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.