Chapter 10. Gases
Watch Bozeman Videos & other videos on my website for additional help: Big Idea 2: • Gases
10.1 Characteristics of Gases
Read p. 398-401. Although relatively few substances exist as gases under typical conditions, they are very
important.
• Supports life, waste receptacle for exhaust gases, shields us from harmful radiation, etc
Ch 12 Ch 11 Ch 10
Shape
Definite Takes the shape of the container
Not Definite
Volume
Definite
Definite
Not Definite – will expand to fill the entire
container Spacing Particles are close to
each other.
Particles are close to each
other.
Particles are very far
apart from each other.
Movement of Particles
Only vibration in bonds
Diffusion - Does not
flow
Constantly moving and
SLIDING past each other.
Diffusion - slow
Constantly moving and colliding
Diffusion - fast
Type of mixtures formed
heterogeneous
Homogeneous or heterogeneous
(depends on polarity)
Homogeneous
Compressible Not compressible
Not compressible
COMPRESSIBLE –
large amount of empty
space between the
particles
When pressure is
applied to a gas, its
volume decreases
(Boyle’s Law).
Density Density – usually high
densities (sink in water)
Density units – g/cm3
Density – usually low
densities (sink or float in
water)
Density units – g/mL
Density – usually low
densities
Density units – g/L
Properties/IMFs Motion of particles is
limited to vibration
within crystalline
structure
Properties (BP, VP,
viscosity, surface tension)
are related to IMFs
Minimal to no IMF.s
Can be described in
terms of amount of gas
(moles, pressure,
volume, and
temperature.
10.2 Pressure
Read p. 401-404.
All gases exert PRESSURE on their surroundings.
• Pressure – the force exerted by gas molecules as they strike the surfaces around them.
The gases most familiar to us are the ones that make up our atmosphere (N2, O2, Ar, CO2, Ne, He, CH4, …)
• Together they exert ATMOSPHERIC pressure on us, and on the earth.
Atmospheric pressure is measured with a BAROMETER (Invented by Italian physicist Torriceli). • If a tube is completely filled with mercury and then inverted into a container of mercury
open to the atmosphere, the mercury will rise 760 mm up the tube.
2 factors that can change atmospheric pressure:
1. Altitude
• At higher elevations there is a smaller amount of “air” above you, so the
atmospheric pressure would be less (barometer reads < 760 mm Hg).
• At lower elevations – greater atmospheric pressure.
2. Weather (humidity)
• In the tropics, theres more H2O molecules in the air. So atmospheric pressure is
greater (Bad hair days)
• In dry regions and deserts, humidity is very low. Few H2O molecules in the air
leads to lower atmospheric pressure.
The history of the barometer – Ted talk. 1. 2. 3. 4. 5. Measuring Pressure with Barometers and Monometers (notes and pics)
Pressure SI unit is the PASCAL (Pa).
Important non SI units used to express gas pressure include:
atmospheres (atm)
torr (torriceli)
millimeters of mercury (mm Hg)
kilopascal (kPa)
pounds per square inch (psi)
1 atm = 760. mm Hg = 760. torr = 101, 325 Pa = 101.325 kPa = 14.7psi
1. Perform the following conversions
a. 657 mmHg to torr
b. 830 torr to atmospheres
c. 7.8 kPa to atmospheres
d. 1200 Pa to mmHg
Examples
Barometer with Hg Pic (We will draw 3 different pics here) – See p.403
2. In the lab, a barometer indicates that the atmospheric pressure is 764.7torr. A sample of
gas is placed in a flask attached to an open-end mercury manometer. The height of the
mercury in the open end arm is 136.4mm, and the height in the arm in contact with the
gas in the flask is 103.8mm. What is the pressure of the gas in the flask (a) in
atmospheres, (b) in torr. (Draw and Label the barometer)
10.3 The Gas Laws
Read p. 404-407.
The equations that express the relationships
among T (temperature), P (pressure),
V (volume), and n (number of moles of gas)
are known as the GAS LAWS.
