(Lab 1) Regression Analysis - Graphing Exercises Part 2 Of 2

(16pts) Experiment 1

A researcher follows the rate of a reaction by measuring the volume of H₂ gas generated over time from a reaction under study. The H₂ from the reaction is collected over water and the volume measurements at specific points in time are indicated below. The temperature is 25 C and the vapor pressure of water is 23.8 mmHg. The total pressure of the gas above the water level is 758 mmHg.

Time (min)	Volume (mL)
0.0	0.0
0.5	17.0
1.0	34.0
2.0	71.0
3.0	95.0
4.0	174.0
5.0	215.0
6.0	234.0
7.0	282.0
8.0	315.0
9.0	355.0

(2pts)

Write a formula which converts the H₂ volume data to units of millimoles.

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(2pts)

Prepare a table of data showing time, volume, and millimoles of gas using the ideal gas law.

You may export an image of a table from Excel if you'd like and import it into this text entry area, and for calculating millimoles of gas you may want to try using the Excel cell formula feature. Feel free to ask a TA how this works.

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(5pts)

Plot the data in an x-y plot with time along the x-axis on graph paper by hand and determine the slope and y-intercept using a ruler. Upload an image of the plot here.

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(5pts)

Using a plotting program like Excel, plot a computer generated plot of data and determine the slope, y-intercept, and correlation coefficient. Use the program to print this information on the graph as well. Upload the image of your graph here.

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(2pts)

From the slope of both plots, determine the rate of reaction expressed as change of H₂ (millimoles) per unit time. Don't forget units. How do these rates between the two plots compare? (Best to determine the percent difference in values here.) Which rate do you think would be more representative of the data (i.e., less bias)?

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(8pts) Experiment 2

In one of the lab experiments in this course you will be measuring absorption of light of aqueous solutions that have different concentrations of light absorbing solutions at a specific wavelength (or color) of light. The absorption of light follows Beer's Law, which is A = cl where, A is absorbance, is a constant at given wavelength, c is the concentration of solution in molarity, and l is the length dimension light passes through the solution.

In a laboratory experiment, a chemist prepared different concentrations of solution with a light absorbing solute and measured the absorbance of each solution. In the absorbance measurements, the solutions were placed in sample holders where light propagates through 5.00 cm of sample. So, the length, l, equals 5.00 cm in all these measurements. The following data is collected:

Concentration (M)	Absorbance
0.000	0
0.102	0.0089
0.249	0.0205
0.502	0.0463
0.748	0.0641
1.052	0.0903
1.485	0.1335

(0.5pts)

Which variable is the independent variable?

Choose...ConcentrationAbsorbance

(0.5pts)

Which variable is the dependent variable?

Choose...ConcentrationAbsorbance

(5pts)

Using Excel, make a plot of the data with the appropriate variables as x and y. Using the linear regression analysis of the plotting program, determine the best-fit slope and y-intercept of the data. Be sure to include units!

Have the program:

• Plot the data with axes labeled with units.
• Plot the linear regression line through the data.
• Print the results of slope, y-intercept, and correlation coefficient on the graph.
• Make sure plot has x and y axes labeled correctly with units (if any).

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(2pts)

From your analysis, determine best value of . Be sure to have correct significant figures.

(8pts) Experiment 3

In the laboratory, a scientist examines the compressibility of a non-ideal gas. The non-ideal gas can be described by the following equation of state:

Z=PVRT=B0+B1PZ=PVRT=B0+B1P

where Z is the compressibility factor. While varying P, the scientist determines Z from known values of n, V, and T and obtains the following data.

P (atm)	Z
1.31	0.9950
9.76	0.9675
24.35	0.9489
49.83	0.9063

(0.5pts)

Which variable is the independent variable?

Choose...PZ

(0.5pts)

Which variable is the dependent variable?

Choose...PZ

(5pts)

Using Excel, make a plot of the data with the appropriate variables as x and y. Using the linear regression analysis of the plotting program, determine the best-fit slope and y-intercept of the data. Be sure to include units!

Have the program:

• Plot the data with axes labeled with units.
• Plot the linear regression line through the data.
• Print the results of slope, y-intercept, and correlation coefficient on the graph.
• Make sure plot has x and y axes labeled correctly with units (if any).

Upload the image of your graph here.

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(2pts)

From your analysis, determine best value of B₀ and B₁. Be sure to have correct significant figures.

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(9pts) Experiment 4

Later in this course you will see that the rate of reactions depend on concentration and this dependence is referred to as the "order" of the reaction. This concentration dependence provides insight into the molecular step-by-step process by which the reaction occurs.

In the laboratory, a biochemist performed an experiment by monitoring a reaction. In this case, the concentration of a reactant, [A], is measured as a function of time. Prior to the experiment, the biochemist hypothesized that the reaction follows "second order kinetics" which follows the relationship

1[A]=1[A]0+kt

where [A] is the molarity concentration of A at time, t, and [A]₀ is the initial concentration. The, k, is constant during the reaction and for that reason is called a rate constant. In this case the following data was obtained.

Data:

Time (min)	[A] (molarity)
10	0.51
20	0.42
30	0.36
40	0.31

(2pts)

Transform the data given in the lab manual so that it would show linear dependence in the case of a second order reaction.

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(5pts)

Make a computer generated plot of the data with the appropriate variables as x and y consistent with the second order equation given.

Using a linear regression calculation, determine the slope and the y-intercept of the best fit of the data and have the program print the values on the graph. Be sure to include units!

Upload your plot here.

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(2pts)

From your analysis, determine the best values of k and [A]₀ and don't forget the units and significant figures.

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