Trends amount until equilibrium is reached. The logarithmic

Trends
in Gibbs Free Energies of Formation, Heat Capacities, Enthalpies of
Vaporization, and Viscosities vs. Strait Alkane Length

 

Table 1: Thermodynamic and fluid properties vs.
length of straight alkane

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length1 2 3 4

 
 
Alkane

 at Boiling Point

 

Methane

-50.8

8.6

37.39

10.3

 

Ethane

-32.9

15.7

52.49

11.0

 

Propane

-23.4

19.5

73.60

7.4

 

Butane

-15.6

23.4

98.49

7.0

 

Pentane

-9.2

26.7

120.1

11.7

 

Hexane

-4.2

31.5

196.5

6.5

 

Heptane

1.3

32

224.7

6.5

 

Octane

6.4

36.3

255.6

7.5

 

 

            The table above was constructed at
first through the use of Google. Finding reliable data tended to be easier the
smaller the alkane was. Usually the source used for one property of methane
always had the next five alkanes as well. Searches about octane viscosity, for
example, either did not have a reliable source, or cost a hefty fee to look at.
Most of heptane’s and octane’s values came from Knovel. Knovel always gives
reliable, verified information, which ended up saving a lot of time. One source
that was particularly astounding to me was a 332 page paper written by James S.
Chickos and William E. Acree, Jr1. It contains tabulated data for
thousands of molecules’ enthalpies of vaporizations over many temperature
ranges. The references alone are over three pages as well.

Figure 1 Alkane Length vs. Gibbs Free Energies of
Formation2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1: Alkane length vs. Gibbs Free
Energies of Formation 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The plots above are graphical representations
of the tabulated data. They were generated using Matlab and aid in the visual
discovery of trends. The first three plots generally have the same shape. The
Gibbs free energy plot has the most logarithmic progression of the three with a
high slope at the beginning that tapers off. The first six alkanes have
negative Gibbs free energies of formation. This means that under the same
pressure and temperature, the constituent elements of that alkane will react and
produce some amount until equilibrium is reached. The logarithmic shape may be
due to how the reaction quotient changes with alkane length as well. As stoichiometric
constants shift due to the approximate doubling of hydrogen atoms with respect
to carbon, the reaction quotient essentially goes to zero. The
resulting change in Gibb’s also decreases according the following5

 

Enthalpy and Heat Capacity are both related
in that they deal closely with molecular vibrations and specific energy changes
of molecules. As mass of molecule increases, with a constant source of energy
would result in overall less internal motion. A simplified and classical
approach to energy says

If the claim
is that temperature is the perceived molecular velocities (and other more
complicated forms of movement), the above equation explains how an increase in
mass would result in some decrease in velocity, which is related to
temperature. The mass depends on the molecular weights of both hydrogen and
carbon. The resulting velocities end up being related inversely to the square
roots of the mass.

           

            There are much more complicated phenomena occurring deeper
beyond simple translational molecular motion. This simplified model gives a
rough understanding of why changes in enthalpy or heat capacities are positive
as a function of alkane length. As for viscosity, the data was difficult to
find reliably at one specific temperature, so errors that propagate through
changes in temperature may be slightly present. The general trend is they
decrease with alkane length, but slightly increase as the change of state
happens at heptane and octane. Intuitively, this makes no sense. Low
viscosities are associated with less resistance to shear forces which are
characteristic of gases. The discrepancy may stem from the viscosity depending
on the temperature differently for liquids vs. gases.

           

            Extrapolation is very much possible for the
enthalpy and heat capacity gas due to their linearity. It would be possible for
the Gibb’s graph as well but the error would increase greatly as the
extrapolated value increased. Extrapolation would be risky for the viscosity
graph but still possible. The points do follow as general pattern of decreasing
but once the state of matter change happens it may not prove effective.

 

 

Plagiarism
and Academic Dishonesty as accordance to Arizona State University

 

            My definition of plagiarism is the use of another’s
ideas or words without giving the company/person/collection of people proper
credit. There are many websites today that can assist teachers and students in
the detection of plagiarism. I, personally, have had teachers use these
websites throughout all of my high school years whenever I submitted something
on blackboard. They work by crosschecking the text of a paper verbatim to
sources on the internet. Most websites return a percentage match that shows what
percent your paper was copied from the internet. The first time I used one of
these websites I was shocked when a paper turned