THE IDEAL GAS LAW In Chapter 1, we discussed
Avogadro’s law
,
Equal volumes of gases measured under the sa
me conditions of temperature and pressure
contain equal numbers of molecules; or the vo
lume of a gas at cons
tant temperature and
pressure is directly proportional to the number of moles of gas.
V = k(P,T)n
Eq. 7.5
n is the number of moles of gas, and k(P,T)
is a proportionality cons
tant that depends upon
the pressure and the temperature of the gas.
We have three equations that relate the volume of a gas to the pressure, temperature,
and number of moles of the gas. Boyle's,
Charles', and Avogadro's Laws can all be
combined into one
ideal gas law
.
The volume of a gas is proportional to the
number of moles of t
he gas and its absolute
temperature and inversely proportional to its pressure.
PV = nRT
Eq. 7.6
R is the proportionality constant, known as the ideal gas law constant (R = 0.0820578 L⋅
atm
⋅mol
-1⋅K
-1). The use of the ideal gas law is revi
ewed in detail in Appendix B, but we
present one example of its use here. Example 7.2
A weather balloon with a volume of 1.0
x
10
3 L will collect data at a height of 10 km,
where the temperature is -50
oC and the pressure is 120 torr. How many grams of
helium should be pl
aced in the balloon to completely
fill it under these conditions?
The pressure in atmospheres is
120 torr760 torr/atm
= 0.158 atm
The temperature in kelvins is T = -50
+ 273 = 223 K, and the volume is 1.0x10
3 L. We are
asked for the amount of gas, represented by n
in the ideal gas law, so we solve Equation
7.6 for n and substitute the given values of P, V and T to obtain the number of moles of helium needed.
n =
PVRT
=
(0.158 atm)(1.0
×^10
3 L)
(0.0821 L
⋅atm
⋅K
-1⋅
mol
-1)(223 K)
= 8.6 mol
The molar mass of helium is 4.0 g/mol, so the mass of helium required is
8.6 mol
4.0 g×
mol
= 34 g He
Chapter 7 States of Matter and Changes in State
© by
North
Carolina
State
University