Keq = [P]/[R]
Why are they using the amounts of reactants left over in the equation?
Equlibrium constant
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Keq = [P]/[R]
Why are they using the amounts of reactants left over in the equation?
Think about what an equilibrium constant is. Too often students think too superficially and are quick to apply formulas. An equilibrium constant is some number that gives you the relative concentrations of products and reactions at equilibrium. Okay, now define the process that's occurring above. You have some A and some B and you mix them together to form C. After you have done the mixing, the system has reached equilibrium. So at equilibrium some A has reacted with some B to form 3 moles of C. Given the chemical equation, it's relatively straight forward to work out that 3 moles of A reacted and 6 moles of B reacted.
Now, the key question is: what are the species' concentrations at equilibrium? Well, you have 3 moles of C - that's given. If you have 3 moles of C, you also have 3 moles of D. Now the interesting question is how much you have of A and B at equilibrium. Well, the 3 moles of A and 6 moles of B reacted to form C and D! In other words, they're not there anymore! At equilibrium, you have 2 moles of A left and 6 moles of B. Thus, the correct Keq expression is: 3*3/2*6^2.
Now, the key question is: what are the species' concentrations at equilibrium? Well, you have 3 moles of C - that's given. If you have 3 moles of C, you also have 3 moles of D. Now the interesting question is how much you have of A and B at equilibrium. Well, the 3 moles of A and 6 moles of B reacted to form C and D! In other words, they're not there anymore! At equilibrium, you have 2 moles of A left and 6 moles of B. Thus, the correct Keq expression is: 3*3/2*6^2.
Thanks!
I have another related question.
Say that the system was not at equilibrium, then we calculate Q using a similar formula, Q = [P]/[R]. So if we are asked to calculate Q, they would have to tell us how much of the reactants have reacted by that given point in time so we can determine the ratio of [P]/[R] present at that given point. This would also mean that Q would change with time in the reaction, increasing as we reach equilibrium. Am I correct?
I have another related question.
Say that the system was not at equilibrium, then we calculate Q using a similar formula, Q = [P]/[R]. So if we are asked to calculate Q, they would have to tell us how much of the reactants have reacted by that given point in time so we can determine the ratio of [P]/[R] present at that given point. This would also mean that Q would change with time in the reaction, increasing as we reach equilibrium. Am I correct?
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Q would not necessarily have to increase. The general rule is that Q will approach K: if Q < K (i.e. more reactants than products), then Q will increase, as you say. On the other hand, if Q > K (i.e. more products than reactants), Q will decrease.
Think about it this way - don't think about Q as a number to be calculated. Think about what it means. Q measures the distance some system is from equilibrium. So for instance, imagine bringing hot food into your room. At first, it's really hot and the room is much colder, relatively speaking. So you're far from thermal equilibrium. If there was such a value as Q and K for thermal equilibrium, Q would be very far from K - the two values would be very different.
So think of Q as a simple measure of how distant a system is from equilibrium. The farther it is from equilibrium, the more Q will differ from K. The direction it differs depends on the direction the system differs from equilibrium. If there are too many products as compared to equilibrium, Q > K and vice versa. K is really just a special value of Q - the value of Q when the system is at equilibrium.
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Fantastic! In general this Q highlights the cleverness of the MCAT. The Keq is always a ratio of products to reactants, which must always involve ANY products or reactants than can be expressed as concentration (i.e. no solids or liquids). The subtlety of having you determine the reactant concentrations as amount left rather than just giving them to you illustrates how the MCAT rewards critical thinking WAY MORE than plugging and chugging.
Good luck!
