10.1 characteristics of gases read p. 398-401

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.


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


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 :





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


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 :


etc).





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)

http://bit.ly/phet-chem-simulations

http://bit.ly/phet-gas-laws

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.


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.


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.

https://www.youtube.com/watch?v=JKJ2n64EvRc&t=5s

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.

10.1 characteristics of gases read p. 398-401

Documents