Entropy (and free energy)
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I was doing some practice papers and there was one question that asked for an interpretation of delta Stot. It was a large positive number, 8000, and from what I understand all that entropy suggests is whether the reaction is spontaneous or not, i.e. if total entropy is positive then it is spontaneous. However, the answer was that "the reaction goes to completion". Could you explain that and suggest anything else a high entropy value means for a reaction, what a high equilibrium constant means for a reaction and what a high rate constant means for a reaction? Thank you.
Corrie writes ....
Total entropy change not only indicates the spontaneous direction of a reaction, but also the extent to which it will go. The larger the positive value of the total entropy change, the further the reaction will go towards the products.
When it comes to the equilibrium constant and rate, you must first make a clear distinction between 'how far?' and 'how fast?'. Quantities like total entropy change, the equilibrium constant, something called free energy (Delta G) and the EMF of a cell (if your reaction could be represented by a reaction in an electrochemical cell) are all linked mathematically and can all can be used to indicate 'how far' a reaction will go until it reaches equilibrium.
That doesn't mean to say it will go when you mix the reactants together. That depends on the rate.
For instance, a mixture of hydrogen and oxygen, when mixed, appears to do nothing because the rate at room temperature is infinitely slow. The positive value for the total entropy change, the large value of K and the EMF (for a fuel cell using hydrogen and oxygen) etc will all tell us that this reaction can go in the direction of water, and the size of these quantities will also tell us that the reaction will go to completion, i.e. the equilibrium will be far over to the right. Add a lighted matched or catalyst to a mixture of hydrogen and oxygen and you will see (and hear!) evidence for this spontaneous direction!
In many textbooks there are tables relating values for these quantities to the extent of an equilibrium.
Thus for total entropy change values of -200 J mol-1 K-1 or less, an equilibrium would lie completey over to the left, i.e. the reaction cannot happen. For a value of about -40, the equilibrium would lie predominantly on the reactant side, for a value of + 40 it is predominantly on the product side, and for values above +200, the reaction would go to completion.
The corresponding values for K would be 10-10, 10-2, 102,and >1010.
These values tell you how feasible a reaction is, not whether it will happen at room temperature. That depends on the rate, which in turn depends on the rate constant, which in turn depends on the activation energy! The higher the activation energy, the smaller the rate constant and the slower the rate would be, irrespective of what the total entropy change value, or K, told you about the direction and how far the reaction could go.
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updated: 21 January 2008