BOYLE’s Law: The Pressure-Volume Relationship
• What is constant: temperature and moles
• Relationship: inversely proportional
o This means that as the pressure increases, the volume decreases (and vice versa).
o It’s helpful to think about the fact that pressure is caused by the number of
COLLISIONS of particles with the wall of the container.
o Balloon scenario – squeezing a balloon decreases its volume and increases
pressure.
▪ This will bring the gas molecules closer and the gas molecules will collide
MORE with each other (and walls of the balloon).
• Graph : plot of P vs.V is a hyperbola.
I’m Robert
Boyle, and I
came up with my
law way back in
1622.
THINK about it: The working of the lungs illustrates Boyle’s Laws.
• As we breathe in, the diaphragm moves down, and the ribs expand; therefore, the volume
of the lungs increases.
• According to Boyle’s law, when the volume of the lungs increases, the pressure
decreases; therefore, the pressure inside the lungs is less than the atmospheric pressure.
• Atmospheric pressure forces air into the lungs until the pressure once again equals
atmospheric pressure.
• As we breathe out, the diaphragm moves up and the ribs contract; therefore, the volume
of the lungs decreases, pressure increases, and air is forced out.
P1 V1 → P2 V2 P1 and V1 are the original conditions. P2 and V2 are the new conditions.
• Units :
o The units for P1/P2 need to be the same. Any units can be used (atm, mm Hg,
etc).
o The units for V1/V2 need to be LITERs.
1. If a 1.23 L sample of a gas at 53.0 torr is put under pressure up to a value of 240. torr at a
constant temperature, what is the new volume?
Boyle was “Very Pretty”
Examples
CHARLES’s Law: The Temperature-Volume Relationship
• What is constant: pressure and moles
• Relationship: directly proportional
o This means that the volume of a gas increases with increasing temperature (and
vice versa).
o If the temperature is increased, the gas particles gain KINETIC ENERGY, move
around more and occupy more space.
o Balloon scenario – consider a hot air balloon. What happens when heat (fire) is
turned on? The gas molecules will move faster and collide more causing the
balloon to expand (volume increases).
• Graph : plot of V vs.T is straight (linear) line.
V1 T2 → V2 T1 T1 and V1 are the original conditions. T2 and V2 are the new conditions.
• Units :
o The units for Temperature must be in KELVIN! (no exceptions)
▪ Remember: K = oC + 273
▪ Absolute zero: 0 K = –273 oC.
o The units for V1/V2 need to be LITERs.
2. A sample of gas at 15oC and 1 atm has a volume of 2.58L. What volume will this gas
occupy at 38oC?
Charles liked to watch”TV”
I’m Jacques
Charles, and even
though my friend
Gay-Lussac
published the
official law, he was
so nice to name it
after me, since I
originally had the
idea in 1787!
Examples
GAY-LUSSAC’s Law: Pressure and Temperature relationships
• What is constant: volume and moles
• Relationship: directly proportional
o This means that the pressure of a gas increases with increasing temperature (and
vice versa).
o If the temperature is increased, the gas particles gain kinetic energy and move
around more. The particles will have more energy and collisions with the walls
of the container (and with other gas molecules) will be more forceful and the
pressure will increase.
• Graph : plot of P vs.T is straight (linear) line.
P1 T2 → P2 T1 T1 and P1 are the original conditions. T2 and P2 are the new conditions.
• Units :
o The units for Temperature must be in KELVIN! (no exceptions)
▪ Remember: K = oC + 273
▪ Absolute zero: 0 K = –273 oC.
o The units for P1/P2 need to be the same. Any units can be used (atm, mm Hg,
etc).
3. A gas at 25oC in a closed container has its pressured raised from 150. atm to 160. atm.
What is the final temperature of the gas?
