Page 43 - Essentials of physical chemistry

Ideal and Real Gas Behavior 5

Jacques-Alexandre-César Charles to try to duplicate this phenomenon. As a result Charles observed
that the volume of a gas is directly proportional to its temperature.
V
V / T or ¼ C 2
T

Here, C 2 is a different constant than the C 1 used in Boyle’s data. The principle behind the hot air
balloon is that hot air expands so the density of the air is lighter in the balloon than the outside air to
the extent that the whole ‘‘air ship’’ is lighter than the surrounding air and it rises.
A simple experiment capable of precise date is given on the Purdue ‘‘History of Chemistry’’
Internet site using a 30 mL syringe to give a precise measurement of the total volume of the gas
sample as the temperature is raised and measured with the thermometer in the gas. The volume of a
100 mL erlenmeyer flask with a one-hole rubber stopper and thermometer can be measured by
weighing the flask, stopper, and thermometer ‘‘empty’’ and then reweighing when filled with water
with the stopper and thermometer in place. The difference in mass divided by the density of the
water at room temperature gives the volume of the interior of the flask. When the flask has been
emptied and dried, a hypodermic needle attached to a 30 mL precision syringe is pushed through the
rubber stopper with the syringe set near zero. Then the flask is placed deep into an ice bath,
thermally equilibrated, and the stopper is placed in the neck of the flask to the same position as
before. The flask is removed from the ice bath and the total volume (flask plus syringe) is noted as
the apparatus warms up. A hair dryer can be used to provide heat for a reading at 408C. The use of
the precise syringe is a clever way to improve an experiment with simple equipment. The data
obtained are given on the Purdue site as in Table 1.2.
If we plot this and use a modern mathematical way of fitting the ‘‘best’’ line to the data that
minimize the square of the deviations between the actual position of n data points and the fitted line,
n 2 n
P P
2 i (y i f i ) i y i
we can use R 1 P n 2 and y n to evaluate the ‘‘goodness of fit’’ to the line of the
i (y i y)
2
function f (x) (Figure 1.3). The numerical value of R is routinely available using the Excel
2
program for personal computers and R ! 1 for a perfect fit to the line. Using Excel for a least-
squares fit of a line to the nine data points we obtain an equation V ¼ 0:3843(T C) þ 108:85 with

TABLE 1.2
Charles’ Law Data
Temperature, 8C Gas Volume, mL
0 107.9
5 109.7
10 111.7
15 113.6
20 115.5
25 117.5
30 119.4
35 121.3
40 123.2

Source: Purdue University, History of Chemistry,
http:==chemed.chem.purdue.edu=genchem=
history=boyle.html