Lecture 6 An introduction to RICE calculations An introduction to how to do equilibrium calculations using the RICE set up will be introduced This method will be used for the next two months in every conceivable chemical system to calculate system concentrations and K values Sadly you will get so used to this kind of calculation and the approximations that simplify its application that you will not remember the young lasses and lads you were when first introduced this material But trust me no matter how sophisticated you get in working equilibrium calculations it all is based on the concepts in this lecture But first time out for a big picture reminder that equilibria is just thermodynamics nFE G Electrochemistry Thermodynamics RTlnK Equilibria In comparing these formulas think of a reaction as falling down either a free energy hill a gradient of energy release or a concentration change that drives the reaction toward equilibrium at the bottom of the hill A B AAA AAA BBB BBB A B G Q B A Q changes from Q 0 K B A Q changes from BB AA K Equilibrium Q K In the picture note that whether you start with all A or all B or somewhere in between you can find a Q value When Q is less than K the reaction shifts from left to right When Q is greater than K the reaction shifts from right to left Q When Q reaches K you are at equilibrium Another way to present this concept is by graphing the relative amounts of the reactants A and B in this case to show on the left side the values when A is in excess and Q K in the middle the time during which Q K and there is no change in the rate of A or B forming on the right side the values when B is in excess and Q K Left side Q K Q K Right side Q K Right side You will learn that finding whether Q is greater or less than K is a useful trick to understand what a reaction is doing Generalized treatment of equilibrium calculations The RICE diagram Rather than draw a graph of concentrations why not put them in an array Shown below is the general form of a reaction in which compounds A and B react to form compounds C and D Underneath the reactions a matrix is created in which we can put various concentrations at different times The RICE expression in which RICE is an acronym for the following R I C E Reaction Initial Concentration the non equilibrium or Q values Change in concentration from initial to equilibrium Equilibrium concentration the values used to calculate K Reaction Initial Change Equilibrium aA CA CA A A bB cC CB CC CB B CC C B C dD CD CD D D data used to calculate Q data used to calculate K Note that by convention we let C values be the concentrations not at equilibrium and we let concentration at equilibrium Also note that we can use the values in the boxes to calculate Q and K Keq C c D d A a B b Q CCcCDd CBbCAa And the game we play for the rest of the semester is to make up chemistry questions in which we are provide numbers for K Q and parts of the array and then solve for unknowns Below are some general categories of equilibrium problems We will use the following equilibrium as an example A famous reaction 3H2 N2 2NH3 and form the RICE expression below with a given K value Reaction 3H2 N2 2NH3 Initial C H2 C N2 C NH3 Change C H2 H2 C N2 N2 C NH3 NH3 Equilibrium H2 N2 NH3 With K NH3 2 H2 3 N2 3 8 data used to calculate Q data used to calculate K Problem Type 1 The simplest case Everything is already at equilibrium What is Keq if N2 0 1M H2 0 5M and NH3 0 057M How do you do this problem Stick the values into the RICE expression where they belong at equilibrium and then substitute them into the equilibrium expression K and solv Reaction 3H2 N2 2NH3 Initial C H2 C N2 C NH3 Change C H2 H2 C N2 N2 C NH3 NH3 Equilibrium 0 5M 0 1M 0 057M data used to calculate Q data used to calculate K K 0 057 2 0 5 3 0 1 3 8 Guess what you get to do this really simple kind of problem once on a quiz to feel good about yourself And then never again high school is over Problem Type 2 How to manipulate your way around the RICE array A fun kind of problem to see how well you can deal with the stoichiometric relationships and the use of change of concentration in the middle row Given K 3 8 and N2 0 3 H2 0 2 CNH3 0 04 fill in rest of chart Step 1 find the NH3 from K calculation Reaction 3H2 N2 2NH3 Initial C H2 C N2 0 04 Change C H2 H2 C N2 N2 C NH3 NH3 Equilibrium 0 2 0 3 Step 1 find from K K 3 8 x2 0 3 0 2 3 0 035 Step 2 Find the C NH3 NH3 term which is 0 04 0 0035 Reaction 3H2 N2 2NH3 Initial C H2 C N2 0 04 Change 0005 C H2 H2 C N2 N2 Equilibrium 0 2 0 3 0035 Step 3 Use Stoichiometry to find the rest of the second row Reaction 3H2 N2 Initial C H2 C N2 Change 0075 0025 Equilibrium 0 2 0 3 2NH3 0 04 0005 0035 Step 4 Perform a little math to find the starting concentrations for CH2 and CN2 Reaction 3H2 N2 Initial 1925 2975 Change 0075 0025 Equilibrium 0 2 0 3 2NH3 0 04 0005 0035 A few things to note Because NH3 was decreasing in amount in the first step the H2 and N2 must have been increasing in other words the reaction was going in reverse and must have started with Q K This kind of problem rarely shows up on tests but if you can understand it you are going to be a whiz at working RICE problems Problem Type 3 The real problem Given all of the initial concentrations and K find the equilibrium concentrations Why is this the real problem Because it is what you would do in real life You know the initial concentrations because you are the one who put the stuff in the container and K values are constants found in tables just like thermodynamics values If I start with 0 1M NH3 how much N2 do I have at equilibrium Reaction 3H2 N2 2NH3 Initial 0 0 0 1M Change C H2 H2 C N2 N2 C NH3 NH3 Equilibrium H2 N2 NH3 note that we assume 0 for the concentrations not mentioned what we want to calculate So what to do now How about replacing the six unknowns in the second and third rows with values …
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