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Boyle's Law Verification

Purpose

    The purpose of this data analysis is to analyze the set of data from 1662 on which Boyle's law was formulated, present it in graphical form, and interpret the results.  The data were downloaded from Giunta's Classical Chemistry site.


Introduction
   
    Boyle's law states that as the volume of a gas decreases, the pressure of that gas increases if other variables such as temperature and the number of moles are held constant.   In other words, Boyle's law states that the pressure and volume of a gas are inversely related.  The law can by represented by the following equations:

P1V1 = P2V2 = constant       (eq.1)
P1 = constant / V1              (eq.2)
P1 = constant (1/ V1)          (eq.3)

where P is the pressure, V is the volume, and the subscripts 1 and 2 refer to the initial state before and the final state after the pressure-volume change, respectively.  Eq. 2 shows more clearly that there is an inverse relationship between pressure and volume.  Since volume is in the denominator, as it increases, the pressure decreases.  Conversely, as the voloume decreases, the pressure increases.

Data and Analysis


    A plot of pressure vs. volume was made, and a power regression line fitted to the data.  The equation for the trendline is provided in the upper, right-hand corner of the graph.


volume pressure
48 29.125
46 30.5625
44 31.9375
42 33.5
40 35.3125
38 37
36 39.3125
34 41.625
32 44.1875
30 47.0625
28 50.3125
26 54.3125
24 58.8125
23 61.3125
22 64.0625
21 67.0625
20 70.6875
19 74.125
18 77.875
17 82.75
16 87.875
15 93.0625
14 100.438
13 107.813
12 117.563
pressure vs. volume graph

    The equation for the trendline, with some rounding and simplification, can be shown to verify Boyle's law, in the form of (eq. 2).

y = 1400 x -0.99 =~1400 x-1 = 1400/x


where y is the pressure and x is the volume.
     Alternatively, to further verify Boyle's law, a linear graph was produced by graphing the pressure, P, as a function of the inverse of volume, (1/V).  This result clearly shows that pressure and volume are inversely related to each other:


pressure vs. inverse volume

In conclusion, Boyle's law is verified by the analysis of the experimental data; the pressure and volume of a gas sample at a given temperature are inversely related to each other.