UNIT 10 - GASES
KINETIC
MOLECULAR (K-M) THEORY OF MATTER (p. 385 – 387 & p. 419 – 420 in text book)
- based on the idea that particles of mattter are always in motion
- assumptions of the K-M Theory
1.) Gases consist of large numbers of tiny
particles that are far apart relative to their size.
This
means that _________________________________________________________
______________________________________________________________________
2.) Collisions between gas particles and
between particles and container walls are elastic
collisions. This means that
________________________________________________
______________________________________________________________________
______________________________________________________________________
3.) Gas particles are in constant,
rapid, random motion.
This
can be inferred because ______________________________________________
4.) There are no forces of attraction
or repulsion between gas particles.
This
means that _________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
5.) The average kinetic energy of gas
particles depends on the temperature of the gas.
This
means that _________________________________________________________
Also,
__________________________________________________________________
- GASES BEHAVE NEARLY
IDEALLY UNDER CONDITIONS of _________ temperature,
_________ pressure, &
_________ molar mass.
PROPERTIES OF GASES
- In order to fully describe a gas, four
measurable quantities must be stated.
* PRESSURE: ________________________________________________
units: 1 atm = _____ mm Hg = _____ torr = _____ kPa = _____ Pa
measured with a ___________________
* TEMPERATURE: ____________________________________________
units: degrees Celsius (oC), Kelvins (K), or oF (oF not usually used in class)
how to convert from oC to K?____________________________________
** “STP” stands for
“Standard Temperature and Pressure”. The
conditions at STP are exactly 1 atm pressure and
exactly 0 oC. **
* VOLUME: _________________________________________________
units: 1 Liter (L) = _____ mL = _____ cm3 = _____ dm3
* QUANTITY: _______________________________________________
units: moles how to convert
from grams to moles? __________________
THE IDEAL GAS EQUATION
(p. 434 – 436 in text book)
P
V = n R T
"P" stands for
__________________, must be in units of __________________
"V" stands for
__________________, must be in units of __________________
"n"
stands for __________________, must be in units of __________________
"T" stands for
__________________, must be in units of __________________
"R" stands for the
Ideal Gas Constant , has a value of 0.0821 with units of
L . atm
mole . K
EXAMPLE 1:
Q: What
pressure is exerted by 0.325 moles of hydrogen gas in a 4.08 L container at 35 oC?
A: P V = n R T solving
for P
...
P = n R T
V
n = 0.325 moles (correct unit)
T = 35 oC (need to convert to K)
V = 4.08 L (correct unit)
T = 35 oC + 273 = 308 K
P = (0.325 moles) (0.0821 L atm/mole K) (308 K) =
2.01 atm
(4.08 L)
EXAMPLE 2:
Q: What mass
of chlorine gas, Cl2, in grams, is contained in a 10.0 L tank at 27 oC and 3.50 atm
of
pressure?
(Answer: 101 grams)
EXAMPLE 3:
Q: A gas at
20.0 oC and 3.98 atm
contains 1.45 moles of gas particles. What volume does
the gas
occupy?
(Answer: 8.77 L)
GAS LAWS (p. 421 – 433
in text book)
* Unlike Ideal Gas
Equation, the "Gas Laws" describe one gas undergoing a change
in conditions.
The Gas Laws are also different from
the Ideal Gas Equation because you do not have to convert any
units except temperature that has to
be in Kelvins.
Combined Gas Law:
P1 V1 = P2 V2
T1 T2
* All of the other gas laws
can be derived from the combined gas law. *
~ Boyle's Law
- describes relationship between pressure
and volume when temperature is constant
- because temperature is constant, it can
be excluded from the equation
- so, equation for Boyle's Law is
____________________________
- pressure & volume are
__________________ proportional
- graph of pressure vs. volume would have
the general shape of
EXAMPLE: A sample of gas occupies 15 liters under 2.1 atm of pressure.
What would the volume of the gas be if the pressure were decreased to
1.2 atm?
(Assume that temperature is constant.)
~ Charles' Law
- describes relationship between volume and
temperature when pressure is constant
- because pressure is constant, it can be
excluded from the equation
- so, equation for Charles' Law is
____________________________
- volume & temperature are ________________
proportional
- graph of volume vs. temperature
would have the general shape of
EXAMPLE: When I purchase a helium balloon at the store
(where the temperature is 25 oC) for my
friend’s birthday, the clerk fills the balloon to a volume of 20.0 liters. When I go outside, the balloon shrinks to a
volume of 17.9 liters. What is the
temperature outside?
~ Gay-Lussac's Law
- describes relationship between pressure and
temperature when volume is constant
- because volume is constant, it can be excluded
from the equation
- so, equation for Gay-Lussac's Law is
_________________________
- pressure & temperature are _______________
proportional
- graph of pressure vs. temperature would have
the 
general shape of
EXAMPLE: An aerosol can has
an internal pressure of 2.75 atm at room temperature
(25 oC).