Examples
AVOGADRO’s Law: The Moles-Volume Relationship
• What is constant: temperature and pressure
• Relationship: directly proportional
o This means that the volume of a gas increases with increasing number of moles
(and vice versa).
o You put more moles of gas in a balloon , the volume will expand.
o As more moles of a gas are placed into a container (or balloon) if conditions of
temperature and pressure are to remain the same, the gas must occupy a larger
volume.
o What’s interesting is that he had another component to his law – equal volumes
of gases at the same temperature and pressure contain equal numbers of
particles (moles), even if the gases are different!!!
▪ What that means is that if you have 1 mole of one gas, such as CO2, and
also 1 mole of a different gas, such as N2, that both of those moles will
occupy the same volume, as long as their pressure and temperature is the
same.
• Graph : plot of V vs. n is straight (linear) line.
V1 n2 → V2 n1 V1 and n1 are the original conditions. V2 and n2 are the new conditions.
• Units :
o The units for “n” must be in MOLES! (no exceptions)
▪ So, if you are given grams, molecules, formula units, etc., then you must
convert to moles
▪ Remember:
molar mass (g) = 1mol = 6.02 x 1023 atoms/molecules/formula units
o The units for V1/V2 need to be LITERs
Can also use Stoichiometry!!! (See 10.4 why we can)
10.4 Combined Gas Law & The Ideal-Gas Equation
Read p. 408-412.
COMBINED Gas Law: all gas laws in ONE equation (Boyles, Charles, Gay-Lussac, & Avogadro’s Laws)
• When you work your math, it is best to start with the Combined Gas Law Equation. All
you do is write down the combined equation and then cross off the variables that remain
constant (if any). If a variable is not mentioned in a problem (frequently amount), you
can assume that variable has remained constant.
• What is constant: any variable can be constant
1’s are the original conditions. 2’s are the new conditions.
• Units :
o The units for P1/P2 need to be the same. Any units can be used (atm, mm Hg,
etc).
o The units for V1/V2 need to be LITERs.
o The units for Temperature must be in KELVIN! (no exceptions)
▪ Remember: K = oC + 273
▪ Absolute zero: 0 K = –273 oC.
o The units for “n” must be in MOLES! (no exceptions)
4. Diborane gas (B2H6) has a pressure of 3.45torr at a temperature -15oC and a volume of
3.48L. If conditions change such that the temperature is 36oC and the pressure is 468torr,
what will be the volume of the sample?
Examples
22
22
1
1
1
1
Tn
VP
Tn
VP=
GAS LAWS OVERVIEW
LAW VARIABLES CONTROL
VARIABLES
MATH
RELATIONSHIP FORMULA
BOYLE’S
CHARLES’S
GAY
LUSSAC’S
AVOGADRO’S
COMBINED
Helpful PhET simulations: bit.ly/phet-chem-simulations or bit.ly/phet-gas-laws
(Also watch AP YouTube video: 3.4-3.6 ~29.5 min)
Learning Objective Essential Knowledge
Unit 3.4 SAP-7.A Explain the relationship between the macroscopic properties of a sample of gas or mixture of gases using the ideal gas law.
SAP-7.A.1 The macroscopic properties of ideal gases are related through the ideal gas law: EQN: PV = nRT. EQN: PA = Ptotal × XA, where XA = moles A/total moles; EQN: Ptotal = PA + PB + PC + ... SAP-7.A.2 In a sample containing a mixture of ideal gases, the pressure exerted by each component (the partial pressure) is independent of the other components. Therefore, the total pressure of the sample is the sum of the partial pressures. SAP-7.A.3 Graphical representations of the relationships between P, V, T, and n are useful to describe gas behavior.
IDEAL GAS equation: An ideal gas is a hypothetical gas whose P, V, and T behavior is completely described by the ideal-gas equation. The way to identify that you have this type of problem (and not one of the previous types) is that CONDITIONS WILL NOT BE CHANGING!!!
• Helpful Tip: PV = nRT problems don’t typically have a P1, V1, P2, T2, etc
situations. Initial values/final values type of problems require using Boyles,
Charles, Gay-Lussac, Avogadro’s, or Combined Gas Law.
