# Experimental data analysis

1. Record your data table of temperature vs. volume here.

2. Construct a graph by hand or using a spreadsheet program, plotting the values of temperature on the x-axis and air volume on the y-axis.

Initial temp. 21 Deg C, Vol. 100mL

Ice -3 Deg C, Vol. 91.84mL

Water 100 deg. C, Vol. 126.87mL

Gas Piston Removed: Temp. Deg. C Vol. mL

100 126.87

95 125.31

90 123.48

85 122.11

80 120.21

75 118.39

70 116.58

65 115.08

60 113.31

55 111.66

50 109.91

45 108.21

40 106.49

35 104.76

30 103.08

25 101.37

21 100

3. Draw a straight line through the points.

4. Determine the slope of the line and record its value here. Be sure to include the units for this slope value. If you are using a spreadsheet program, use its built-in function to find the slope of the straight line. In Excel, use the function SLOPE (y-values, x-values).

5. Is the volume of air proportional to its temperature?

Assignment 1 of Procedure 2

1. Record your table of measured data, air volume and pressure in atm. Add a third column for the value of

(1 / pressure), with units of "reciprocal atm" or 1/atm.

Gas Vol. mL Pressure atm Liquid Vol. mL

150.00 1.ooo 0

130.00 1.154 20.00

116.00 1.364 40.00

90.00 1.667 60.00

70.00 2.143 80.00

50.00 3.000 100.00

2. Construct a graph by hand or using a spreadsheet program, plotting the values for (1 / pressure) on

the x-axis and air volume on the y-axis.

3. Draw a straight line through the points.

4. Determine the slope of this line and record its value here. Be sure to include units for this slope value. If you are using a spreadsheet program, use its built-in function to find the slope of the straight line. In Excel, use the function SLOPE (y-values, x-values).

5. Is the volume of air proportional to its "reciprocal pressure", i.e., inversely proportional to its pressure?

Assignment 1 of Procedure 3

1. For this part of the experiment, the temperature is the room temperature of 21C and the pressure is the room pressure of 1 atm. The gas constant, R = 0.08 = 0.082057 (L*atm)/(K*mole), so make sure to convert your temperature value to Kelvin. For each of the 4 total volumes of air, record and calculate the following:

Initial Mass of Gas Piston: 111.420g before 3 more increments of 50 mL of air

(a) the mass of air (g):#1 111.480g

#2 111.540g

#3 111.599g

#4 111.659g

(b) the volume of air (L)

(c) the calculated MW of air (g/mol)

Average the four values for the MW and report it here.

2. If you look up the composition of air, you will find that it is composed of:

N2, 78.084%

O2, 20.947%

Ar, 0.934%

CO2, 0.033%

There are some other gases present, but in very small quantities that do not influence its overall properties. The percentages shown above are by VOLUME.

Given the composition of air, it is possible to calculate a theoretical value for its apparent molecular weight as the weighted average of the individual components. The formula for this is:

MW(air) = (MW(1) * Volume-Percent(1) + MW(2) * Volume-Percent(2) + ...) / (100)

Note that the molecular weight of a component is for the entire molecule of the component, not the individual atom.

Calculate and record the theoretical molecular weight using the four components listed above.

3. How well does the theoretical value for the molecular weight of air compare with your experimentally determined value? Find the percent deviation according to:

% deviation = 100 * (experimental MW - theoretical MW) / (theoretical MW)

4. The molecular weights discussed here are for DRY air, but air often has some water vapor mixed in with it. Would you expect the apparent MW of non-dry air to be less or more than for dry air? Explain.

THIS MAY HELP

Procedure 1

1. This procedure will test the proportionality of volume and temperature for a sample of air.

2. Take a gas piston from the Glassware tab of the Labware Shelf and place it on the Workbench.

3. Fill the piston with 100 mL of air from the air cylinder on the Chemicals Shelf.

4. Take a thermometer from the Tools tab of the Labware Shelf and drop it on the gas piston. On a piece of paper record the first set of data values: room temperature and a volume of 100 mL.

5. Take a constant temperature bath from the Tools shelf and drop it directly onto the gas piston. Let the air inside of the piston cool until it reaches a steady temperature. (The default setting of the constant temperature bath is "ice".)

6. Open the Data window, then click on the gas piston to see the volume inside. Click on the "pushpin" to lock the Data window to the gas piston.

7. Record the temperature and volume of the air inside the gas piston.

8. Open the Properties window, click on the bath and set its temperature to 100C.

9. When the air temperature stabilizes at its highest temperature, record the volume and temperature of the air.

10. Remove the gas piston from the bath and watch it cool down. Record the temperature and volume of the air for every change of temperature of 5C or so.

