Chemistry Experiment #2: Graphical Data Analysis

09-01-04

Section 30

This laboratory experiment looks at the mass and diameter of seven steel ball bearings, using a vernier caliper to determine diameter, and an electronic analytical balance to determine mass. Graphical data analysis then allows us to observe the relationships between mass and diameter and to obtain a trendline in order to determine the diameter of an unknown ball bearing.

Section I

Data Table 1: Mass and Diameter (D) of Ball Bearings

Mass (g)

Diameter (mm)

D^2

D^3

1/D

1/D ^2

1/D^3

log(D)

10^D

1

1.05

6.3

39.69

250.047

0.15873

0.025195263

0.003999

0.799340549

1995262.315

2

2.04

7.8

60.84

474.552

0.128205

0.016436555

0.002107

0.892094603

63095734.45

3

3.52

9.4

88.36

830.584

0.106383

0.011317338

0.001204

0.973127854

2511886432

4

5.6

11

121

1331

0.090909

0.008264463

0.000751

1.041392685

1E+11

5

6.19

11.3

127.69

1442.897

0.088496

0.007831467

0.000693

1.053078443

1.99526E+11

6

7.96

12.4

153.76

1906.624

0.080645

0.006503642

0.000524

1.093421685

2.51189E+12

7

11.9

14.1

198.81

2803.221

0.070922

0.005029928

0.000357

1.149219113

1.25893E+14

Graph 1 with trendline: Graph 2 with trendline:

Graph 3 with trendline: Graph 4 with trendline:

Graph 5 with trendline: Graph 6 with trendline:

Graph 7 with trendline: Graph 8 with trendline:

Section II

Using our straight line formula from Graph 2, y=26.133x – 18.832, the predicted value for the diameter of the unknown ball bearing is y = 32.1 mm. This value is inaccurate, possibly due to errors in measurement of the ball bearings.

1. Density of each ball bearing:

1: 0.17 g/mm3

2: 0.26 g/mm3

3: 0.37 g/mm3

4: 0.51 g/mm3

5: 0.548 g/mm3

6: 0.642 g/mm3

7: 0.844 g/mm3

2. The average density of the steep ball bearings is 0.48 g/mm3. If the known density of steel is 0.785 g/mm3, the average obtained by our measurements is inaccurate.

3. Three significant figures ought to be reported for the slope and y intercept in the trendline analysis, using the equation from Graph 2, due to the value for x having three figures.