• Units : *** Have to have certain units to plug into equation***(no exceptions!)
▪ The units of “R” force us to have P, V , n, and T in specific units when
doing the calculation. Let me show you why in the examples below.
▪ Other numerical values of R in various units are given in Table Ch 10.2.
PV = nRT
P = pressure, atmospheres V = volume, Liters n = moles T = temperature, Kelvin
R = 0.08206 𝑳 ° 𝒂𝒕𝒎
𝒎𝒐𝒍 ° 𝑲
P R value R units
atm 0.08206
𝐿 ⋅ 𝑎𝑡𝑚
𝑚𝑜𝑙 ⋅ 𝐾
Torr (or mmHg)
62.36 𝐿 ⋅ 𝑡𝑜𝑟𝑟
𝑚𝑜𝑙 ⋅ 𝐾
kPa 8.314 𝐿⋅𝑘𝑃𝑎
𝑚𝑜𝑙⋅𝐾 OR
𝐽
𝑚𝑜𝑙⋅𝐾
Let’s do some Algebra….Rearrange Ideal Gas Equation to solve for each variable: P = V = n = T =
1. Assuming ideal behavior, how many moles of Helium gas are in a sample that has a
volume of 8.12 L at a temperature of 0.00 oC and a pressure of 1.20 atm?
Examples
2. Calculating the Molar Mass of a Gas from Ideal Gas Law
A 2.00 L container will hold about 4.00 g of a gas at 18.0 oC and 1.08 atm. Calculate the molar
mass for this gas.
3. Use the following unbalanced chemical equation:
Al(s) + HCl(aq) ⟶ AlCl3 (aq) + H2(g)
35 g Al(s) reacts with excess HCl(aq) according to the chemical equation shown above.
What is the volume (in L) of H2 gas produced at a temperature of 345 K and a pressure of
1.12 atm?
Examples
Gas Stoichiometry
• We can use Stoichiometry ☺ sometimes instead of using gas law equations, but only
under 1 condition!!!
• Suppose you have 1 mol of an ideal gas at 0oC (273K) and 1 atm pressure. Then what
volume does the gas occupy?
• Using PV=nRT….
• Thus is MOLAR VOLUME of an ideal gas at 0oC (273K) and 1 atm.
• The conditions of standard temperature (0°C) and standard pressure (1 atm) are
called “STP conditions”.
• So… 1 mol of any gas behaving ideally at STP occupies a volume of 22.4L.
1 mol = 22.4L at STP This is Molar volume
BEWARE: can only use this for GASES and only at STP!!!
4. How many liters of oxygen gas at STP are required to react with 7.98 liters of ethane gas
(C2H6) at STP in a combustion reaction? (HINT: chemical changes…need a balanced
equation)
Examples
5. A process requires 42 L of ammonia. How many moles of nitrogen should be used,
assuming the reaction was performed under standard conditions? (HINT: chemical
changes…need a balanced equation)
6. 5.33 x 1023 molecules of hydrogen gas reacts with excess chlorine gas, how many liters of
hydrogen chloride gas could potentially be formed at STP? (HINT: chemical changes…need a balanced equation)
Examples
10.5 Further Applications of the Ideal-Gas Equation
Read p. 412-415.
Molar Mass and Gas Densities
• How can the ideal gas equation be used to solve for density and molar mass of a gas?
• Remember: Density d = 𝒎
𝑽 (m = mass, V = volume)
• Gases use density units of grams/Liters.
• If you rearrange the ideal-gas equation with “M” as molar mass (g/mol) we get….
(BEWARE not to confuse “M” molar mass with Molarity from Ch 4)
PV = nRT and V = 𝒎
𝒅
(from density equation… Substitute V density equation into ideal gas)
𝑷𝒎
𝒅= 𝒏𝑹𝑻
(rearrange variables to get the desired units of molar mass = g/mol)
𝑚
𝑛=
𝑑𝑅𝑇
𝑃
𝑴 = 𝒅𝑹𝑻
𝑷
Now rearrange the molar mass equation of a gas to solve for density (d):
𝒅 = 𝑴𝑷
𝑹𝑻
The “Meow-Meow” formula… cats put “DiRT” over their “Pee”!!!
