Spreadsheet Simulation of a High School Dance

This Excel worksheet is designed to help you experiment with equilibrium 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" 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	k_f

Then, the forward rate is R_f = k_f[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 decrease 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	k_r

Then, the reverse rate is R_r = k_r[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 males and females are starting dancing at the same speed as the couples are stopping, then there will be no net change and 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 R_f = R_r where:

R_f is the forward rate
R_r 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 (k_f) and reverse (k_r) directions.

Load this Excel simulation onto your computer. This simulation calculates the number of people dancing and not-dancing. It draws a graph of the result. In the simulation you can change the numbers of people at the dance (type new values into the blue areas, and change the type of music to simulate changes to experimental conditions). Use the simulation¹ to do the following:

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

2. What happens if you change the type of music to a less popular variety (the simulation assumes that most people will dance to rock music, less to country, and almost no one if it is ballet music)? Changing the music type makes the forward reaction slow down, and the reverse reaction speed 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(s) in this simulation is(are) 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)?

6. Use the information you have collected in this simulation to prove that the following statement is false: "at equilibrium, there is an equal amount of reactant and product."

¹ The sizes of the rate constants in this simulation have 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.