1.1: Part A- Percent change

Section 1: Calculating % Change and Difference and Diffusion

Part A: Calculating Percent Change and Percent Different

Percentage Different and Percent Change are different terms with different calculations. In general, you will compare before and after scores within the same individual with percent change. You will compare two scores from different sources with % different. This is not always the case, but most often it is the correct procedure.

In statistics, they will have different T-tests for each example (within vs between subjects T-tests). The percentage different says nothing about the statistical significance, only the magnitude of change or difference- relative to the values. Thus, two really large numbers with small differences will have very small % differences, but two really small numbers with that same small difference would be much larger.

A. Percent change will be measured by (After- Before)/ Before. Depending on the variable it may decrease or increase as an improvement. For example, if it was time to finish a given running distance the time would decrease with improvement and be represented with a negative number.

If I ran a mile in 8 minutes and 30 seconds before training, and 8 minutes flat after it would be easiest to calculate in seconds or minutes. It would be (8.0 minutes - 8.5 minutes) divided by 8.5 minutes.

Thus, the negative number here represents an improvement. -0.50/ 8.5= -0.0588

Take -0.0588 and multiply by 100 to get percentage. 0.0588 x 100= 5.88 and round to the number of significant figures you need- in this case two significant figures gives -5.9 % change.

(Look up rules for significant figures. In short when multiplying or dividing use the smallest number of digits for any value in the set. For addition and subtraction use the least accurate number).

Now if I wanted to compare two racers in a mile run, I would want the % difference in the two times.

B. Percentage different would be the same numerator of 0.5. The denominator is now the average of the two values. So add the values- 8.5 + 8.0 = 16.5. There are two values so 16.5/2= 8.25 min.

Now 0.50 divided by 8.25 equals 0.0606 or 6.06% or 6.1% different with two significant figures. In this case, the percentage difference is greater than the percent change but only by a little. Rounding down for numbers 0-4 and round up for 5-9. See other sources for more information on significant figures.

Please Note: When using time, you must always convert seconds into hundredths of a minute if the final expression is in minutes. The units will not change the answer for percentage difference. If we were to use seconds for the same calculations:

8 x 60= 480, and 8 x 60 + 30 seconds = 510. Divide by the original- 510 you get 30/510= 5.8%

What about if you were measuring a value that increases with training.

Say I could do 21 push-ups before training and 30 after. So after- before = 30-21= 9

Now, I divide by before or 21. Now, 9/21 is = 0.42857 so rounded to 2 sig figs à 43%. If I was comparing two individuals, I would use the same difference or 9. But now 21+30 = 51,

Now divide by 2, you get 25.5. Final calculation is 9/25.5= .3529 or 35%. Note the percent change is larger than the percent different here because 25.5 is larger than 21.

Part B: Diffusion- Temperature and Density/Concentration Effects

Chemistry is literally the properties and interactions of molecules with one and another. Molecules will move or be transported in many different ways. One of the critical processes in the human body, as well as all living creatures, is diffusion. There are two main types of diffusion- simple and facilitated. Simple diffusion can happen anywhere, but it often takes place across some membrane. Facilitated diffusion does require a membrane that has a protein channel or carrier to aid the diffusion.

In diffusion, the particles will move from high concentration to low concentration. It will continue to occur until an equilibrium has occurred between the two sides of the membrane or within a given compartment. Equilibrium is noticed when the forward and reverse movement is equal.

I. The rate of diffusion can be altered by several factors such as temperature, pressure, the viscosity of the media, the concentration differences. If is across a membrane, the surface area, membrane thickness, and permeability to that molecule or substance will be factors. The first part of this experiment will use 3 temperatures of water and food coloring.

A. First you will need 3 clear glasses of water. Tap water is fine.

B. Whatever amount of water you have in each glass (about 3/4^th full) make sure all glasses have about the same amount. Roughly 300 milliters is fine.

C. You will need to heat the water to almost boiling, have another glass in the freezer for about 10-15 minutes, and have the third just sitting out.

D. Add about 5 drops of food coloring to each glass as quickly as possible. If it takes more than 5 seconds to add the food coloring record this difference and take it into account. Be sure not to disturb the glasses or stir the water, which will cause the water to mix with the food coloring.

E. Record the start time.

F. Record the time of each temperature to almost fully disperse (spread fully and evenly).

II. The second part of this experiment will look at the difference between 3 waters with varying amounts (concentrations) of sugar in them. By adding more sugar, you are increasing the density and in this example the viscosity of the solution. The term viscosity refers to the internal resistance of a solution to change in shape or how substance flows. High viscosities will not flow easily, and low viscosities will flow easily. Density is the weight per volume. The density of pure water is 1 gram per milliliter. Adding sugar will increase it above 1 gram/ml. The conditions here are none, a moderate amount (5 teaspoons), and a large amount (10 teaspoons). The importance here is to see a difference between the conditions.

A. Again, fill all glasses to the same level you did in the first experiment (about 500 mls.).

B. This time all glasses will have water at room temperature.

C. Add 5 heaping teaspoons of sugar to the second glass and stir thoroughly to wear almost no sugar is visible. Salt may be used instead of sugar as well.

D. Add 10 heaping teaspoons to the third glass and mix thoroughly again. If you are not getting almost complete dissolution of the sugar add more water to all glasses and stir the 2^nd and 3^rd.

E. Add the food coloring again and note the time or start the stopwatch (on most smart phones).

F. Record the times to fully dissociate again.

Section 1- Worksheet 1:

Table 1: Effect of Temperature on Diffusion

Temperature	Start time	Finish time	Total diffusion time	% Difference
Hot
Room
Cold

*Note: the shortest diffusion will have no % difference. Use- (longer – shorter)/shorter

Table 2: Effect of Concentration on Diffusion

Concentration	Start time	Finish time	Total diffusion time	% Difference
No sugar
5 teaspoons
10 teaspoons

Section 1- Questions

1. Which temperature was the first to diffuse or dissociate? Which was last?

2. What was the % difference between conditions?

3. Can you explain why this was the result?

4. What caused the differences in diffusion?

In the second experiment:

5. What happened to the density of water as we added more sugar or salt?

6. Does the density of the water increase with more sugar or salt in it?

7. How did density affect the diffusion rate?

8. If we had a cell phospholipid bilayer membrane, would a lipid soluble or water-soluble molecule diffuse through more quickly or more easily? Why? (look it up)