12.1 General Properties/ Kinetic Molecular Theory
Some characteristics are familiar to all gases
and are listed below.
1) Gases expand spontaneously to fill their
containers.
2) Gases form homogenous mixtures with each
other.
3) Gases have a low density and high velocity.
4) Gases are highly compressible.
Under ordinary temperature and pressures the
most common compound gases are metallic. This
is not to say that other compounds cannot be
vaporized into gases. Gases have a high kinetic
energy(KE). Kinetic energy is the "energy that
matter possesses due to it's motion'.
Scientists have devised a kinetic Molecular Theory
based on the motion of particles.
1) Submicroscopic gas particles move in straight
lines.
2) Molecules collide with the containers as well as
each other without loss of energy.
3) Trapped gases consist of mostly empty space,
the actual volume of molecules is small.
4) There are negligible attractive forces among
gases.
5) All gases have the same average kinetic energy
at the same temperature.
Pressure by definition "is the force exerted on a unit
area".
In the English system the pressure units is pounds per
square inch (psi). Atmospheric pressure can be measured
using a mercury barometer.
The millimeter of mercury is also called a torr.
* Convert between units
Exp: Convert o.637 atm to torr.
Ordinarily gas temperatures are measured with a
thermometer and expressed in Celsius. However,
absolute temperature which is expressed in
Kelvin(k) is used in solving gas problems. Temperature
varies the pressure of a gas in a fixed volume. Increasing
temperature increases the rate of collisions which
increases the pressure.
Common reference points of temperature and
pressure called standard temperature and pressure(STP)
were selected in order to compare volumes of gases.
st = 273.15K or 0°C
sp = 1 atm or 760 torr or 760 mm Hg or 101.325 k Pa
Four variables are usually sufficient to define the
condition or state of a gas.
1) Temperature (T)
2) Pressure (P)
3) Volume (V)
4) Number of moles (n)
12.4 Boyle's Law (pressure-volume)
Robert Boyle determined the relationship
between pressure and volume through a series
of experiments. * The volume of a fixed mass of
gas at a constant temperature is inversely proportional
to the pressure.
Multiplying both sides of the equation by V shows
that the product of volume and pressure are constant.
PV = constant or PV = K
Inverse proportionality means when one factor increases
the other decreases. At a constant temperature and fixed
amount of gas, changes in the pressure will produce
a constant product of pressure x volume.
V1P1= V2P2
Exp: Starting volume 6.18 liters at 776 torr find the
volume of gas at pressure 827 torr.
This example gives you V1 = 6.18, P1 =776torr, and
P2 = 827torr. We need to solve for V2.
Isolate V2 from the this equation V1P1= V2P2
Now substitute the given numbers and calculate
the answer.
12.5 Charle's Law (volume-temperature)
In 1787 J.A.C. Charles performed experiments in
which the volume of a fixed quantity of gas was
measured at a constant pressure but different
temperatures.
A relation of two different temperatures to a volume
of gas:
Exp: 2.67 liters of a gas, measured at 42°C are heated
to 65°C at constant pressure. What is the new volume
of gas?
Given to us is V1 = 2.67L, T1 = 42°C, and T2 = 65°C.
We need to solve for V2.
Now plug in your numbers.
12.6 Gay-Lussac's Law (pressure-temperature)
"The pressure exerted by a fixed quantity of gas at
constant volume is directly proportional to the absolute
temperature (kelvin)".
P= KT
Exp: The gas in a stoppered Erlenmeyer flask exerts a
pressure of 0.77 atm at 16°C. What will the pressure be
if the temperature is raised to 29°C?
We need to solve for P2.
Given the initial volume, pressure, temperature, and
final values of any two variables, find the value of the third.
Note (Fixed quantity of gas)
Exp: What would be the volume at STP of 4.62 liters of
nitrogen gas at 729 torr at 18°C?
What is being asked for?
Given to us is initial volume = 4.62L
" pressure = 729torr
" Temperature = 18°C
The question asks for a volume at STP. V2 is what is
being asked of you to find. Earlier we gave you STP.
This equation was derived from the relationship of all gas
laws which is:
Using subscripts 1, and 2 for initial and final values
gives us:
To solve for a value that is needed you must first isolate
that variable from this equation.
12.8 Dalton's Law of Partial Pressure
"The total pressure of a mixture of gases is the sum
of the partial pressure exerted by each of the gases in the
mixture".
P total = PA + PB + PC
*Be able to find the total pressure given the partial pressure
of each type of gas.
*Find a partial pressure of a remaining gas given the total
pressure of a gaseous mixture and information from which
partial pressure of other gases can be found.
Exp: If in a gas mixture the partial pressure of ethane is
190 torr, of propane 470 torr, and of butane 680 torr, find
the total pressure of the mixture.
P= 190torr + 470torr + 680torr = 1340torr
Exp: If the total pressure in oxygen generator is 674torr
and the temperature of the system is 32°C at which the water
vapor pressure is 21.7 torr. What is the partial pressure of the
oxygen?
PO2= P- pH2O
674 - 21.7 = 652 torr
12.9 Avogadro's Law(volume-quantity)
"Equal volumes of different gases at the same
temperature and pressure contain the same number of
molecules".
Exp:
" When measured at the same temperature and pressure,
the ratios of volumes of reacting gases are small whole
numbers".
A single equation exists that can tie together the
different proportionality's of the measurable properties
of gas.
R = 0.0821 L-atm
mol . K
This equation states that pressure is inversely related to the
volume while the # of gas molecules and absolute
temperature varies directly with volume.
Given three of the four variables, the other variable can be
found.
Exp: What pressure will be exerted by 0.300mol of gas in
a 4.00L container at 15.0°C.
First: What is the question asking for?
Second: What are the given variables in the equation?
This question states what pressure so what we are looking
for is P. Rearrange the equation so you isolate the P.
Now plug the known variables into the equation and solve
for P.
Did you remember to change your temperature to kelvins and
the constant for R?
12.11 Molar Mass and Gas Density
When measuring and calculating gas density, the ideal
gas equation can be very useful.
The density of a gas is given by the expression:
Rearranging the equation we can now calculate molar mass.
Exp: What is the density of carbon tetrachloride vapor at
612 torr and 98°C?
First: What are you being asked for? Density, so we will
use this equation.
Second: In order to appropriately solve this equation we
have to convert the temperature to kelvin, pressure to
atmosphere, and determine the molar mass of CCl4.
M of CCl4= 12.0+ (4) (35.5)=154g/mol
98°C= 98+ 273.15= 371K
Third: plug in appropriate #s into the equation.
Notice That the atms cancel out as well as the moles and
kelvins. What you are left with is g/L.
If we had not changed our temperature to Kelvin's and our
pressure to atmosphere, they would not have canceled out
and the answer would be incorrect.
Forth: Solve the problem.
d= 4.10 g/L