Transcript Gas Notes (Chapter 10) Part 1

Gas Notes (Chapter 10)
Part 1
Gases are made up of atoms and molecules
just like all other compounds, but because
they are in the form of a gas we can learn a
great deal more about these molecules and
compounds. It might seem a bit confusing
because we can’t see most gases, but we
know they exist.
I. Let’s look at some of the
Nature of Gases:
• 1. Expansion – gases do NOT have a definite
shape or volume.
• 2. Fluidity – gas particles glide past one another,
called fluid just like a liquid.
• 3. Compressibility – can be compressed because
gases take up mostly empty space.
• 4. Diffusion – gases spread out and mix without
stirring and without a current. Gases mix
completely unless they react with each other.
II. Kinetic Molecular Theory
of Gases
Particles of matter (any type) are in
constant motion! Because we
know this we have a few
assumptions that we make about
gases, called the Molecular
Theory of Gases:
• 1. Particles of a gas are in constant, straight-line
motion, until they collide.
2. Gases consist of a large number of tiny particles;
these particles are very far apart, therefore gas is
mostly empty space.
• 3. Collisions between particles of a gas and the
container wall are elastic. Which means there is
no loss of energy.
• 4. There are no forces of attraction or
repulsion between particles of gases.
http://www.bcpl.net/~kdrews/kmt/kmtpart4.html#Part%204
5. The average kinetic energy of gas
particles depends on the temperate of the
gas. KE=1/2 mv2 (m=mass in kg and
v=velocity is m/sec)
http://www.bcpl.net/~kdrews/kmt/kmtpart5.html#Part%205
III. Ideal VS Real Gases
• Ideal gases always obey the kinetic
theory. (Closest to ideal would be the
noble gases.)
• Real gases vary from the kinetic
theory at various temperatures and
pressures.
IV. Volume, Pressure, Temperature,
Number of Moles (Descriptions of
Gases)
• 1. Volume – refers to the space matter
(gas) occupies. Measured in liters (L).
1L = 1000mL
• 2. Pressure – the number of times particles
collide with each other and the walls of the
container (force exerted on a given area).
Measured in atmospheres (atm).
http://chemmac1.usc.edu/bruno/java/pressure.html
1atm = 760 millimeters Hg ( Barometers use Hg)
1atm = 760 torr (Named after Torricelli for the
invention of the barometer)
1atm = 101.3 kPa - kilopascals
Practice: Convert 4.40 atm to mmHg.
Convert 212.4kPa to mmHg.
• 3. Temperature – as temperate increases
gas particles move faster, as temperature
decreases gas particles move slower.
Measured in Kelvin (K).
K = 273 + C
Practice: Convert 32.0°C to K.
Convert 400. K to °C.
• 4. Number of Moles – tells you how much
of a certain gas you have
1 mole = number of grams of the compound
or element (molar mass)
STP – “standard temperature and pressure”
which is 0C and 1.00 atm.
V. Gas Laws - How do all of pressure,
temperature, volume, and amount of a gas
relate to each other? Rules for solving gas law
problems: 1st write down what is given and
what is unknown, 2nd identify the gas law you
want to use, and 3rd rearrange the formula to
solve for the unknown and then solve the
problem. (If temperature is involved, it MUST
be converted to Kelvin! K = 273 + C)
A. Boyle’s Law - Pressure and Volume
(when temperature remains constant)
V1P1 = V2P2
V1 = initial or old volume
V2 = final or new volume
P1 = initial or old pressure
P2 = final or new pressure
Inverse Relationship (As pressure increases,
volume decreases and as pressure decreases,
volume increases.)
1a. A gas occupies 3.00L at 1.00atm of pressure.
What volume does it occupy at 5.00atm?
2a. What is the new pressure when 80.0mL of gas at
500.mmHg is moved to a 100.mL container?
3a. A gas at 800.torr of pressure has a volume of
5.00L. What volume does this gas occupy at
1.00X103torr of pressure?
