reaction or physical change progress AND thus their spontaneity or ∆G (non-standard )is decreasing till it becomes zero.  This seems like a depressing eventuality for all chemical reactions BUT NOT so! We can use this understanding to our advantage to manipulate chemical reactions through the concept of Le Chateliers Principle.

Before we dive into the Le Chateliers Principle lets first remember that chemical reactions that are spontaneous (have a preferred pathway = ∆G = negative) DIE because of 2 reasons:

1:  Runs out of the limiting reagent with completion reactions (Very High or Low Keq values).*

*  Very Large or Very Small Keq values have one direction so preferred that equilibrium is 

                       virtually impossible and thus the reverse or opposing reaction is so non-spontaneous  

                       (∆G = LARGE (+)) that the reaction runs completely in one direction with a VERY LARGE  

                       NEGATIVE DG.  

Example:  

      a) Combustion Reactions (very large Keq) – CO₂ and H₂O do not Reform the Hydrocarbon and O₂

                           thus combustion stops when we run out of the Fuel (hydrocarbon) or O₂ (whichever is the  

                          limiting reagent).

      b) Precipitation reactions (very small Keq which we call Ksp) – The solid barely dissolves thus                                    when we have ions that can precipitate the precipitation occurs until one of the ions runs out first.

         Which ever is the Limiting reagent.             

2:  Reaches equilibrium in each direction in the process with a ∆G = 0 BUT with Either Products

or Reactants Favored!   These reactions have values of ∆G that are near zero (- 30 to + 30 kJ/mol)

Chemical Reactions that are not completion reactions and thus are reversible can be manipulated to make one direction more spontaneous than the other by changing the concentrations of the reactants or products (changing the value from Q) or by changing the temperature.

                                       Le Chateliers Principle works due to the principles Q vs Keq.

Le Chateliers Principle states that when a reaction is at equilibrium (Q = Keq) and a stress is placed on a this equilibrium system the system will “shift” to the reactants side or the products side of an chemical equation that will result in “relieving”  (or undoing )the stress.  This “shift” is the initial increase in spontaneity of either the forward or reverse reactions that will work toward equilibrium until it is reestablished.  In reestablishing equilibrium, the system relieves the stress by regaining the same value of Q that equals Keq before the stress was applied (if the temperature is held constant!)

By shifting to the right, the reaction will effectively decrease the concentration of the reactants (and relieve the stress) as the forward reaction becomes more spontaneous. You must identify that the Stress is what we did (by increasing the concentration of the F₂) and Response is what reaction did to relieve the stress. The relief of the stress is INITIAL Change that the reaction does spontaneously by moving in the More spontaneous direction created by the stress.  This is just Q vs Keq!

The forward reaction becomes more spontaneous (increasingly more negative ∆G) as we increase the concentration of  F_2.  This increase in [F₂] will force the reaction Quotient (Q) which equals Keq during equilibrium to BECOME SMALLER THAN Keq and the forward reaction becomes more spontaneous and now there is a favored thermodynamic pathway for the forward reaction.  We say that reaction will ‘SHIFT TO THE RIGHT” to mean that the forward reaction is now more spontaneous.  This “SHIFT” is the RESPONSE of the reaction from the STRESS of increasing [F₂].  

END of NOTES

©MrGrodskiChemistry 2021