Chapter 7
Gases
A gas consists of small particles that move rapidly in straight lines
until they collide;
they have enough kinetic energy to overcome any attractive forces;
gas molecules are very far apart relative to their size;
gas molecules have very small volumes compared to the volumes of
the containers they occupy;
have kinetic energies that increase with an increase in temperature;
collisions of the gas cause pressure (force /unit area)
Atmospheric pressure
is the pressure exerted by a column of air from
the top of the atmosphere to the surface of the
Earth;
is about 1 atmosphere at sea level;
depends on the altitude and the weather;
is lower at high altitudes where the density of
air is less;
What causes atmospheric pressure?
Gravity
A barometer
measures the pressure exerted by the gases in
the atmosphere
indicates atmospheric pressure as the height in
mm of the mercury column
A water barometer would be 13.6 times taller
than a mercury barometer because the density
of Hg is 13.6 times as dense as water
The relationship between pressure and volume for a fixed amount of gas
Note that the initial product between
pressure and volume is 4L*1atm = 4 L atm
In the final diagram: 2L*2atm = 4 Latm
Decreasing the volume to ½ results in a
doubling of the pressure
We find that the product of volume and
pressure is equal to a constant
PV = a constant
Initial
Final
During exhalation, the diaphram moves up, the
lung volume decreases, and the pressure within
the lungs increases. In this case however
air flows from the higher pressure in the lungs
to the outside to relieve the increase in pressure
During inhalation, the diaphram moves down
causing the the lungs to expand
the pressure in the lungs decreases
air flows towards the lower pressure in the
lungs
If the sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm,
what is the new volume when the pressure is increased to 1.40 atm (T constant)?
pressure x volume = constant
6.4 L *0.7 atm = 4.48 Latm = V x 1.4 atm
.
V = 3.2 L
6.4 L; 0.7 atm
3.2 L; 1.4 atm
Final volume
Temperature and Volume
Suppose we had a frictionless piston and a gas
enclosed within the piston. What could we say
about the pressure inside and outside of the piston if
the piston was notionless?
pressure P (inside) = P (outside)
temperature (inside) = temperature (outside)
Supppose we now heat the gas inside the piston
What happens to the number of collisions a
molecule makes against the wall if we heat
a gas?
the number of collisions increase causing
an increase in the pressure inside
What will happen to the volume of the gas
if the pressure outside the piston does not
change and the pressure inside increases?
V/T(K) = constant
Temperature and Pressure
Suppose we now heat the gas enclosed
in the cylinder keeping the volume
constant
Notice that temperature must be in K
P/T = constant
Pressure and the amount of gas , n
Suppose now that we double the number
of molecules in the same volume and at
the same temperature. What will that do
to the number of collisions with the
walls?
the pressure?
If we allow the pressure to return to it
original value, what will happen to the
volume?
n is directly proportional to pressure
A Summary of The relationship between T, P, V, and n
P x V = constant
P/T = constant
P/n = constant
V/T = constant
The volume, temperature, pressure and amount of gas pressent can be summarized into one
simple equation: PV = nRT
When the temperature and amount of gas (n) are kept constant, nRT are equal to a constant
When the volume and amount of gas is kept constant, P/T = nR/V, nR/V is a constant
At constant pressure and amount of gas (n), V/T = nR/P; nR/P is a constant
A. Pressure _______, when V decreases at constant n, T.
B. When T decreases, V _______ at constant n, P.
C. Pressure _______ when V changes from 12 L to 4 L at constant n, T
D. Volume _______ when T changes from 15 °C to 45 °C at constant n, P.
triples
Vapor pressure: the pressure vapor
exerts against the atmosphere;
Boiling occurs when the vapor pressure of water
equals the atmospheric pressure above it
Denver CO
STL MO
New Orleans LA
pressure cooker
One last thing: Notice in our discussion of
gases, we never mentioned any particular gas;
that is because the ideal gas law (PV=nRT)
applies equally to all gases
Partial pressures
The total pressure exerted by a mixture of gases is the sum of the individual partial pressures;
remember the volume occupied by the gas is the same for all gases because their molecular
volume is small in comparison. Gases in a mixture are always at the same temperature.
Gases diffuse from higher pressure to lower
pressure
When sensors in a car detect a collision, they cause the decomposition of sodium azide, NaN3
Upon collision, a sensor initiates a current to flow through a conductor that heats up to 300 ° C
and causes NaN3 to detonate.
1) 2 NaN3 → 2 Na + 3 N2 (g)
(2) 10 Na + 2 KNO3 → K2O + 5 Na2O + N2 (g)
(3) K2O + Na2O + 2 SiO2 → K2SiO3 + Na2SiO3 (silicate glass)
Solving Some Problems Using the Gas Laws
When sensors in a car detect a collision, they cause the decomposition of sodium azide, NaN3
NaN3
Na (s) +
N2(g)
This generates the gas nitrogen within 0.03 seconds which fills the air bags.
How many liters of nitrogen are filled at 1 atm pressure (760 mm Hg) and 0 °C (STP) if
the air bag contains 132 g of sodium azide?
2NaN3
2Na (s) +
NaN3 MW = 23 + 3*14 = 65 g/mol
3N2(g)
How many mols of NaN3 are present?
132g/65g/mol = 2.03 mol
2 mol of NaN3 produces 3 mol of N2
PV = nRT
1atmV =3*0.0821(273); V = 67.2 L
A partially filled weather balloon has a volume of 750 L when filled with He at 8 °C and
760 mm Hg. What is the new volume of the balloon when it rises to an altitude where
the temperature is -45 °C and the pressure is 100 Hg?
How much He is there in the balloon originally?
PV = nRT
760 mm Hg/760 mm Hg/atm =1.0 atm; K = (8 °C +273) = 281 K; V = 750 L;
R = 0.0821 Latm/(Kmol)
n = PV/RT;
n = 750 L*1.0 atm/[0.0821 Latm/(K mol)*281 K]
n = 32.5 mol He
V = nRT/P;
P = 100mm/760mm/atm = 0.13 atm ; T (273-45)= 228 K; n = 32.5 mol
V = 32.5 mol*0.0821 (Latm/Kmol)*228 K/0.13 atm
V = 4680 L