What is the pressure in the can if I leave it outside in the sun and the
temperature goes up to 35 oC?
Applications of the
Ideal Gas Law (p. 436 – 438 in text book)
EXAMPLE #1:
Q: At 28 oC and 0.974 atm, 1.00
L of gas has a mass of 5.16 grams. What is the molar mass of this gas?
A: P V = n R T * given T, P, V
& R is constant, we must solve for n *
n = P V = (0.974 atm) (1.00 L) =
0.0394 moles
R T (0.0821 L atm/mole K) (301 K)
moles = grams
MM
MM = grams = 5.16 grams = 131 g/mole
moles 0.0394 moles
EXAMPLE #2:
Q: What is the
molar mass of a gas if 0.427 grams of the gas occupies a volume of 125 mL at
20.0 oC
and 0.980 atm? (A: 83.8 g/mole)
*Honors only
EXAMPLE 3:
Q: What is the density of argon gas, Ar, at
a pressure of 551 torr and a temperature of 25 oC?
A:
density = mass
P V = (mass/MM) R T
volume
P = (mass/MM) R T
P MM = mass
Density = P (MM)
V
R T
V
R T
P = 551 torr x 1 atm =
0.725 atm
T = 25 oC + 273 = 298 K
760
torr
D = (0.725 atm) (39.9 g/mole)
= 1.18 g/L
(0.0821 L atm/mole
K) (298 K)
EXAMPLE
4:
Q: The
density of a gas was found to be 2.0 g/L at 1.50 atm
and 27 oC. What is the molar mass of
the gas? (A: 33 g/mole)
GAS STOICHIOMETRY (p.
440 – 443 in text book)
* chemical
reaction is happening
* deals with two different substances (at least 1 is a gas)
* given chemical equation
* assume reaction occurs at STP unless otherwise noted
--------------------------------------------------------------
STOICHIOMETRY STEPS
~ Balance the
equation
~ Write the important information from the problem
1st addition to
“train tracks”: use
molar mass of given substance (if given a # of grams) or
use 22.4 L =
1 mole of gas @ STP (if given liters)
2nd addition to
“train tracks”: use
coefficients in the mole ratio
3rd addition to
“train tracks”: use
molar mass of unknown substance (if problem asks for grams) or
use 22.4 L =
1 mole of gas @ STP (if problem asks for liters)
Example # 1
How many
Liters of carbon dioxide gas can be produced from the decomposition of 4.50
grams of sodium carbonate?
Na2CO3 à Na2O + CO2
4.50 g Na2CO3 | 1
mole Na2CO3 |
1 mole CO2 | 22.4 L CO2 = 0.951 L CO2
| 106 g Na2CO3 | 1 mole Na2CO3
| 1 mole CO2
Example # 2
How
many grams of aluminum are needed to completely react with 16.0 L of oxygen?
Al + O2
à Al2O3
(Ans: 25.7 g)
STOICHIOMETRY MAP (updated and improved!!)
* DEALS WITH A MIXTURE OF
DIFFERENT GASES *
1.) The sum of the
pressures of the individual gases equals the total pressure exerted by the
mixture of gases.
PTOTAL = Pgas1 + Pgas2 + ...
EXAMPLE: A mixture
of oxygen and nitrogen exerts 1.1 atm of
pressure. What is oxygen's partial pressure if the pressure of the
nitrogen gas is 0.8 atm?
2.) The pressure of a gas "collected over water" is equal to
the atmospheric pressure minus the vapor pressure of the water.
Pgas = Patm
- Pwater
EXAMPLE: A 44.6 mL
sample of carbon dioxide is collected over water at 765 mm Hg pressure and 25 oC. What is the vapor pressure of the
"dry" gas? (The vapor pressure of water at 25 oC is 23.76 mm Hg. You will have to look up
this value on a table or this value must be given to you.)
3.) The partial
pressure of a gas is equal to the "mole fraction" multiplied by the
total pressure.
Px = (moles
x) . Ptotal
“Px“ = partial pressure of certain gas
(total moles)
* "mole
fraction" = (moles x)
(total moles)
EXAMPLE: A mixture
of gases contains 2.0 moles of He and 4.0 moles of
oxygen. If the mixture exerts a pressure of 801 torr,
what is the partial pressure of the oxygen?
GRAHAM'S LAW OF
EFFUSION (p. 387 in text book)
* compares the rates of
effusion of different gases
* lighter gases (lower molar
masses) effuse faster than heavier gases (higher molar masses)
rate A
= MM
B
rate
B MM
A
the rate of gas A compared to the rate
of gas B is equal to the square root of the inverse of the molar masses of the
gases
EXAMPLE 1: Compare
the rates of effusion for oxygen gas and hydrogen gas.
EXAMPLE 2: An unknown
gas effuses 1.18 times faster than SO2. What is the molar mass
of the unknown gas?
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