B. Charles’ Law -Volume and Temperature
(when pressure is constant) Figure 10-11
page 316
V1 = V2
T1
T2
T1 = initial or old temperature
T2 = final or new temperature
Direct Relationship (As temperature
increases, volume increases and as
temperature decreases, volume decreases.)
1b. A gas has a volume of 500.mL at 298K. What
volume does it have at 373K?
2b. A gas had a volume of 250.mL and a
temperature of 125C. What is the final
temperature (in K) if the volume is changed to
100.mL?
3b. This initial volume of a gas is 250.mL at 30.0C.
What is the temperature of the gas with a new
volume of 667mL?
C. Gay-Lussac’s Law - Pressure and
Temperature (when volume is constant)
• P1 = P2
• T1 T2
• Direct Relationship (As temperature
increases, pressure increases and as
temperature decreases, pressure decreases.)
Temperature and Pressure (GayLussac’s Law) Gas Demonstrations
• Inverted Fountain
As the temperature of the gas increases the
pressure of the gas increases. (Inverting the
flask into the water showed that the pressure
increased because water was pulled into the
flask.)
1c. The gas in an aerosol can is at 3atm of pressure
at 298K. What would the gas pressure in the can
be at 325K?
2c. At 120.C the pressure of a sample of nitrogen
gas is 769torr. What will the pressure be at
205C?
3c. A gas at 32.0C has a pressure of 0.0400atm. If
the temperature increases to 44.0C what is the
new pressure of the gas?
D. Combined Gas Law - Pressure, Temperature,
and Volume (None of the variables are constant)
V1P1 = V2P2
T1
T2
1d. A helium filled balloon has a volume of 50.0mL
at 298K and 1.08atm. What volume will it have at
0.855atm and 203K?
2d. Given 700.mL of oxygen at 7.00C and 7.90atm
of pressure, what volume does is occupy at 27.0C
and 4.90atm of pressure?
3d. A gas has a volume of 1.140L at 37.0C and
620.mmHg. Calculate its volume at 0C and
760.mmHg.
Gas Worksheet #1 is due next class!
E. Daltons Law of Partial Pressures
The pressure of each gas in a mixture
is called the partial pressure of that
gas. Daltons Law of Partial Pressure
states that the total pressure of a
mixture of gases is equal to the sum
of the partial pressures of the
component gases.
PT = P1 + P2 + P3 + ……. PT = total
pressure
P# = the partial pressures of the individual
gases
• 1e. A mixture of gases has the following partial
pressure for the component gases at 20.0C in a
volume of 2.00L: oxygen 180.torr, nitrogen
320.torr, and hydrogen 246torr. Calculate the
pressure of the mixture.
• 2e. What is the final pressure of a 1.50L mixture
of gases produced from 1.50L of neon at
0.3947atm, 800.mL of nitrogen at 150.mmHg and
1.2oL of oxygen at 25.3kPa? Assume constant
temperature. (Hint use Boyle’s law.)
Daltons Law applied to Gases Collected by Water
Displacement – Figure 10-15 page 324
Patm or PT= Pgas + PH2O
Patm or PT= barometric pressure or total
pressure
Pgas = pressure of the gas collected
PH2O = vapor pressure of water at specific
temperature (Found on page 899 of you
textbook.)
• 3e. Oxygen gas from the decomposition reaction of
potassium chlorate was collected by water displacement at
a pressure of 731torr and a temperature of 20.0C. What
was the partial pressure of the oxygen gas collected?
• 4e. Solid magnesium and hydrochloric acid react
producing hydrogen gas that was collected over water at a
pressure of 759mmHg and measured 19.0mL. The
temperature of the solution at which the gas was collected
was 25.0C. What would be the pressure of the dry
hydrogen gas? What would be the volume of the dry
hydrogen gas at STP?
F. Ideal Gas Law (PV = nRT) – to use
this law, all units must be as follows:
•
•
•
•
•
P = pressure in atm
V = volume in liters
n = number of moles
T = temperature in Kelvin
R = (0.0821L) (1atm)
(1mol) (1K)
• R is the ideal gas constant (page 342 in book
describes where this constant came from.)
