1 - Nutball
Measurium: Collecting and Measuring a Bunch of Bubbles
Tripp Atkins, vernona@clemson.edu
Josh Carpenter, jscarpe@clemson.edu
Jeff Moreland, jmorela@clemson.edu
Kip Walker, rawalke@clemson.edu
Group Hecuba
English 102, section 101
Friday, March 12, 1999
Abstract
The purpose of the Measurium Project is to develop an apparatus that collects and measures a gas produced by the reaction between baking soda and vinegar. By using common household materials, we constructed a three-chambered apparatus to collect and measure the gas. We repeated the experiment ten times and found that the vinegar was a the limiting reactant. By using the graphs of the data as a model, we can approximate the amount of gas produced by large or smaller reaction between baking soda and vinegar.
Introduction
The purpose of the Measurium Project is to find out how much gas would be released in the reaction of a known amount of baking soda and a known amount of vinegar. In the reaction, the sodium bicarbonate releases carbon dioxide and forms water.
HC2H3O2 + Na(CO3)2 H2O + CO2
We are to design an apparatus in which the reaction can take place with wide ranges of vinegar and baking soda, and the amount of Carbon Dioxide gas that is produced in the reaction can be collected and measured. The results of the reactions are to be plotted on a dimensional graph, from which we can construct a model to then find the amount of gas produced by any combination of reactants.
Methods
Apparatus Description
In order to collect and measure a gas, we must first develop a closed system, to prevent any lose of gas into the atmosphere. Our apparatus is a closed three chambered system that acts as a water displacement device. Due to our limited materials and time, a completely closed system was impossible. The first chamber (Chamber A) is where the reaction between the baking soda and the vinegar takes place. Chamber A is made from a plastic 20 oz. Coke bottle, and is connected to Chamber B by a small piece of rubber tubing (Tube 1). The second chamber (Chamber B) is where the water displacement takes place. Chamber B is a two-liter soda bottle filled approximately 4/5 full of water. The tube connected to Chamber A (Tube 1) enters through the top of the bottle and must remain above the water level. A second tube (Tube 2) exits Chamber B and goes into the third chamber (Chamber C). The end of Tube 2 must be below the water level in Chamber B, as close to the bottom of the bottle as possible. The other end of Tube 2 goes into the third chamber (Chamber C). Chamber C acts a collecting chamber for the displaced water. All of the joints where the tubes either enter or leave any of the chambers (Joint 1, Joint 2, Joint 3) were sealed using modeling clay. (See Figure 1.1)
Logic of Apparatus
The logic of the apparatus is as follows: the reaction takes place in Chamber A producing a gas. The gas flows up through Tube 1 and enters Chamber B. In Chamber B, the gas causes an increase in pressure, which in turn causes water to exit Chamber B via Tube 2 and enter Chamber C. The water in Chamber C will be equal to the amount of gas produced in Chamber A. (See Figure 1.2)
Experimental Procedure
We followed the following procedure when conducting these experiments. First we made a simple funnel out of a sheet of paper to make the addition of baking soda to Chamber A easier. We then added a known amount of baking soda to Chamber A using a tea spoon. Next, we measured out a given amount of vinegar using a Pyrex measuring cup. We quickly poured the vinegar into Chamber A, and then one of us placed our hand over the top of Chamber A to prevent any gas from escaping. Once the reaction stopped, we measured the amount of water that was displaced into Chamber C using a Pyrex measuring cup.
Materials
• 2-2 ft. sections of plastic tubing (Tube 1, 2)
• 20 oz. soda bottle (Chamber A)
• two-liter soda bottle (Chamber B)
• large plastic cup (Chamber C)
• baking soda
• vinegar
• water
• modeling clay (Joint 1, 2, and 3)
• table spoon
• Pyrex measuring cup
• sheet of notebook paper
Results
We collected data for ten experiments, and the experiments yielded the results found in Table 2.1. From these test results, we constructed a dimensional plot grouping the results according to the amount of baking soda used (experiments 1-4 were grouped, experiments 5-7 were grouped, and experiments 8-10 were grouped). We then constructed a plot of the grouped data according to the amount of vinegar used versus the amount of gas produced. (See Figure 2.1)
We then used a method of dimensional analysis called Rayleigh's Method to determine two dimensionless ratios for the data.
Step 1: List Important Variables
Vg = Volume of Gas
Vb = Volume of Baking Soda
Vv = Volume of Vinegar
Step 2: Set up Function
Vg = ( ki (Vb)ai (Vv)bi
Vg = k(Vb)a (Vv)b
Step 3: Substitute Dimensions
L3 = (L3)a (L3)b
L3 = L3a + 3b
Step 4: Solve for a
L: 3 = 3a + 3b
a = 1 - b
Step 5: Determine Ratios
Vg = k(Vb)1 - b (Vv)b
Vg = k (Vb) (Vv / Vb)b
Vg / Vb = f (Vv / Vb)
The first ratio is the Volume of the vinegar used over the Volume of baking soda used (Vv/Vb). The second ratio is the Volume of the gas produced over the Volume of baking soda used (Vg/Vb). See table 2.2. The data found in Table 2.2 yields the dimensionless plot shown in Figure 2.2.