1. Find the molar mass of a gas at 27 oC and 1.50 atm that has a density of 1.95 g/L.
2. The molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6
g/mol. The surface temperature is 95 K, and the pressure is 1.6 atm. Assuming ideal
behavior, calculate the density of Titan’s atmosphere.
Examples
10.6 Gas Mixtures and Partial Pressures
Read p. 415-418. Dalton observed:
• This law is used when you have a mixture (solution) of 2 or more GASES which DO
NOT react chemically.
• For a mixture of ideal gases in a container, the TOTAL PRESSURE exerted is the SUM
of the individual PARTIAL PRESSURES. (as long as volume, temperature, and
moles are constant!!!)
o PARTIAL PRESSURE is the pressure exerted by a specific gas in gaseous
mixture.
• DALTON’s law of partial pressures: In a gas mixture the total pressure is given by the
sum of partial pressures of each component:
Pt = PA + PB + PC …for however many gases you have!
Pt = total pressure PA + PB + PC = different gases
o What is constant: Volume, temperature, and moles
o Units: any pressure units (as long as all pressures are the same units)
PA = Ptotal × ꞳA,
where ꞳA = 𝑚𝑜𝑙𝑒𝑠 𝐴
𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑙𝑒𝑠
Ptotal = PA + PB + PC
Since gas molecules are so far apart, we can assume that they behave ideally.
• And if each gas behaves ideally, then PV = nRT can also be used to find the pressure of
each gas. Once you solve for EACH of the gas pressures, then ADD the pressures up to
solve for the TOTAL pressure.
𝑃𝐀 = 𝑛𝐴 𝑅𝑇
𝑉 𝑃𝐵 =
𝑛𝐵 𝑅𝑇
𝑉 𝑃𝐶 =
𝑛𝐶 𝑅𝑇
𝑉 so Pt = PA + PB + PC…..
• OR if you know the moles of each gas in the mixture, you can ADD up the TOTAL
moles (nt) and solve for Pt using PV = nRT.
𝑃𝑡 = 𝑛𝑡 𝑅𝑇
𝑉 since V&T are constant
Mole Fractions: Using Dalton’s Partial Pressures
• Mole Fraction: the ratio of the # of moles of a given component in a gas mixture to the
total # of moles in the mixture.
𝑋 𝐴 = 𝑛 𝐴
𝑛 𝑡𝑜𝑡𝑎𝑙=
𝑛 𝐴
𝑛 𝐴 + 𝑛 𝐵 + 𝑛 𝐶 … .
Remember: A, B, C are different gases.
• If you wanted to solve for the pressure of only 1 gas in a mixture of other gases….
PA = XAPt = (𝑛 𝐴
𝑛 𝑡𝑜𝑡𝑎𝑙 ) 𝑃𝑡
PA = pressure for a certain gas (any units of pressure can be used) XA = mole fraction (nA/nt)… since moles divide by moles, the units will cancel. Pt = total pressure of all gases in container (any units of pressure can be used)
1. A gas mixture at OoC and 1.15 atm contains 0.010 mol of H2, 0.015 mol of O2, and 0.025
mol of N2. Assuming ideal behavior, what are the partial pressures of hydrogen gas(H2),
oxygen gas (O2) and nitrogen gas (N2) in the mixture?
Examples
10.7 Kinetic-Molecular Theory – VERY IMPORTANT!!!
Read p. 418-421.
Learning Objective Essential Knowledge
Unit 3.5 SAP-7.B Explain the relationship between the motion of particles and the macroscopic properties of gases with: a. The kinetic molecular theory (KMT). b. A particulate model. c. A graphical representation.
