What Little and Big Mean for Equilibrium

As we discuss solving equilibrium problems, we will be using the terms big and little, and it is therefore very important that you understand what those terms mean in this context. We’ll look at what the terms mean for the equilibrium constant (K), as well as the amount of change in a system reaching equilibrium (x).

Equilibrium Constant Size

Since the equilibrium expression is always written with the products on top of the fraction and the reactants on the bottom, the value of K tells us the relative amounts of those two at equilibrium. A system with a large K value has more products than reactants at equilibrium. A system with a small K has more reactants than products.

How big is big and how little is little?

When chemists say that a reaction has a large K, we usually mean that the value of K is greater than 104. When we say that the value of K is small, we usually mean that the value of K is smaller than 10-4. That means that, to a chemist, a value of 0.0005 is middle-ground, as is a value of 4500.

Change (x) size

When  chemists label an equilibrium problem as a “little x problem” they mean that the value of x is so small that it has virtually no effect on measurable concentrations (although it will always have an effect on a value of 0). This is really a matter of significant figures. Here’s what we mean:

Imagine the equation     y = 1.50 + 2x.      If     x=0.3     then     y = 2.10.     

If, instead     x = 0.0003,     then     y = 1.5006,     BUT after applying the significant figure rules, we would end up with     y = 1.50.     The value of x was small enough that it has no measurable effect on y

So, a “big x” is any value that is large enough to matter after sig fig rules are applied.

So, in the case of     y = 1.50 + 2x,     a value of     x = 0.006     would be “big” because the answer would be     y = 1.51.

So, big (in this case) does not mean BIG, it means significant

If this doesn’t make sense, let’s try a human example:

Imagine that you are walking down the street and see Michael Jordan (as of today, he is worth 2.1 billion dollars). If, as you watch, he accidentally drops a dollar, his net worth doesn’t change. He is still worth $2.1 billion. (Of course his net worth does actually change, but that amount of money is SO small compared to his net worth that no one cares.) That single dollar is insignificant to Jordan's net worth.

A moment later, you see a homeless person find the dollar. That same dollar that meant nothing to Michael Jordan might save the life of a broke, hungry person on the street. 

In other words, the “size” of that dollar depends entirely on the number you are subtracting it from (2.1 billion) or adding it to (0).