gas laws notes
TRANSCRIPT
Gas Laws
Table of Contents:
I. Kinetic Molecular Theory
II. Ideal vs. Real Gases
III. Vapor Pressure
IV. Avogadro's Law
V. Boyle's Law
VI. Charles' Law
VII. Gay-Lussac's Law
VIII. Combined Gas Law
IX. Dalton's Law of Partial Pressures
X. Ideal Gas Law
XI. Density of Gases
XII. Graham's Law of Diffusion
POWER POINT SLIDES
Gas Laws
I. Kinetic Molecular Theory
The four tenets (for our purposes) of the KMT of gases
A. The particles of a gas move in random straight-line motion.
check THIS SITE out
B. The volume of the gas particles themselves are insignificant
compared to the volume of the overall container.
C. The intermolecular forces of attraction (IMF's) between
particles are considered negligible (KE>IMF)
Why? gases are typically nonpolar and exhibit extremely weak VanDerWaals
forces, higher temp = faster motion
D. Collisions between particles is considered elastic meaning
no energy is lost.
What would happen to gases if this were not true?
II. Ideal vs. Real Gases
An ideal gas is a gas which obeys all of the tenets of the KMT and
adheres to gas law calculations all of the time.
There are NO ideal gases because, in truth, gas particles exhibit
some IMF's (however small) and can be liquefied
under conditions of high pressure and low temperature.
Therefore all gases are real gases which act like ideal gases under
all but the aforementioned conditions. The gases
with the smallest forces of attraction will be the most ideal, and
also the hardest to liquefy. The gases with relatively
large forces of attraction will be the least ideal and easiest to
liquefy.
MOST IDEAL GAS: #1 He (bp=4K) #2 H2(bp=20K)
LEAST IDEAL GASES: Rn (bp=211K), NH3(bp=240K),
H2O(bp=373K)
III. Vapor Pressure - CLICK HERE (for applet)
Definition: The upward force exerted by a liquid as it's particles
jump into the gaseous phase.
A. High vapor pressure (v.p.) - liquids with high vapor
pressure tend to have relatively weak IMF's therefore jump
easily into the gaseous phase.
1. Examples: Acetone, Ethanol, gasoline, perfumes
(notice that all of theses liquids give off a strong odor)
2. Table H - use this table to determine the v.p. of different
liquids at given temperatures.
B. Low vapor pressure - liquids with strong IMF's will not
readily turn into a gas
C. Boiling Point - The b.p. of any liquid is the temperature at
which it's Vapor Pressure = Atmospheric Pressure
D. Increasing the temperature of a liquid will increase it's
Vapor Pressure.
1. You will notice that the lower the vapor pressure of a
liquid the hotter you will need to heat it to get it to boil.
CHALLENGE QUESTION: What are the TWO ways to
get a liquid to boil?????
IV. Avogadro's Law - 1 mole of any gas at STP (273K,
101.3kPa) occupies 22.4 Liters
*see derivation under Ideal Gas Law notes.
V. Boyle's Law
A. History -
B. There is an INVERSE relationship between the pressure
and volume of a has at constant temperature.
1. As pressure on a gas increases it's volume will decrease
and vice versa.
a. Example: As the pressure on a gas is doubled it's
volume will be reduce to one half.
2. Any pressure x volume in this sample = constant. P x V
= k
3. Therefore P1 x V1 = P2 X V2
a. PRACTICE PROBLEMS:
(1) The pressure on 5 L of gas increases from
101.3 kPa to 202.6kPa at constant
temperature. What is the new volume it will
occupy? 2.5L
(a) The sample of gas initially at 2 atm and
occupying 6.4L is allowed to expand to
9.6L at constant temperature. What will the
new pressure be? 1.33 atm
(2) If the pressure on 30L a gas triples it’s
volume will be? 10L
b. ONLINE PRACTICE: CLICK HERE
ONLINE ANIMATION: CLICK HERE
VI. Charles' Law
A. History -
B. There is a DIRECT relationship between the
temperature(absolute) and volume of a gas at constant
pressure.
1. As the temperature of a gas increases it's volume also
increases proportionately. Therefore if you double
temperature (K) of a gas the volume will also double.
Halving the temperature will halve the volume.
2. You will notice from the graph above that dividing any
volume by it's corresponding temperature equals a
constant.
Therefore:
3. Practice Problems:
a. A 20 L sample of oxygen is heated from 20oC
to 40oC at constant pressure. What is the new
volume?
21.37L
b. What temperature must a 15 ml sample of
gas initially at 600K be changed to to occupy
5 ml?
200K
4. Online Practice: CLICK HERE
Online Animations: CLICK HERE
5. Demo: green-fountain--chemistry-experiment.mov
VII. Gay-Lussac's LawA.
B. This is the same relationship as Charles' Law therefore the
equation and the graph will be synonymous.
C. Practice Problem
1. The temperature on a gas at 50 kPa, at
constant volume, is raised from 200oC to
400oC. What is the new pressure in kPa, torr?