SAP-7.B.1 The kinetic molecular theory (KMT) relates the macroscopic properties of gases to motions of the particles in the gas. The Maxwell-Boltzmann distribution describes the distribution of the kinetic energies of particles at a given temperature. SAP-7.B.2 All the particles in a sample of matter are in continuous, random motion. The average kinetic energy of a particle is related to its average velocity by the equation:
EQN: 𝑲𝑬 = 𝟏𝟐⁄ 𝒎𝒗𝟐
SAP-7.B.3 The Kelvin temperature of a sample of matter is proportional to the average kinetic energy of the particles in the sample. SAP-7.B.4 The Maxwell-Boltzmann distribution provides a graphical representation of the energies/ velocities of particles at a given temperature.
The KINETIC-MOLECULAR theory (KMT)was developed to explain gas behavior (gas movement).
• A model that explains why real gases approach the behavior of the ideal gas law
(PV=nRT)
• KMT attempts to explain the properties of an ideal gas. (5 postulates below)
• Kinetic molecular theory gives us an understanding of pressure and temperature on the
molecular level.
o Ideal Gas Behavior: Higher Temperatures, Lower pressure
• It is a theory of moving molecules.
Gas Law’s vs KMT Explanation
Gas Law KMT Explanation
Boyle’s Law When the volume of the container decreases, the particles collide with the sides more often.
More collusions increase the pressure in the container.
Charles’s Law When the temperature increases, particles move faster, causing more and stronger collusions with the sides of the container.
The volume increases to keep the pressure constant.
Avogadro’s Law Adding more particles to a container causes more collusions with the sides of the container.
The volume increases to keep the pressure constant.
Gay-Lussac’s Law When the temperature increases, particles move faster, causing more and stronger collusions with the sides of the container.
The pressure increases when the volume is constant.
To help you with EXPLAINING ……Application to the Gas-Laws
• So what would happen to gas molecules if there was an increase in volume of the
container (at constant temperature):
o As volume increases at constant temperature, the average kinetic energy of the
gas remains constant (KE directly related to T, not V).
o Therefore, u (velocity/speed) is constant.
o The gas molecules have to travel further to hit the walls of the container.
o Leads to less collusions
o Therefore, pressure decreases. (Boyles law)
• So what would happen to gas molecules if there was an increase in temperature (at
constant volume):
o If temperature increases at constant volume, the average kinetic energy of the gas
molecules increases. (directly related)
o There are more collisions with the container walls.
o Therefore, u (velocity/speed) increases.
o The change in momentum in each collision increases (molecules strike harder).
o Therefore, pressure increases. (Gay-Lussac Law)
KMT Summary: (KNOW THIS WELL) The Kinetic Molecular Theory (KMT) tells us WHY ideal gas behave as they do.
1. Gases are composed of molecules that are in continuous motion, travelling in straight
lines and changing direction only when they collide with other molecules or with the
walls of a container
2. The pressure exerted by a gas in a container results from collisions
between the gas molecules and the container walls. The magnitude
(size) of the pressure is determined by how often and how hard the
molecules strike.
3. The average kinetic energy of the gas molecules is directly
proportional to the kelvin temperature of the gas. KE increases as T
increases = greater motion of the gas particles = velocity or speed
(u) of gas molecules increase.
4. The gas particles are so negligibly small compared with the distances between them that
the volume of the individual gas particles is assumed to be ZERO (negligible).
See ch 10.9 – This is UNTRUE for REAL gases.
5. Intermolecular forces (forces between gas molecules) are negligible. Gas molecules
exert no attractive or repulsive forces on each other or the container walls; therefore,
their collisions are elastic (do not involve a loss or gain of energy).
See ch 10.9 – This is UNTRUE for REAL gases.
Let’s Watch Michael Farabaugh Ch 10 video on Maxwell-Boltzman diagrams – provides graphical representation of energies/velocities of particles at a given temperature. (AP loves these graphs..hint hint)
The diagram at right can be found on the bottom of Draw Diagram into Notes
p. 403. It shows the distribution of molecular speeds
for nitrogen gas at two different temperatures.
