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Gases
Chapter 5 Problems: 14, 19, 20, 21,
26, 32, 34, 36, 40, 42, 43, 44, 47,
48, 50, 52, 54, 59, 60, 63, 66, 67,
76, 84, 88, 102,
Graham’s law
problems
Elements that exist as gases at 250C and 1 atmosphere
5.1
5.1
Physical Characteristics of Gases
•
Gases assume the volume and shape of their containers.
•
Gases are the most compressible state of matter.
•
Gases will mix evenly and completely when confined to
the same container.
•
Gases have much lower densities than liquids and solids.
5.1
Force
Pressure = Area
(force = mass x acceleration)
Units of Pressure
1 pascal (Pa) = 1 N/m2
1 atm = 760 mm Hg = 760 torr
= 101,325 Pa
= 14.7 psi
= 29.92 in. Hg
Barometer
5.2
10 miles
4 miles
Sea level
0.2 atm
0.5 atm
1 atm
5.2
Boyle’s Law
P α 1/V
This means Pressure and
Volume are INVERSELY
PROPORTIONAL if moles
and temperature are
constant (do not change).
For example, P goes up as
V goes down.
P1V1 = P2 V2
Robert Boyle
(1627-1691).
Son of Earl of
Cork, Ireland.
Charles’s Law
If n and P are constant,
then V α T
V and T are directly
proportional.
V1
V2
=
T1
T2
• If one temperature goes up, the
volume goes up!
Jacques Charles (17461823). Isolated boron
and studied gases.
Balloonist.
Gay-Lussac’s Law
If n and V are
constant,
then P α T
P and T are directly
proportional.
P1
P2
=
T1
T2
If one temperature goes up,
the pressure goes up!
Joseph Louis GayLussac (1778-1850)
Combined Gas Law
• The good news is that you don’t
have to remember all three gas
laws! Since they are all related to
each other, we can combine them
into a single equation. BE SURE
YOU KNOW THIS EQUATION!
P1 V1
P2 V2
=
T1
T2
No, it’s not related to R2D2
And now, we pause for this
commercial message from STP
OK, so it’s really not THIS kind
of STP…
STP in chemistry stands for
Standard Temperature and
Pressure
Standard Pressure =
1 atm
(or an equivalent)
Standard Temperature
= 0 deg C (273 K)
STP allows us to
compare amounts of
gases between different
pressures and
temperatures
Avogadro’s Law
V a number of moles (n)
V = constant x n
Constant temperature
Constant pressure
V1/n1 = V2/n2
5.3
Ideal Gas Equation
Boyle’s law: V a 1 (at constant n and T)
P
Charles’ law: V a T (at constant n and P)
Avogadro’s law: V a n (at constant P and T)
Va
nT
P
V = constant x
nT
P
=R
nT
P
R is the gas constant
PV = nRT
5.4
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
(1 atm)(22.414L)
PV
R=
=
nT
(1 mol)(273.15 K)
R = 0.082057 L • atm / (mol • K)
5.4
Density (d) Calculations
PM
m
d=
=
V
RT
m is the mass of the gas in g
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
Solve for n, which =
mass/molar mass
Or,
dRT
M=
P
d is the density of the gas in g/L
5.4
A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm
and 27.00C. What is the molar mass of the gas?
PV = nRT
2.10 L X 1 atm
n=
0.0821
L•atm
mol•K
x 300.15 K
n = 0.0852 mol
n=
g
M
M = 54.6 g/mol
5.3
Gas Stoichiometry
What is the volume of CO2 produced at 370 C and 1.00
atm when 5.60 g of glucose are used up in the reaction:
C6H12O6 (s) + 6O2 (g)
6CO2 (g) + 6H2O (l)
g C6H12O6
mol C6H12O6
5.60 g C6H12O6 x
6 mol CO2
1 mol C6H12O6
x
= 0.187 mol CO2
180 g C6H12O6
1 mol C6H12O6
V=
nRT
=
P
mol CO2
V CO2
L•atm
x 310.15 K
mol•K
1.00 atm
0.187 mol x 0.0821
= 4.76 L
5.5
Dalton’s Law of Partial Pressures
V and T
are
constant
P1
P2
Ptotal = P1 + P2
5.6
Consider a case in which two gases, A and B, are in a
container of volume V.
nART
PA =
V
nA is the number of moles of A
nBRT
PB =
V
nB is the number of moles of B
PT = PA + PB
PA = XA PT
nA
XA =
nA + nB
nB
XB =
nA + nB
PB = XB PT
Pi = Xi PT
mole fraction (Xi) =
ni
nT
5.6
A sample of natural gas contains 8.24 moles of CH4,
0.421 moles of C2H6, and 0.116 moles of C3H8. If the
total pressure of the gases is 1.37 atm, what is the
partial pressure of propane (C3H8)?
