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How far will chemical reactions proceed?
The equilibrium constant can be calculated from the standard free energy of reaction. This means that we can obtain tabulated values and use them to make predictions about which reactions are possible. Moreover, we can predict the extent of reaction. This means that we can determine what fraction of the reactants is converted to products at equilibrium. This is best done using a systematic approach that is based on a reaction table. In the table we will have three rows, Initial, Chance and Equilibrium. We can call this an ICE table to help think of how to organize the information. The initial row is simply the initial value of the concentration of each reactant and product. The change is the amount of each product that reactants in the form of an unknown (e.g. x) with appropriate stoichiometric coefficients to multiply the unknown value. We can call x a progress variable. Finally, we sum the initial and change rows to give the equilibrium row. Then we substitute the expressions from the equilibrium row into the equilibrium constant. We must be sure to raise each expression to the appropriate power. In general this expression can give rise to a polynomial that cannot be solved analytically. We will avoid these applications in the problems and focus on cases where the polynomial is either easily factored or is a quadratic or linear function. THe concept is the important aspect of these problems. We can always solve higher order polynomials using a computer once we understand the principle of how to apply a progress variable.
Calculation of a progress variable
In theory any of the reactants or products could be chosen to give a progress variable. Often it is most convenient to choose a reactant species and in addition to select the species with the lowest value of the stoichiometric ceofficient. Then we must multiply the progress variable by the appropriate stoichiometric ratio for each species in the table. It is easiest to work with whole numbers. This is the major consideration that motivates our choice of progress variable. Of course, it does not need to be called x, but the choice must make it clear that it is an unknown and that we will determine it by solving the polynomrial obtained by substitution into the equilibirum constant..
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