Transcript Gases

Gases
Chapter 10 AP Chemistry
I. Characteristics of Gases
•
air 78% Nitrogen
21% Oxygen
• normal solids &
gases become vapors
• composed of nonmetals
• simple formulas low
molar mass
• expand to fill
container
spontaneously
• molecules are far apart
– have no I.F.
• most important
properties – temptvolume, # of molecules
II. Pressure
• Atmospheric Pressure
P = F/A force/area
SI = measured in Pascal's
Pa = 1N/m^2 one Newton/meter sq
1N = 1kg-m/s^2
Atmos. Pressure = 1x10^5 Pa or 1x10^2 kPa
Measuring Atmospheric Pressure
•Based on a
principle developed
by Evangelista
Torricelli in 1643, the
Mercurial Barometer
is an instrument
used for measuring
the change in
atmospheric
pressure
Pressure Units
• 1 atmos = 760 mmHg = 760 torr
you got it! 1 torr = 1 mmHg
• 1 atmos = 1.01325 x 10^5 Pa
= 101.325 kPa
Robert Boyle (1627-1691)
•
Gases are Kool
So as pressure increases the volume
decreases
The value of the constant depends on
the temperature and amount of the
gas
Jacques Charles (1746-1823)
•
Gases are Kool
• Increase the temp increase the vol
Joseph-Gray-Lussac (1788-1823)
•
Example
Amadeo Avogadro
• Using Lussas’s Law
• Double the number of moles of a gas
at the same T&P doubles the volume
• Later it was found that at STP ( one
atm and 0 deg C) one mole (6.02 x
10^23 molecules) of any gas
occupies exactly 22.4 liters of that
gas.
•
Ex 1. One mole of any gas occupies?
• PV = nRT
• V = nRT/P
• Avogadro’s # = 22.4 l
Ex 2. using the Ideal Eq
• A sample of KNO3 is heated
producing O2 gas in a 750 ml flask
under 2.8 atms of pressure. If the
temperature is 53.6 deg C how many
moles are produced?
Combined Gas Law formula
• P1V1N1=N1R1T1 = P2V2N2=N2R2T2
If the moles are held constant we can
determine how changes in tempt,
pressure, and volume will effect the
gas.
• Using the combined gas law formula
P1V1/T1 = P2V2/T2
Ex 1 combined Gas Law
• If one liter of air at room temp 25 deg
C and one atmos is compressed to a
volume of 3.3 ml at a pressure of
1000 atm. What is the new temp of
the sample?
Density – Molar Mass and the Ideal Gas Eq.
• Derive M= dRT/P and d = MP/RT
• Given D= mass/vol N = m (mass)/M
(molar mass)
Ex. Density prob.
• What is the density of carbon
tetrachloride at 714 torr and 125 deg
C?
Gas Mixtures and Partial Pressures
Combining formulas
• P total = P1 + P2 + P3 …. =
• P1 = n1 RT/V1
+ n2
RT/V2 ….. =
• Pt = nt = RT/V
• At cons. temp and volume the total
pressure of a gas sample is
determined by the number of moles
of a gas present – whether a single
gas or a mixture.
Ex prob.
• A gaseous mixture made of 10g of
oxygen and 10g of methane is
placed in a 10 liter vessel at 25 deg
c. What is the total pressure in the
vessel?
Partial Pressures and Mole Fractions
• The ratio of partial pressure of one
component of a gas to the total
pressure is
• P1 = n1RT/V
= n1
Mole
Pt = nt RT/V
nt
Fraction
Mole fraction of gas 1 denoted X1
• The partial pressure of a gas is equal
to its mole fraction times the total
pressure
X1 = P1 or P1 = X1Pt
Pt
Ex Prob.
• A synethic atmosphere is created by
blending 2 mol percent CO2, 20 mol
percent O2 and 78 mol percent N2. If
the total pressure is 750 torr calc the
partial pressure of the oxygen
component.
Collecting Gas Over Water
•Its an old trick but it
just might work!
•A sample of KClO3
is decomposed
producing O2 gas
over water. The
volume of the gas
collected is 0.25 l
at 25 deg C and
765 torr. How
many mole of O2
are collected?
Collecting Gas over Water
•Pressure of Water
Table
Temp
Pressure
Torr
0
4.58
25
23.76
35
42.2
65
187.5
100
760
Adjusting for Water Pressure
• Pt = 760 torr = PO2 + PH2O
• PO2 = 765 – 23.76 = 741.2
• PO2 = 741.2/760 = 0.975 atm
N1= PV/RT 0.975atm * O.25 l K*mol
(273 +25 k) ).0821 L* atm
= 9.96 x 10^-3 moles
How many grams of KClO3 were
decomposed?
Kinetic Molecular Theory (KMT)
A. A gas consists of molecules in constant
random motion
• Ek (energy kinetic) = ½ m X speed^2
B. KMT & Ideal Gases (5 postulates)
1. Size of gas molecules are negligible
compared to the average distance
between them.
2. Molecules travel in random patterns in
straight lines in all directions at various
speed. Properties are same in all
directions.
(KMT postulates)
3. Intermolecular forces are weak
except when they collide. Molecules
travel with unchanging speeds until
they collide with each other or the
sides of the container.
4. Collisions between molecules are
elastic ( no energy is lost)
5. The average Ke of a molecule is
proportional to the absolute
temperature.
C. The ideal gas law from KMT
• Pressure in KMT depends upon the
collisions frequency and the force
exerted – p is port freq x average
force
• Average force = mass and average
speed mu (momentum)
• Freq = is also proportional to the
average speed mu ( faster means
more collisions per unit time)
• Freq is inversely proportional to the
gas volume Inc. vol decrease freq
collisions
• Freq is directly proportional to the N
number of molecules in the gas vol.
• P is port ( mu x 1/v x N) x mmu
• PV is port (Nmmu^2) or
• Mmu^2 = ke port T
• So if the average KE of a molecule of
mass m and average speed mu is ½
mmu^2 then PV port to NT also
postulate 5 and N is port to moles of
gas then PV = nRT
Molecular Speeds Diffusion and Effusion
• Molecules are constant random
motion, therefore molecular speed
varies over a range of values.
• At any temp molecular speed varies
widely but most are close to the
average speed corresponding to the
max in the distribution curve
• Note the distribution of molecules at
diff speeds is temp dep (called a
maxwell distribution
Diffusion and Effusion
• The root-mean square (rms)
molecular speed, mu, is a type of
average molecular speed equal to
the speed of a molecule having
average molecular kinetic energy
• Mu =
Diffusion and Effusion
• R = molar gas constant (careful units
must match)
• T = absolute tempt
• M = molar mas of the gas
• Diffusion – is the process whereby a
gas spreads out through another gas
to occupy the space uniformly
- molecules move chaotically
(randomly)
- molecules never travel very far in
one direction
Diffusion and Effusion
- complicated to calculate rate
• Effusion – the process in chich a gas
flows through a small hole in a
container
- Graham’s law of effusion – at cons.
tempt & pressure the rate of effusion
of gas molecules is inversely
proportional to the square root of the
molecular weight of the gas
- Rate of effusion depends upon
cross sec. of whole, # mol per unit
vol, average molecular speed
Graham’s Law
• Because mu (average speed) = the
square root of 3RT/M M = molar
mass
• Then Graham’s Law
Rate of effusion is port 1/ square root
of the molar mass
• Calc. the ration of effusion rates of
molecules of CO2 and SO2.