Unit 8
Chapter 10: Gases
Pages 383-413
There will be a guided reading assignment
in Mastering. It is highly recommended that
you complete this assignment to better
Answer these for bonus points added to
your test! This assignment will close the
morning of your test for this topic.
understand chapter concepts.
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Gases
Crush the Can Demonstration
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
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a small volume of water is in a can
the can is heated and the water boils and the can is then filled with water vapor
the can is quickly sealed and cooled
Atmospheric pressure collapses the can!
o
o
H20(g) condenses to a very small volume - so it cannot counteract the atmospheric pressure so it
collapses.
As a gas the volume completely occupied the can pressing outward.
Characteristics of Gases –
Expand spontaneously to fill its container (V of a gas = V of container)
Highly compressible
Two or more gases will form a homogeneous mixture regardless of identities or proportions
Pressure
1 atm = 760 mm Hg = 760 torr = 101,325 Pa
SI unit pascal is newtons per meter squared (N/m2)
1 atm = 29.92 in Hg = 14.7 lb/in2 (psi)
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Boyles Law
PV = k
Plot of P vs V is a hyperbola.
o
o
o
o
Pressure and volume are inversely related
holds true only at very low pressures
a gas that strictly follows this law is considered IDEAL
Useful for predicting new volumes when pressure is changed at constant temperature
Charles Law
V/T = k
T in Kelvins
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
Volume and temperature are directly related.
at constant pressure
Avogadro
at 25₀C and 1 atmosphere each balloon has 2.5 x 1022 molecules (0.041 mols)
Equal volumes of all gases have the same number of molecules. (Same temp & pressure)
moles
Mathematical equation: V = an
constant
The volume of a gas maintained at a constant temp and pressure is directly proportional to the no. of moles of the gas.
*Double # moles will double volume @ constant temperature and pressure!
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Ideal Gas Law
Combines Boyles Law, Charles Law and Avogadro's Law
V α 1/P
VαT
Vαn
using R as proportionality constant
Ideal gases are hypothetical gases whose pressure, volume, and temperature behavior is completely described by the
ideal-gas equation.
R = gas constant
STP
= Standard temperature and pressure 273 K and 1 atm
1 mole of a gas at STP equals 22.4L - This is the molar volume of an ideal gas.
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Example 1: Calcium carbonate, CaCO3 (s), decomposes upon heating to give CaO (s) and CO2 (g). A sample of
CaCO3 is decomposed and the CO2 is collected in a 250 mL flask. After the decomposition is complete, the
gas has a pressure of 1.3 atmospheres at a temperature of 31₀C. How many moles of CO2 gas were
generated?
Example 2: Tennis balls are usually filled with air or nitrogen gas to a pressure of slightly above atmospheric
pressure to increase their bounce. If a particular tennis ball has a volume of 144 cm 3 and contains 0.33g of
nitrogen gas, what is the pressure inside the ball at 24 ₀C?
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Further application of the Ideal gas equation
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can be used to determine the density of a gas
can be used to determine the molar mass of a gas
can be used to determine the volumes of gases formed or consumed in chemical reactions
molar mass (which equals the number of grams in 1 mole of a substance)
Example 1: What is the density of CCl4 vapor at 714 torr and 125₀C?
Example 2: Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21₀C and 740.0 torr.
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Yesterday we discussed the ideal gas law
Gases are often reactants or products in chemical reactions.
Example: If the amount of gas produced from the decomposition of NaN3 is 36 L at 1.15 atm and 26.0 ⁰C,
how many grams of NaN3 must be decomposed?
Balance:
NaN3 (s) → Na(s) + N2 (g)
Step 1: calculate moles of nitrogen using the Ideal gas law
Step 2: use moles of nitrogen to determine moles of sodium nitride
Step 3 - convert moles sodium nitride to grams
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Example: In the first step in the industrial process of making nitric acid, ammonia reacts with oxygen at 850
⁰C and 5.00 atm and produces nitrogen monoxide and water vapor. How many liters of NH 3 (g) at 850⁰ C
and 5.00 atm are required to react with 1.00 mol of oxygen?
Let's write the equation and balance it.
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Partial Pressures/Dalton & Gas Mixtures
How do we deal with gases composed of a mixture of two or more substances?
J. Dalton - the total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were
present alone.
Pt = total pressure = P1 + P2 + P3...
each gas within a mixture behaves independently
using moles, where nt = total moles
nt = n1 + n2 + n3...
In a mixture at the same temperature and constant volume
Pt = nt RT
V
Example: A mixture of gases made from 6.00 g of O 2 and 9.00 g of CH4 is placed in a 15.0 L vessel @ O⁰C.
What is the partials pressure of each gas & total pressure?
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Mole Fractions
P1 = n1RT/V = n1
mole fraction of gas 1 to the total number of moles in the mixture
Pt = ntRT/V = nt
P1 = n1
P t = nt
solving for P1
P1 =
The partial pressure of a gas in a mixture is its
mole fraction x the total pressure!