Pi = Xi PT
PT = 1.37 atm
0.116
Xpropane =
8.24 + 0.421 + 0.116
= 0.0132
Ppropane = 0.0132 x 1.37 atm = 0.0181 atm
5.6
Bottle full of oxygen
gas and water vapor
2KClO3 (s)
2KCl (s) + 3O2 (g)
PT = PO2 + PH2 O
5.6
5.6
Chemistry in Action:
Scuba Diving and the Gas Laws
P
Depth (ft)
Pressure
(atm)
0
1
33
2
66
3
V
5.6
Kinetic Molecular Theory of Gases
1. A gas is composed of molecules that are separated from
each other by distances far greater than their own
dimensions. The molecules can be considered to be points;
that is, they possess mass but have negligible volume.
2. Gas molecules are in constant motion in random directions.
Collisions among molecules are perfectly elastic.
3. Gas molecules exert neither attractive nor repulsive forces
on one another.
4. The average kinetic energy of the molecules is proportional
to the temperature of the gas in kelvins. Any two gases at
the same temperature will have the same average kinetic
energy
5.7
Kinetic theory of gases and …
• Compressibility of Gases
• Boyle’s Law
P a collision rate with wall
Collision rate a number density
Number density a 1/V
P a 1/V
• Charles’ Law
P a collision rate with wall
Collision rate a average kinetic energy of gas molecules
Average kinetic energy a T
PaT
5.7
Kinetic theory of gases and …
• Avogadro’s Law
P a collision rate with wall
Collision rate a number density
Number density a n
Pan
• Dalton’s Law of Partial Pressures
Molecules do not attract or repel one another
P exerted by one type of molecule is unaffected by the
presence of another gas
Ptotal = SPi
5.7
Deviations from Ideal Behavior
1 mole of ideal gas
PV = nRT
PV = 1.0
n=
RT
Repulsive Forces
Attractive Forces
5.8
Effect of intermolecular forces on the pressure exerted by a gas.
5.8
Van der Waals equation
nonideal gas
2
an
( P + V2 ) (V – nb) = nRT
}
}
corrected
pressure
corrected
volume
5.8
Velocity of a Gas
The distribution of speeds
of three different gases
at the same temperature
The distribution of speeds
for nitrogen gas molecules
at three different temperatures
urms =
M
3RT
5.7
Gas diffusion is the gradual mixing of molecules of one gas
with molecules of another by virtue of their kinetic properties.
NH4Cl
NH3
17 g/mol
HCl
36 g/mol
5.7
Gas Diffusion
relation of mass to rate of diffusion
• HCl and NH3 diffuse
from opposite ends of
tube.
• Gases meet to form
NH4Cl
• HCl heavier than NH3
• Therefore, NH4Cl
forms closer to HCl
end of tube.
GAS DIFFUSION AND
EFFUSION
• diffusion is the
gradual mixing of
molecules of
different gases.
• effusion is the
movement of
molecules through
a small hole into an
empty container.
GAS DIFFUSION AND
EFFUSION
Graham’s law governs
effusion and diffusion of
gas molecules. KE=1/2
mv2
Rate for A
Rate for B
M of B
M of A
Rate of effusion is
inversely proportional
to its molar mass.
Thomas Graham, 1805-1869.
Professor in Glasgow and London.
GAS DIFFUSION AND
EFFUSION
Molecules effuse thru holes in a
rubber balloon, for example, at
a rate (= moles/time) that is
• proportional to T
• inversely proportional to M.
Therefore, He effuses more
rapidly than O2 at same T.
He
Graham’s Law Problem 1
1 mole of oxygen gas and 2 moles of ammonia are
placed in a container and allowed to react at 850
degrees celsius according to the equation:
4 NH3(g) + 5 O2(g) --> 4 NO(g) + 6 H2O(g)
Using Graham's Law, what is the ratio of the
effusion rates of NH3(g) to O2(g)?
Graham’s Law Problem 2
What is the rate of effusion for H2 if 15.00 ml
of CO2 takes 4.55 sec to effuse out of a
container?
Graham’s Law Problem 3
What is the molar mass of gas X if it effuses
0.876 times as rapidly as N2(g)?