- Physical Chemistry I
Spring 2012, Unique 52135
Lecture Summary, 26 March 2012
Equilibrium: We have already seen
that the point of equilibrium in any reaction is defined by delta(G)
= 0 and where the composition of the system has achieved values
determined by the equilibrium constant, Kp. We now
need to develop a method for determining at what value of the
reaction coordinate from 100% reactants to 100% products equilibrium
occurs. We will call this point z(eq). There
is a fairly systematic procedure for doing this:
1. Make sure your reaction equation has correct stoichiometry.
2. Use tables to determine delta(Grxn0 ) and Kp. It would also be helpful to write down the equation for Kp from the stoichiometrically balanced formula at this point.
3. Set up a table describing all components (reactants and products) in the reaction.
4. Determine the initial conditions (number of moles of each species present at the start of the reaction).
5. Determine the composition at equilibrium in terms of z(eq). Reactants will lose moles and products will gain moles.
6. Determine the total number of moles of the system. This number is a constant and can be calculated at any z, but it is most helpful to calculate this at z(eq).
7. Determine the mole fraction at equilibrium of each species.
8. Determine the partial pressure at equilibrium of each species.
9. Plug these partial pressures into your equation for Kp. If you have done everything correctly, you will now have an equation that relates Kp to z(eq) and the total pressure of the system.
10. Solve for z(eq). This might require making some simplifying assumptions in order to solve the problem analytically. If Kp << 1, assume that z(eq)~0. If Kp >> 1, assume that z(eq)~1. If at this point one of these assumptions makes your solution undefined, go back to step 1 and flip the reaction.
11. Plug in numbers and determine z(eq).
Really quite straightforward.