True or False: At a given temperature, each
molecule in a gas sample is moving at the
same speed.
True or False: As the temperature of a gas sample
is increased, the average speed of the gas molecules
increases.
True or False: The distribution curve tends to broaden
as the temperature is increased, indicating that the range
of molecular speeds increases at a higher temperature.
What’s Happening?
❏ As the temperature of nitrogen gas increases there
are more molecules moving at higher speeds.
❏ The average speed of the molecules is increasing.
❏ However, there are still some molecules with
slower speeds.
Examples
(c) The average kinetic energy per molecule of a gas is equal to ½ mv2
(where m = mass and v = velocity). This information helps us to compare the average speeds of
different gases at a given temperature. How should the following gases be arranged in order of
increasing average speed at 298 K: N2(g), Ne(g), CO2(g)
(d) What does the diagram below tell us about the relationship between molecular speed and
molar mass? (See figure 10.14 on page 422)
According to figure 10.14 (read p.422), which of these gases has the largest molar mass?
List them from smallest to largest. (KNOW THIS PICTURE)
10.8 Molecular Effusion and Diffusion
Read p. 421-426.
Speed (velocity):
o Symbol is u or v
o The speed of a gas is related to its mass
o Consider two gases at the same temperature: the LIGHTER gas has a FASTER
rms (speed) than the heavier gas.
1. Consider 3 gases all at 298K: HCl, H2, and O2. List the gases in order of increasing
average speed.
2. How is the speed of N2 molecules in a gas sample changed by
a. Increase in temperature
b. Increase in volume
c. Mixing with a sample of Ar at the same temperature.
Examples
Effusion vs Diffusion: Graham’s Law Two consequences of the dependence of molecular speeds on mass are:
1. DIFFUSION is the spread of one substance throughout a space or process by which a
gas spreads through a space occupied by another gas.
o Diffusion is FASTER for LIGHTER gas molecules.
▪ Example: Mixing gases – opening a bottle of perfume or cooking in
kitchen. Eventually its odor (gas particles) can be detected in another
location of house.
o Diffusion is SLOWED by COLLUSIONS of gas molecules with one another.
▪ Example: Consider someone opening a perfume bottle: It takes a while to
detect the odor, but the average speed of the molecules at 25oC is about
515 m/s (1150 mi/hr).
2. EFFUSION is the escape of gas molecules through a tiny hole into an evacuated space.
(AKA balloon)
o Only those molecules which hit the small hole will escape through it.
o Therefore, the FASTER the speed the more likely it is that a gas molecule will hit
the hole.
o Although different from diffusion, the MATH is the same
Effusion
1
2
2
1
M
M
r
r=
Lab Experiment: Diffusion process between HCl and NH3
o Glass tube (buret) and add cotton balls to each side.
o One end of tube add 5 drops of acid while at the same time add 5 drops of base.
o Put stoppers in glass ends so no gas escapes.
o Start timing reaction to find a “white ring on the glass where the acid and base meet to
form SOLID NH4Cl”.
o What is happening in the experiment?
o The acid and base particles evaporate off the cotton and travel inside tube.
o Distances traveled are NOT the same due to MOLAR MASSES (Graham’s Law
equation).
Draw Lab Set:
Graham’s Law (Rate of Diffusion) – the rate of the mixing of the gases
o Consider two gases with molar masses, M1 and M2, and with diffusion rates, r1 and r2,
respectively.
M1 and M2 = molar mass units in g/mol.
1. LAB: Calculate the Rate of Diffusion between HCl and NH3: (This is the
THEORETICAL YIELD - Will need this for lab)
What does this value mean?
2. Calculate the “rate of effusion” of N2 and O2 gases.
Examples
10.9 Real Gases: Deviations from Ideal Behavior
Read p. 426-429.