71.1 kPa , 533.7 torr
D. Cool online animation CLICK HERE
E. Green Fountain Demo CLICK HERE
VIII. The Combined Gas Law
The Combined Gas Law is nothing more than the combination of
the three laws we have just discussed. In most circumstances it is
preferable to simply use the CGL when answering questions
about temp, volume and pressure of any gaseous sample. It has
the advantage of being able to incorporate changing two variables
at once and still being able to calculate for the third. If anything
is held constant, simply cross that out of the equation.
A. Practice Problems:
1. A 100ml sample of gas initially at 200K and 2 atm is
heated to 400K and the pressure is reduced to 1 atm.
What will the new volume be?
2. The volume of a gas-filled balloon is 30.0 L at 313 K
and 153 kPa. What would the volume be at STP?
IX. Dalton's Law of Partial Pressure
A. Dalton's law of partial pressures states that the
total pressure exerted by a gaseous mixture is
equal to the sum of the partial pressures of each
individual component in a gas mixture. This
empirical law was observed by John Dalton in
1801 and is related to the ideal gas laws. (This is the
same John Dalton
who proposed the idea of the "atom")
B. Ptotal = P1 + P2 + . . . Pn
• Pt is the total pressure of a sample which contains a mixture
of gases
• P1, P2, P3, etc. are the partial pressures (in the same units) of
the gases in the mixture
It is important to understand that the partial
pressure, as well as partial volume is a
direct result of the molar ratio (fraction) of
each gas.
C. Example:
1. A sample of gas contains 1 mole O2 and 1 mole He and 2
moles of N2 at STP. What are the partial pressures of each
component?
D. Gas Collection over Water:
1.
2. In order to ensure that a sample of gas will contain only
the gas you are intending they are typically collected
through water displacement, or "over water." However,
there is an unavoidable problem. The gas will contain
some water vapor due to the vapor pressure of water at
that temperature. This means that the total pressure
inside the bottle is the sum of two pressures - the gas
itself and the added water vapor.
WE DO NOT WANT THE WATER VAPOR
PRESSURE.
So we get rid of it by subtraction.
Pdry gas = Ptotal - Pwater vapor Table H For
cool video click HERE
PRACTICE PROBLEMS:
3. A sample of hydrogen gas is collected over water at 14.0 oC. The pressure of the resultant mixture is 113.0 kPa.
What is the pressure that is exerted by the dry hydrogen
alone? Pdry gas =835.8mmHg
4. A mixture of oxygen, hydrogen and nitrogen gases exerts
a total pressure of 278 kPa. If the partial pressures of
the oxygen and the hydrogen are 112 kPa and 101 kPa
respectively, what would be the partial pressure exerted
by the nitrogen? Pnitrogen = 65 kPa
5. 130 mls. of oxygen gas is collected over water at 22oC
and 753torr. What is the volume of the dry gas alone?
Step 1- from table H we determine the v.p. of H2O= 6kPa or
45 torr.
PT = PO2 + PH2O
PO2 = 753 torr - 45 torr
PO2 = 708 torr
Step 2- VO2 = (708 torr / 753 torr) x 130mls
VO2 = 122.2 mls.
Follow-up question: What volume would this gas occupy
at STP?
Using the CGL and the answer from above: VO2 =
119 mls
X. Ideal Gas Law
Only ONE set of conditions are given,
Moles or mass of a gas is given/asked.
A. PV=nRT
The ideal gas law is used when:
1. Only ONE set of conditions are given
2. Moles or mass of a gas is given/asked
B.
C. These units are derived according to which pressure value
is given: R = PV/nT
D. Avogadro's Law:
E. Practice Problems:
1. What is the volume of 3.00 moles of Cl2 at 300. torr
and 500. K? 312L
2. What would the pressure be on 10.0g H2 if it occupied
20.L at a temp. of -100.0oC? 3.5atm, 360kPa, 2700torr
F. Online Practice: CLICK HERE
XI. Density of Gases
A. At STP the density calculation is quite simple. We can use
the formula D = m/V
Since all gases will occupy 22.4L (avogadro's Law) calculating
density is simply a matter of
substituting in the gases molar mass.
Densities of common gases at STP:
1. DCO2 = 44 g / 22.4 L = 1.96 g/L
2. DO2 = 32 g / 22.4 L = 1.43 g/L
3. DN2 = 28 g / 22.4 L = 1.25 g/L
4. DXe = 131.3 g / 22.4 L = 5.86 g/L
5. DHe = 4 g / 22.4 L = .18 g/L
B. If a gas is not at STP you need to incorporate the Ideal Gas
Law as well.
1. D = m * P / n * R * T (in terms of mass and moles) or
2. D = m.w. * P / R * T (in terms of m.w.)
C. Practice problems:
1. What is the density of hydrogen sulfide gas if the pressure is
205kPa and the temperature is 220K? 3.8 g/L
2. Two moles of a gas at 150 K have a density of 2 g/L and a
mass of 45g. What is the pressure of the system? 5.84 L
3. What is the density of ammonia gas at 683 torr and 250.1K?
0.744 g/L
XII. Graham's Law of Diffusion
A. Diffusion is the ability of a gas to pass through a medium from
high to low concentration.
B. The diffusion rate of gases are directly related to their molar
masses, the SMALLER a gas the FASTER it diffuses through a
medium.
C.
D. Think running backs in football. Small and agile guys get
through the line faster than bigger, more bumbling ones.