What Happens in an Equilibrium?
 
This worksheet is designed to help you experiment with equlibrium calculations.  It is based upon an analogy to a high school dance.  The "equation" at this dance is:  

1 male + 1 female  1 dancing couple

The forward reaction
How fast this reaction proceeds in the forward direction depends on: 
Condition Symbolized by:
  • the "concentration"2 of boys present

[boys]

  • the "concentration" of girls present

[girls]

  • the "rate constant" which is a number that depends on how much the people want to dance

kf 

Then, the forward rate is Rf = kf[boys][girls]
At the start of the dance the [boys] and [girls] will be very high so the rate of the forward reaction is high.  After a period of time, the [boys] and [girls] will decrease as they form dancing couples, so the rate of the forward reaction will derease with time.

 
Of course, if the couple wishes, they may decide to stop dancing, so then the equation would be:
 

1 male + 1 female  1 dancing couple

The reverse reaction
How fast this reaction proceeds in the reverse direction depends on: 
Condition Symbolized by:
  • the "concentration" of dancing couples

[couples]

  • the "rate constant" which is a number that depends on how much the people don't want to dance

kr

Then, the reverse rate is Rr = kr[couples] 
At the start of the dance the [couples] will be very small so the rate of the reverse reaction is slow.  After a period of time, the [couples] will increase, so the rate of the reverse reaction will increase with time.

 
For convenience, we can combine the two equations into one, to show that both processes go on at the same time:
 

1 male + 1 female  1 dancing couple

The equilibrium reaction
At the dance there will always be some couples starting to dance, while others decide to quit. At some point in time, there will be just as many males and females starting to dance, as there are dancing couples deciding to stop. 

If the number that are starting dancing (the forward rate), and the number stopping (the reverse rate) are the same, then there will be no net change -- an equilibrium is reached. The double arrow is used to symbolize equilibrium. 

Equilibrium is achieved when the rates of the forward and reverse reactions become equal 

At equilibrium Rf = Rr where Rf is the forward rate, and Rr is the reverse rate. 

 
The rate of the forward and reverse reactions depend on the "experimental conditions", such as the type of music being played.  These conditions change the rate constants -- in this case the percentages of people who will start or stop dancing -- in the forward (kf) and reverse (kr) directions.

Load this Excel simulation (if you right click on the link, you can open the spreadsheet in a new window so that you can toggle back to these questions).  This simulation calculates the number of people dancing and not-dancing, and plots the result.  Use the simulation1 to do the following:

1. Observe the results when you have 150 boys, and 200 girls.  Explain why the graph has the shape it does.

2. What happens if you change the type of music to a less popular variety, so that the rate of the forward reaction slows down, and the reverse reaction speeds up?  Explain what happens to the shape of the graph compared to its shape in question 1.

3. The equation has a ratio of 1 male : 1 female : 1 dancing couple.  Use data from the simulation to prove that this ratio does not tell you the number of people present at the dance, or the number of dancing couples.  What factor in this simulation is controlled by the ratio 1 male : 1 female : 1 dancing couple?

4. Change the number of boys to 200, the number of girls to 200 and the number of dancing couples to 0.  What happens to the number of boys, girls, and dancing couples at equilibrium?

5. Change the number of boys and girls not dancing to 0, and the number of dancing couples to 200.  Compare the number of boys, girls, and dancing couples at equilibrium now to what it was in question 4.  What do you notice about an equilibrium if you start on the products side (the dancing couples) as opposed to starting on the reactants side (the boys and girls not dancing)?



Copyright © 1998 - 2008 David Dice


1 The size of the rate constants in this simulation has no real meaning.  They were simply selected to give a reasonable graph in an appropriate time frame.  The calculations will fail if the number of male or females at the dance goes above 400.

2 Square brackets are used in chemistry to indicate concentration, usually in mol/L.   That unit though has no real meaning in this simulation.  Here the concentration would be the number of people divided by the size of the room.  Since the room has a fixed size, using the number of participants is just as meaningful.