The Ideal Gas Law
159
THE IDEAL GAS LAW
Every chemistry textbook describes the basic experiments that relate the volume of a gas sample to its pressure and Kelvin temperature. For a given quantity of gas it may be shown, by combining Boyle's law (PV = k", at constant T)
and Charles' law (V = k'T, at constant/
5 ), that
PV
— = k (a constant)
(I I-2)
This equation predicts the behavior of gases very well except at relatively
low temperatures and at relatively high pressures. Just how low the temperature must be or how high the pressure must be before serious deviations from
this equation are observed will vary from one gas to another. Under extreme
conditions, these equations cannot be used without correction for the volume
occupied by the molecules themselves or for the attractive forces between
neighboring molecules. For every gas, conditions exist under which the molecules condense to a liquid that occupies a fairly incompressible volume. A
hypothetical gas, called an ideal gas, would obey Equation 11-2 under all conditions, and would possess zero volume at a temperature of 0 K. Most gases obey
this equation at normal temperatures and pressures.
Experiments have shown that one mole of any gas (behaving ideally) at the
standard conditions of 760.0 torr (I atm) and 273.2 K occupies a volume of 22.42
liters. These values make it possible to evaluate k for one mole of gas in
Equation 11-2:
/„ . liters\
, _ PV_ _ (760.0 torr) \
mole/ _
torr liter
* ~ T ~
273.2 K
"
62 '
3/ mole K
This constant, known as the "ideal gas constant," is given the special symbol
R. Equation 11-2 would be written as PV = RT for one mole of gas; for the
general case of n moles, it becomes the important ideal gas equation,
PV = nRT
(11-3)
When pressures are measured in atm, it is convenient to have the value of R
in these units too. This may be computed as before, but substituting I atm for/
5
in Equation 11-2.
f 22 42 —1
P PV (1 atm) \
mole/
n e->n<;
liter atm
K = -=- =
-_. .
= 0.08206
:——
T
273.2 K
mole K
159
THE IDEAL GAS LAW
Every chemistry textbook describes the basic experiments that relate the volume of a gas sample to its pressure and Kelvin temperature. For a given quantity of gas it may be shown, by combining Boyle's law (PV = k", at constant T)
and Charles' law (V = k'T, at constant/
5 ), that
PV
— = k (a constant)
(I I-2)
This equation predicts the behavior of gases very well except at relatively
low temperatures and at relatively high pressures. Just how low the temperature must be or how high the pressure must be before serious deviations from
this equation are observed will vary from one gas to another. Under extreme
conditions, these equations cannot be used without correction for the volume
occupied by the molecules themselves or for the attractive forces between
neighboring molecules. For every gas, conditions exist under which the molecules condense to a liquid that occupies a fairly incompressible volume. A
hypothetical gas, called an ideal gas, would obey Equation 11-2 under all conditions, and would possess zero volume at a temperature of 0 K. Most gases obey
this equation at normal temperatures and pressures.
Experiments have shown that one mole of any gas (behaving ideally) at the
standard conditions of 760.0 torr (I atm) and 273.2 K occupies a volume of 22.42
liters. These values make it possible to evaluate k for one mole of gas in
Equation 11-2:
/„ . liters\
, _ PV_ _ (760.0 torr) \
mole/ _
torr liter
* ~ T ~
273.2 K
"
62 '
3/ mole K
This constant, known as the "ideal gas constant," is given the special symbol
R. Equation 11-2 would be written as PV = RT for one mole of gas; for the
general case of n moles, it becomes the important ideal gas equation,
PV = nRT
(11-3)
When pressures are measured in atm, it is convenient to have the value of R
in these units too. This may be computed as before, but substituting I atm for/
5
in Equation 11-2.
f 22 42 —1
P PV (1 atm) \
mole/
n e->n<;
liter atm
K = -=- =
-_. .
= 0.08206
:——
T
273.2 K
mole K