(Note: Write fast, the temperature drops quickly from 100 Deg C down to 40 Deg C, then more slowly to the lab ambient temperature.)

Procedure 2

1. This procedure will test the inverse proportionality of volume and pressure for a sample of air.

2. Clear the workbench by dragging all tools and glassware to the recycling chute.

3. Take a 150 mL Erlenmeyer flask from the Glassware tab of the Labware Shelf and place it on the Workbench.

4. Open the Properties window, click back on the flask, and close the flask with an airtight stopper.

5. Take a pressure gauge from the Tools tab of the Labware Shelf and drop it on the flask. Click on the pressure gauge and in the Properties window select "atm" as the units of measurement. The pressure gauge should now read 1.000 atm.

6. Open the Data window and click back on the flask. You will see that the primary components of air fill the flask's volume. Record the first set of data as 150 mL and 1.000 atm.

7. Click the pushpin button on the Data window to lock its display to the flask.

8. Add 20.00 mL of water to the flask. (This is added as if injected right through the closed stopper.)

9. Record the gas volume and pressure. The gas volume is the total volume of the flask minus the volume of the water. (This gas volume is displayed in the Data window.)

10. Continue to add water in 20.00 mL increments until the liquid (water) volume reaches 100.00 mL. Record the gas volume and the pressure for each increment of water added.

Procedure 3

1. Clear the workbench by dragging all tools and glassware to the recycling chute.

2. Take a new gas piston from the Glassware tab of the Labware Shelf and place it on the Workbench.

3. Drag a balance from the Tools tab of the Labware Shelf and drop it directly on the gas piston. Record the mass of the empty piston.

4. Leave the gas piston on the balance and fill the piston with 50 mL of air from the air cylinder on the Chemicals Shelf. Record the mass of the piston with air.

5. Add 3 more increments of 50 mL of air, and record the total mass of the gas piston and air for each added increment.

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#### Solution Summary

The solution shows how to analyze lab results regarding the relations between pressure, temperature and volume in ideal gas.

SPSS Experimental Design Analysis

1. An experiment was conducted to study the effects of different types of background music on the productivity of bank tellers. Two factors were studied, tempo of the music (A; slow, medium, and fast) and the style of music (B; instrumental, or vocal). For each combination of the two factors 4 branches of the bank were randomly selected, and 5 tellers were randomly sampled within each branch. Then a productivity measure was calculated for each teller at the end of a one-week period. The data is in the file teller.csv

Analyze this data to determine if there is any difference in the mean productivity of tellers by music tempo and/or type. Compare each treatment combination (e.g., A_1 B_2) with every other treatment combination using an appropriate method to handle the family-wise error rate. Produce any relevant figures that you feel might help explain the relationships present in the data.

2. A test preparation company is interested in comparing two preparation program (on-line versus in-person) on how well they prepare students for an admissions test. Ten subjects were randomly assignet to one of the two preparation programs and measured at the end of each of 4 weeks. The data is presented in the table below: (see attached).

Use this data to determine if there is a significant difference in test scores by test preparation method. Describe the tren in test scores over the four weeks of the study (e.g., is it linear, quadratic, etc.). Is the trend the same for online and in-person test preparation programs? Use your proposed model to determine if there are significant differences in the mean scores of In-person and online participants at Week 4. Produce relevant plots to help describe your analysis and to evaluate the assumptions of the model.

3. The data set Reading.csv includes data from a study comparing three different reading curricula for third grade students: (1) comprehension-focused; (2) decoding-focused; and (3) a balanced curriculum. In particular the study was interested in how students' comprehension of reading passages differed across the three curricula. Five schools were randomly selected for each of the three curricula (15 schools in total). After administering the curricula over the course of a year the students' state reading test scores were collected. The data set Reading.csv contains the following information:

- Column 1: Treatment conditions: (1) comprehension-based; (2) decoding-focused; and (3) balanced.

- Column 2: School identifier - this is number between 1 & 5 indicating which school in the treatment condition the student belongs to.

- Column 3: Class identifier - a number between 1 & 3 indicating which classroom within the school a student belongs to.

- Column 4: Student identifier - a number between 1 & 25 indicating the students ID number within the classroom.

- Column 5: Parent's Education - a categorical variable indicating the highest level of education a students parents' achieved: (1) less than high school; (2) some high school; (3) graduated high school/GED; (4) some college; (5) graduated college; (6) post-graduate study.

- Column 6: State test score.

Use the data to determine if there are significant differences between the three reading curricula, and compare them with an appropriate post hoc procedure. Your analysis should attempt to use the student's classroom and their parent's education as a covariate to explain some variation in the outcome. As part fo the analysis you should construct a contrast to test whether the men test score for the balanced group is significantly different from the average of the comprehension - and decoding - focused curriculum means.

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