Avogadro’s Law
Volume is directly proportional to the number of
moles of gas, V  n (T, P constant).
V1 V2

n1 n 2
1
Ammonia burns in oxygen to form nitric oxide (NO)
and water vapor. How many volumes of NO are
obtained from one volume of ammonia at the same
temperature and pressure?
4NH3 + 5O2
1 mole NH3
4NO + 6H2O
1 mole NO
At constant T and P
1 volume NH3
1 volume NO
Amonton’s Law
P  T (n, V constant)
P/T = constant
P1 = P2
T1
T2
2
Sample Exercise 6.5
Labels on aerosol cans caution against incineration
because the cans may explode when the pressure inside
them exceeds 3.00 atm. At what temperature in degrees
Celsius will an aerosol can burst if initially the pressure
inside the can is 2.20 atm at 25°C?
Combined Gas Law
• Boyle’s Law: P × V = constant
• Charles’s Law: V/T = constant
• Avogadro’s Law: V/n = constant
• Combining the gas laws: P V  constant
n T
• If n is constant, then PV/T = constant, and
P1V1 P2V2

T1
T2
3
Sample Exercise 6.6
A weather balloon filled with 100.0 L of He is launched
from sea level (T = 20°C, P = 755 torr). No gas is
added or removed from the balloon during its flight.
Calculate the volume at an altitude of 10 km, where
the temperature of the atmosphere and the gas in the
balloon are both -52°C and atmospheric pressure is
195 torr.
Ideal Gas Law
Combined Gas Law:
P V
 constant  R
n T
Which rearranges to:
PV = nRT
R = universal gas constant = 0.08206 L∙atm K−1 mol−1
P = pressure (in atm)
V = volume (in liters)
n = moles
T = temperature (in Kelvin)
4
The conditions 0 0C and 1 atm are called standard
temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal
gas occupies 22.414 L.
PV = nRT
R=
(1 atm)(22.414L)
PV
=
nT
(1 mol)(273.15 K)
R = 0.082057 L • atm / (mol • K)
Sample Exercise 6.7
Bottles of compressed O2 carried by climbers ascending
Mt. Everest have an internal volume of 5.90 L. Assume
that such a bottle has been filled with O2 to a pressure of
2025 psi at 25°C.
a. How many moles of O2 are in the bottle?
b. What is the mass in grams of O2 in the bottle?
Assume that O2 behaves as an ideal gas
5
Reference Points for Gases
•
Standard Temperature and Pressure
(STP):
•
•
P = 1 atmosphere; T = 0°C
Molar Volume:
•
For one mole of an ideal gas at STP
(calculated from the ideal gas law):
V = 22.4 L
6