1. CHEMISTRY 2000 Topic #3: Thermochemistry and Electrochemistry – What Makes Reactions Go? Spring 2008 Dr. Susan Lait

2. 2 Free Energy Change and Equilibrium We saw that the free energy change for a reaction under any conditions (  r G) can be calculated from the free energy change of the same reaction under standard conditions (  r Gº): where Q is the reaction quotient: We also know that: The forward reaction is spontaneous if ____________ The reverse reaction is spontaneous if ____________. What if  r G = 0?

3. 3 Free Energy Change and Equilibrium When  r G = 0, we can say that: Which rearranges to give: But what is Q at equilibrium? So, we can say that:

4. 4 Free Energy Change and Equilibrium If we know the equilibium constant for a reaction, we can calculate its standard molar free energy change: If we know the standard molar free energy change for a reaction, we can therefore calculate its equilibrium constant: Note that these equations refer to  r Gº (for standard conditions) NOT to  r G (which is ZERO at equilibrium!)

5. 5 Q vs. K So, what’s the difference? Consider a very generic equilibrium reaction: When does Q = K? When is Q < K? When is Q > K? and

6. 6 Free Energy Change and Equilibrium Now, consider a real reaction, the dimerization of NO 2 : Calculate the equilibrium constant for this reaction at 25 ºC.

7. 7 Free Energy Change and Equilibrium Is the dimerization of NO 2 spontaneous at 25 ºC if the partial pressure of NO 2 is 0.4 bar and the partial pressure of N 2 O 4 is 1.8 bar?

8. 8 Free Energy Change and Equilibrium: Acids The acid ionization constant, K a, is the equilibrium constant for the reaction in which an acid ionizes. As an equilibrium constant (and therefore based on activities), K a has no units. e.g. In CHEM 1000, we used pK a as a measure of strength of an acid. An acid with a low pK a was _______________ than an acid with a high pK a. The pK a value for an acid comes from its acid ionization constant: So, we can also say that an acid will be _________________ than another acid whose K a value is smaller. (Even a “big” K a value is pretty small. K a values range from about 10 -50 to 10 10.)

9. 9 Free Energy Change and Equilibrium: Acids Calculate the standard molar free energy of formation for HF (aq).

10. 10 Free Energy Change and Equilibrium:Solubility The solubility product, K sp, is the equilibrium constant for the reaction in which an ionic compound dissolves in water. Like all other equilibrium constants, K sp has no units. e.g. Calculate the solubility of lead(II) iodide in water at 25 ºC. Solubility is reported in #moles of solid soluble in 1L water.

11. 11 Free Energy Change and Equilibrium:Solubility

12. 12 Free Energy Change and Equilibrium:Solubility The problem with simple K sp calculations is that they almost never give good numbers. Why not? Most of the time, there are multiple equilibria that must be considered, but the K sp expression only accounts for one. When PbI 2 is dissolved in water, two complex ions also form: In the case of PbI 2, the “simple” K sp calculation gives almost the same answer as a proper calculation factoring in both complex ions because the K f values for both complex ions are relatively small (compared to some K f values in the 10 30 range). In many systems, however, the complex ion formation is significant enough that it must be accounted for or the K sp calculation will give very poor values.

13. 13 Free Energy Change and Equilibrium:Solubility Complex ions are not the only factor complicating solubility calculations. What equilibria would you have to consider if you wanted to calculate the solubility of sodium carbonate in water? How would you increase the solubility of sodium carbonate in water?