Illustrated Guide to Home Chemistry Experiments

246 DIY Science: Illustrated Guide to Home Chemistry Experiments

In 1662, Boyle quantified the relationship between the volume of
a gas and its pressure, a discovery that became known as Boyle’s
Law. In 1802, Gay-Lussac quantified the relationship between the
volume of a gas and its temperature. That relationship became
known as Charles’ Law, chiefly because Gay-Lussac was kind
enough to credit some preliminary unpublished work done about
15 years earlier by the French chemist Jacques Charles. In 1809,
Gay-Lussac set in place the third of the fundamental gas laws by
quantifying the relationship between the pressure of a gas and its
temperature, a relationship known as Gay-Lussac’s Law. These
three gas laws are inextricably related. All of them specify the
relationship between volume, pressure, and temperature, with
one of those held constant.

Boyle’s Law states that, at constant temperature, the volume
of a gas is inversely proportional to its pressure. For example, if
you double the pressure of the gas you halve its volume and vice
versa. Boyle’s Law can be expressed as the equation:

v 1 · p 1 = v 2 · p 2

where the variables on the left side refer to the values before
a change in volume or pressure and those on the right refer to
the new values after the volume or pressure is changed. If any
three of those values are known, the fourth can be determined
algebraically.

Charles’ Law states that, at constant pressure, the volume of
a gas is proportional to its absolute temperature, specified in
kelvins (see note in Lab 14.2). For example, if you double the
temperature of a gas, you double its volume, and vice versa.
Charles’ Law can be expressed as the equation:

v 1 · T 2 = v 2 · T 1

where the variables subscripted with 1 refer to the values before
a change in volume or temperature and those subscripted with
2 refer to the new values after the volume or temperature is
changed. Again, if any three of those values are known, the fourth
can be determined algebraically.

Knowing Boyle’s Law and Charles’ Law, you can derive Gay-
Lussac’s Law mathematically by substitution (as indeed you
can derive any of these three laws if the other two are known).
Gay-Lussac’s Law states that, at constant volume, the pressure
of a gas is proportional to its absolute temperature, specified in
kelvins. For example, if you double the temperature of a gas, you
double its pressure, and vice versa. Gay-Lussac’s Law can be
expressed as the equation:

p 1 · T 2 = p 2 · T 1

where again, the variables subscripted with 1 refer to the values

before a change in volume or temperature and those subscripted

with 2 refer to the new values after the pressure or temperature

is changed. As before, if any three of those values are known, the

fourth can be determined algebraically.

These three related gas laws are sometimes referred to as

the Combined Gas Law, but although true individually and in

combination, they are insufficient to define a generalized law of

gases. In 1811, the Italian scientist Amedeo Avogadro postulated

the fourth and final fundamental law of gases, referred to as

Avogadro’s Principle, which states that equal volumes of gases at

the same temperature and pressure contain the same number of

particles.

Avogadro’s Principle was the final piece in the puzzle. With the

Combined Gas Law and Avogadro’s Principle, it’s possible to

define a generalized law of gases, called the Ideal Gas Law.

First stated in 1834 by the French scientist Benoît Paul Émile

Clapeyron, the Ideal Gas Law can be expressed as the equation:

pv = nRT

where

p = the absolute pressure of the gas

v = the volume of the gas

n = the number of moles of the gas

R = the ideal gas constant

T = the temperature of the gas in kelvins (K)

The value for R, the ideal gas constant, depends on the units used

for volume and pressure. In SI units, the value of R is 8.314472

joules per mole per kelvin (J · mol–1 · K–1)

The name of this law reflects the fact that it is completely

accurate only for an “ideal” gas, which is to say one that

comprises monoatomic particles of infinitely small volume, at

very high temperature and very low pressure, and in which no

attractions or repulsions exist between particles. Real gases

depart from values calculated using the Ideal Gas Law, because

their atoms or molecules have finite volumes and do interact.

In this chapter, we’ll examine the characteristics of gases and

experimentally verify these fundamental laws of gases.