• 1f. How many moles of CH4 gas are there
in 85.0L at STP?
• 2f. What volume will be occupies by
1.50grams of nitrogen monoxide gas at
348K and pressure of 300.mmHg?
• 3f. A volume of 11.2L of a gas at STP has
how many moles?
G. Solving for Density and /or Molar
Mass of a gas using the Ideal Gas Law
1. Density (units are g/L) Use the Ideal Gas
Law to find moles (n), convert n to grams
OR use the Ideal Gas Law to find the
volume. Divide n (in grams) by the
volume.
• 1g. What is the density of a sample of
ammonia gas, NH3, if the pressure is 0.928
atm and the temperature is 63.0C?
• 2g. What is the density of argon gas at a
pressure of 551 torr and a temperature of
25.0C?
2. Molar Mass (units are g/mol) If density is
given, use the density of the gas to
determine the molar mass (use 1 L at the
volume and solve for n). If a mass is given,
use the Ideal Gas Law to solve for n and
then find the molar mass.
• 3g. The density of a gas was found to be
2.00g/L at 1.50atm and 27.0C. What is the
molar mass of the gas?
• 4g. What is the molar mass of a gas if
0.427g of the gas occupies a volume of
125mL at 20.0C and 0.980atm?
H. Molar Volume of Gases
Recall that 1 mole of a compound contains 6.022 X 1023 molecules
of that compound – it doesn’t matter what the compound is.
One mole of any gas, at STP, will occupy the same volume as
one mole of any other gas at the same temperature and pressure,
despite any mass differences. The volume occupied by one
mole of a gas at STP is known as the standard molar volume of a
gas. It has been found to be 22.4liters. We can use this as a new
conversion factor 1mol of gas/22.4L of same gas. (Avogadro’s
Law states that equal volumes of gases at the same temperature
and pressure contain equal numbers of molecules.
• 1h. What volume, in L, is occupied by 32.0
grams of oxygen gas at STP?
I. Stoichiometry of Gases
Just like mole ratios can be written from an
equation so can a volume ratio-same
concept!
•
2CO(g) + O2 (g)  2CO2 (g)
• 1i. Using the above equation, what volume of oxygen gas
is needed to react completely with 0.626L of carbon
monoxide to form carbon dioxide?
• 2i. How many grams of solid calcium carbonate must be
decomposed to produce 5.00L of carbon dioxide gas at
STP?
• 3i. How many liters of hydrogen gas at 35.0C and
0.980atm are needed to produce 8.75L of gaseous water
according to the following equation?
•
WO3(s) + 3H2(g)  W(s) + 3H2O(g)
J. Graham’s Law IV. Effusion and
Diffusion
• Graham’s Law states that the rates of
diffusion/effusion of gases at the same
temperature and pressure are inversely
proportional to the square roots of their molar
masses. Effusion is the process whereby the
molecules of a gas confined in a container
randomly pass through a tiny opening in the
container. (onions on page 352)
• Rate of diffusion/effusion of A =
Rate of diffusion/effusion of B
√(MB/MA)
MA or B = molar mass of that compound
Gas A is the lighter, faster gas
Rate of diffusion/effusion is the same as the
velocity (or speed) of the gas.
After the rates of diffusion/effusion for two gases are
determined, the gas with the lower molar mass
will be the one diffusing/effusing fastest.
• 1j. Compare the rates of effusion for hydrogen
and oxygen at the same temperature and
• pressure. (Which one effuses faster and how much
faster is it effusing?)
• 2j. A sample of hydrogen effuses through a porous
container about 9 times faster than an unknown
gas. Estimate the molar mass of the unknown gas.
Graham’s Law and Time
Graham’s Law and Time – the time it takes
a gas to effuse is directly proportional to
its molar mass.
tA = MA
t = time
tB MB
• 3j. A sample of an unknown gas flows
through the wall of a pours cup in 39.9
minutes. An equal volume of helium (under
same temperature and pressure) flows
through in 9.75 minutes. What is the molar
mass of the unknown gas?