Example 1: The nitrogen fraction in air is 0.78 (78% of air is nitrogen) If the total pressure is 760 torr then
the partial pressure of nitrogen is….
Example 2: Data collected suggest the atmosphere of Saturn's largest moon has a total pressure of 1220
torr. The atmosphere consists of 82% nitrogen, 12% Argon, and 6% methane. Calculate the partial pressure
of each of the gases.
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More with Mole Fractions…
0.34 g of Neon, 0.08 g of argon and 0.23 g of helium are mixed. What is the mole fraction of
each gas in the mixture? If the total pressure of the mixture is 740 torr, what is the partial
pressure of each of the gases?
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Collecting Gases over Water - commonly done in lab is to calculate moles of gas collected over water
Total pressure inside = sum of pressure of gas + water vapor pressure
(PH2o)
*You can find vapor pressure values in your textbook in Appendix B!
When one collects a gas over water, there is
water vapor mixed in with the gas.
To find only the pressure of the desired gas,
one must subtract the vapor pressure of water
from the total pressure.
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Example: Ammonium nitrite, NH4NO2 decomposes upon heating to form nitrogen in the following
reaction:
511 mL of nitrogen is collected over water @ 26 ⁰C and 745 torr total pressure. How many grams of
ammonium nitrite were decomposed? *vapor pressure of water @ 26 ⁰C is 25 torr
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KMT - Kinetic Molecular Theory
1. Gases consist of large numbers of molecules that are in continuous, random motion.
2. The volume of molecules of a gas is negligible.
3. Attraction and repulsion is negligible.
4. Energy can be transferred between molecules during collisions.
5. The average KE of the molecules is proportional to the absolute temperature (K)
Meaning.....
At any given temperature the molecules of all gases have the same average KE
Even two different gases, at same temperatures have the same average KE
If the absolute temperature of a gas is doubled, the average KE doubles therefore molecular motion increases with
temperature.
INDIVIDUAL molecules move at varying speeds
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At any instant some of the molecules are
moving rapidly, others more slowly.
At higher temps a larger fraction of molecules is moving at greater speeds!
Also shows u - root mean-square (rms) speed at 0⁰ and 100 ⁰C.
u = speed of a molecule possessing av KE
av KE of gas molecules = 1/2 mu2
Meaning....
if av KE increases with increasing temperatures means rms (u) speed increases
Example: A sample of oxygen gas initially at STP is compressed to a smaller volume at constant temperature. What
effect does this change have on:
a) av KE of oxygen molecules
b) av. speed of oxygen molecules
c) total number of collisions of oxygen molecules with the container walls in a unit of time
d) the number of collisions of oxygen molecules with a unit area of the container walls in a unit time.
Implications of av. KE of gas molecules = 1/2mu2
Light gases (He)
or
Heavier gases (Xe)
Will have same av KE @ same temps
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Because m (mass) is much smaller for He it
has a higher u.
=
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Effusion and Diffusion
Demo -
The two gases diffuse towards each other and where they meet ammonium chloride forms ( a white precipitate).
Discuss where they meet.
Diffusion - describe the mixing of gases. The rate of diffusion is the rate of the mixing of gases.
Effusion - the passage of gas through a small opening into an empty space or container. The rate of effusion measures
the speed at which the gas is transferred into the chamber.
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The difference in the rates of effusion for helium and nitrogen, for example, explains why a helium balloon would
deflate faster.
Graham - experimented with gases and found that effusion rates were inversely proportional to the square root of
the mass of the particles
Mathematically: Tells us that a given temperature lighter molecules move faster than heavier
molecules.
Molar mass in g/mol or kg/mol
Example: Calculate the ratio of the effusion rates of N2 and O2.
Why does it take several minutes for the two gases to meet?
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Van der Waal’s Equation
Conditions such as low temperature and or high pressure mean gases do NOT act ideally.
Causes two things:
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Volume becomes significant (larger)
Gas molecules attract each other – London dispersion forces become significant which causes pressure to
decrease because molecules are sticking together and not causing as much pressure
Result overall is that gases are packed too tightly together!
Result on ideal gas law:
PV = nRT
rearranged for P:
Van der Waal’s introduced two constants a and b to address the “two things” above.
P = nRT
-
V – nb
n2a
V2
Correction for molecular attraction
Correction for volume
Rearranged:
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a and b
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Constants a and b are different for each gas. In your text see Table 10.3
a and b increase with increase n amass of the molecule!
Example: If 1.000 mole of an ideal gas were confined to 22.41 L at 0.0 °c, it would exert a pressure of 1.000
atm. Use the Van der Waal’s equation and Table 5.3 to estimate the pressure exerted by 1.000 mol of Cl 2 in
22.41L at 0.0 °c.
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