Discussion
By examining the dimensional data and plot, we can see that as more vinegar was added to the reaction, more gas was produced. By looking at the dimensionless
graph of the experimental data, we can conclude that the vinegar is the limiting reactant in the reaction. Thus, the volume of the gas produced is dependant on the volume of vinegar used, since the two ratios found by Rayleigh's Method both include the volume of the baking soda used. In essence, when the volume of the baking soda is constant, the amount of gas produced is dependant on the volume of vinegar.
Appendix A
How much gas would be released if we were to use 5 pounds of baking soda and 2 gallons of vinegar?
Step 1: Find how many tea spoons are in 5 pounds of baking soda.
Step 2: Find how many mililiters are in 2 gallons.
Step 3: Construct Dimensionless Ratios
Step 4: Find Value for Vg/Vb by looking at the dimensionless plot. The approximate value for Vg/Vb is 25.
Step 5: Find Vg
Appendix B
If we wanted to fill a 1m3 container with this gas, describe the range of baking soda and vinegar quantities that would satisfy this requirement.
Step 1: Find Vg
Step 2: Estimate the ratio Vg/Vb from the ratio found in Appendix A.
Step 3: Find Vv / Vb on the dimensionless plot where Vg / Vb is 47.5. Vv /Vb is approximately 7.5.
Step 4: Claculate Vb.
Step 5: Calculate Vv
References
1. Penrose, Ann M. and Steven B. Katz. Writing in the Sciences: Exploring Conventions of Scientific Discourse. New York: St Martin's Press, 1998.
2. Blaser, Martin J. "Gastric Campylobacter-like Organisms, Gastritis, and Peptic Ulcer Disease". Writing in the Sciences: Exploring Conventions of Scientific Discourse. Ann M. Penrose and Steven B. Katz. New York: St Martin's Press, 1998.
-----------------------
Figure 1.1
Chamber A
Chamber B
Chamber C
Tube 1
Tube 2
Joint 1
Joint 2
Joint 3
Table 2.1: Shows the amount of gas collected when varying amounts of baking soda and vinegar are reacted.
|Experiment |Amount of Baking Soda |Amount of Vinegar |Amount of Gas Produced|
| |(tsp) |(ml) |(ml) |
|1 |1 |100 |650 |
|2 |1 |75 |575 |
|3 |1 |50 |395 |
|4 |1 |25 |285 |
|5 |3 |75 |450 |
|6 |3 |50 |400 |
|7 |3 |25 |250 |
|8 |5 |75 |370 |
|9 |5 |50 |120 |
|10 |5 |25 |135 |
Reaction produces gas in Chamber A
Gas
Gas
Gas
Water displaced into Chamber C
Gas pushes water out through tube in Chamber B
Figure 1.2
Table 2.2: Shows the two dimensionless ratios Vv/Vb and Vg/Vb for each experiment
|Experiment |Vg / Vb |Vv / Vb |
|1 |650 |100 |
|2 |575 |75 |
|3 |395 |50 |
|4 |285 |25 |
|5 |150 |25 |
|6 |133.3333 |16.66667 |
|7 |83.33333 |8.333333 |
|8 |74 |15 |
|9 |24 |10 |
|10 |27 |5 |
1 teaspoon of baking soda = 1.1 grams
(1 tsp / 1.1 g) X (454 g / 1 lb) X (5 lb) =
2063.7 tsp of baking soda
(3785.4 ml / 1 gal) X (2 gal) =
7570.8 ml of vinegar
Vv / Vb = 7570.8 ml / 2063.7 tsp
Vv / Vb = 3.67
Vg / Vb =25
Vg / 2063.7 tsp = 25
Vg = 51.6 L = amount of gas produced
Vg = 1m3 = 1x106 mL
Vg(A) in Appendix A = 5.16 x 105 ml
Vg(B) in Appendix B = 10.0 x 105 ml
Vg(B) is 1.9 times larger than Vg(A)
Therefore,
Vg/Vb(B) is 1.9 time Vg/Vb(A)
Vg/Vb(B) X 25 = 47.5
Vg / Vb = 47.5
1 x 106 ml / Vb = 47.5
Vb = 2.11 x 104 tsp = amount of baking soda
Vv / Vb = 7.5
Vv / 2.11 x 104 tsp = 7.5
Vv = 1.58 x 105 ml = amount of vinegar
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