# The Relationship between Volume and Temperature in the Ideal Gas Law

Introduction
An important area of physical chemistry would be the kinetic theory of gases. The kinetic theory of gases was developed over a long period of time that also included the important involvement of the gas laws (Laider 131). The two gas laws involved are Boyle’s law and Gay-lussac’s law also known as Charles’s law. Boyle’s law states that “the volume of a given quantity of a gas varies inversely as the pressure, the temperature remaining constant” (Barrow 3) in other words:
PV=constant.
Gay-Lussac’s law defines the relationship between temperature and gas volume. It states “the volume of a given mass of gas varies directly as the absolute temperature if the pressure remains constant” (Barrow 6).
V/T= constant
Temperature in this case does not refer to degrees in Celsius. Instead the absolute Kelvin temperature scale is used. The Kelvin scale begins at absolute zero and has a value of -273.15 degrees in Celsius. When either volume or pressure of a gas was varied with temperature using Celsius it was found that the lowest temperature reached was consistently -273.15. Since this was the lowest temperature possible, it made since to then reset this temperature as zero for the Kelvin scale (Huestis 70).
To better understand why the gas laws behave as they do one should also consider some of the properties present in all gases. These properties are: gases can be compressed, gases exert pressure on whatever surrounds them, gases expand into whatever volume is available, and temperature, pressure, volume occupied, and amount present is taken into account when referring to gases (Moore 437-8). Taking in consideration these properties and the gas laws Avogadro then came up with an equation that can be related to all gases and uses a universal constant. He did this by defining and incorporating the base unit of the mole (n), and combing the other gas laws (Laidler 134-135). This single equation he came up with is the most commonly used and is referred to as the Ideal Gas Law.
pV=nRT
The objective of this experiment is to show Gay-Lussac’s law pertains to real gases in a laboratory environment, how the ideal gas law can still be used for gases that are not completely ideal and how absolute zero can be estimated (Huestis 70).
Experimental
For the gas laws and absolute zero lab the temperature inside the tube containing the smaller tube and dibutyl phalate was recorded as an initial temperature. The thermometer used to record the temperature had a precision of + 0.2 degrees Celsius. The volume of the bubble was also recorded. In the case of this experiment a U-tube was not available so a straight tube was used instead with approval of the supervising professor. Since a straight tube was used the volume could be read directly from the apparatus. If a U tube was used the measurements would have needed to be converted from millimeters of bubble length to volume in milliliters. Once the initial data was recorded the tube was then gradually heated to about 100 degrees Celsius. While the tube was heating the volume of gas in the tube (the bubble) was recorded at intervals of about every 10-15 degrees. The experiment was complete once the tube reached close to a temperature of 100 degrees Celsius. This procedure was followed as described in the lab manual.

Results and Discussion
The data gathered from the experiment can be seen in table 1.1
Vol.(mL) Temp C Temp K
6.8 24 297
7.2 34 307
7.4 48 310
7.6 59 332
8.0 72 345
8.2 81 354
8.4 91 364
8.8 92 365
Table 1.1

The temperature was converted to Kelvin by adding 273 to the Celsius temperature.
For example: 24+273=297.
By looking at the table one can see that as the temperature increased the volume the gas occupied also increased. This agrees with Gay-Lussac’s law, as the temperature of a gas increases so does the volume. This makes sense when thinking in terms of particles. Temperature increase causes the movement of particles to also increase. In the gaseous stage particles are already constantly moving and bouncing around. When additional heat is added the particles become even more active so particles begin to move farther and farther apart from each other, occupying more space than what was initially used.
The volume of gas and temperature in Celsius was graphed, the best line of fit was determined and the linear equation was calculated (Figure1.1) The linear equation can be used to then estimate what the value of absolute zero is. Based on the line of best fit the linear equation is:
Y=0.0255x+6.2046
Since absolute zero refers to the volume of gas at zero, Y is assumed to equal zero. The equation is then written as:
0=0.0255x+6.2046
Algebra was then used to determine the value of x.
-6.2046=0.0255x
X= -243.3
Therefore -243.3 is the absolute zero based on the data from this experiment.
The actual value of absolute zero is -273.15 but this inconsistently can be explained in part from experimental error and experimental limitations (Huestis 72).
In this experiment the pressure, amount of moles of gas, and the constant R all remained constant. If all these variables are held constant than the Ideal Gas Law can be rewritten to an equation that would allow one to calculate the constant k. By calculating the constant k one can then see if k remains at roughly the same value. When number of moles and pressure are constant the equation used is:
V=kT rearrange to k=V/T
This equation can then be used to determine how consistently the data from the experiment follows the Ideal Gas Law (Huestis 72). Table 2.2 shows the temperature and constant determined for each volume. Constant k was found by taking the volume of the gas divided by the temperature in Kelvin.
For example 6.8ml/297= 0.0229 = k
Temperature K Volume mL Constant k
297 6.8 0.0229
307 7.2 0.0235
310 7.4 0.0239
332 7.6 0.0229
345 8.0 0.0232
354 8.2 0.0232
364 8.4 0.0231
365 8.8 0.0241
Table 2.2

By looking at Table 2.2 it can be seen that k does in fact remain constant. Since k proves to be a constant for the Ideal Gas Law it can be assumed that it can be used to accurately describe the relationship of pressure, volume, temperature, and amount of real gases.
Conclusion
Looking at Figure1.1 shows how well the experiment produced the data. The data is mostly linear, but there are a few points where the data appears to be a little skewed from the rest. This small inconsistency may be due in part because of the instruments and equipment used. Since a straight tube was used when a U-tube was unavailable, the data might have turned out differently than if the equipment called for was used. Also the data might have been affected by the thermometer used to record the temperature. It is also important though to keep in mind the Ideal Gas Laws is based on the concept that a gas follows Boyle’s and Gay-Lussac’s laws exactly as expected. In real gases though this may not always be the case, and this explains why the Ideal Gas Law can be a very good indicator. But cannot be expected, and cannot give accurate calculations for any gas at any given temperature, pressure, and/or volume.
In the future an experiment that might be done to further explore gas laws and the activity of real gases could involve testing the relationship between volume and number of gas moles. If temperature and pressure were held constant would the volume increase or decrease proportionally along with the number of moles as Avogadro predicted? (Huestis 69)

References
Barrow,G.(1966).Properties of Gas.In Hugus (Ed.),Physical Chemistry (pp.3-
6).NewYork:McGraw-Hill
Huestis, Swank & Tobiason (2003).Gas Laws and Absolute Zero. General Chemistry in
the Laboratory (pp. 69-74).
Laidler, K.(1995) The Gas Laws. The World of Physical Chemistry (pp.131-136).New
York: Oxford University Press Inc.
Moore, J.,Stanitski,& Jurs.(2004)Properties of Gas. In Holdcroft(Ed.),Chemistry The
Molecular Science (pp.436-447).Thompson Steele, Inc.