Learning Objective Essential Knowledge
Unit 3.6
SAP-7.C Explain the relationship
among non-ideal behaviors of gases,
interparticle forces, and/or volumes.
SAP-7.C.1 The ideal gas law does not explain the actual behavior of real gases. Deviations from the ideal gas law may result from interparticle attractions among gas molecules, particularly at conditions that are close to those resulting in condensation. Deviations may also arise from particle volumes, particularly at extremely high pressures.
Real Gases:
o There is no such thing as an ideal gas, but we assume that real gases “behave ideally”.
o According to the KMT (Ch 10.7), 2 of the postulates are UNTRUE for real gases:
o #4 – Real gases DO have volume themselves
o #5 – Real gases DO have interparticle interactions, they do attract, repel, and
collide with each other.
o We make an assumption about real gases “behaving ideally”, from a calculation
standpoint. The math is not that far off.
o In other words, assuming that real gases behave ideally allows us to use the ideal gas law
for ALL gases (PV=nRT)
o KMT postulates #4 & #5 allow us to simplify the math involved. OTHERWISE, the
ideal gas law would have to be replaced with the “real gas law” equation.
o See Ch 10.9: Van Der Walls Equation (NOT ON AP EXAM ☺)
See graphs above: LEFT graph: For 1 mol of an ideal gas, n = PV/RT = 1 for all pressures.
o The higher the pressure the more the deviation from ideal behavior.
RIGHT graph: For 1 mol of an ideal gas, n = PV/RT = 1 for all temperatures. • As temperature increases, the gases behave more ideally. Deviations from ideal behavior - THIS IS WHERE IDEAL GASES DIFFER FROM REAL GASES!!!!!
• At high pressures and low temperatures gas particles come close enough to one
another to make the two postulates of the Kinetic Theory below, invalid.
KMT #4. The gas particles are so negligibly small compared with the distances between
them that the volume of the individual gas particles is assumed to be ZERO (negligible).
HOWEVER with real gases….
o When gases are compressed (high pressures) into a small space, the volumes of the
particles is no longer negligible compared to the volume of the container. The gas
particles size becomes more significant compared to the total volume.
o Therefore, the observed total volume occupied by the gas under these real conditions is
actually large since the gas particles are now occupying a significant amount of that total
volume.
KMT #5. Intermolecular forces (forces between gas molecules) are negligible. Gas molecules exert no attractive or repulsive forces on each other or the container walls; therefore, their collisions are elastic (do not involve a loss or gain of energy). HOWEVER with real gases….
o Some gas particles DO attract or repel one another.
o Low temperature means less energy, so the particles are attracted to one another more.
o Because, in a real gas, the particles are attracted to one another, they collide with the
walls with less force (impact strength), and the observed pressure is less than it an ideal
gas.
AP EXAM FRQ :Ideal Gas Law and Kinetic Molecular Theory
WATCH THIS VIDEO TO ASSIST IN THESE QUESTIONS
Answers: See YouTube video 3.7-3.10 (beginning)
Mg(s) + 2 H+(aq) ⟶ Mg2+(aq) + H2(g)
2. A student performs an experiment to determine the volume of hydrogen gas produced when
a given mass of magnesium reacts with excess HCl(aq), as represented by the net ionic
equation above. The student begins with a 0.0360 g sample of pure magnesium and a solution
of 2.0 M HCl(aq).
(a) Calculate the number of moles of magnesium in the 0.0360 g sample.
(b) Calculate the number of moles of HCl(aq) needed to react completely with the sample of
magnesium.
As the magnesium reacts, the hydrogen gas produced is collected by water displacement at
23.0oC. The pressure of the gas in the collection tube is measured to be 749 torr.
(c) Given that the equilibrium vapor pressure of water is 21 torr at 23.0oC, calculate the
pressure that the H2(g) produced in the reaction would have if it were dry.
(d) Calculate the volume, in liters measured at the conditions in the laboratory, that the H2(g)
produced in the reaction would have if it were dry.