# 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

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!!)

DALTON'S LAW OF PARTIAL PRESSURES (p. 391 – 392 in text book)

* 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?