Unit 3 Chp 10 Notes B and L.pptx

Unit 3

Gases

Elements that exist as gases at 250C

States of substances depends largely on:

1. The balance between the KE of the particles and

2. The

intermolecular forces of

Properties unique to Gases

completely (constant random motion)

Gases are fluid (they flow past ea other) Gases have low density

1/1000 the density of the equivalent liquid or solid

Gases are compressible (when P applied, empty

space between particles)

Gases effuse and diffuse (due to KE)

Gases form homogeneous mixtures (equal

Gas Law Variables

• Volume: mL or L (Variable V)

• Temperature: (Variable T) Since temperature has a direct

relationship with KE, the Celsius scale does not work for gases. We need a new unit called Kelvin (K).

• Pressure: (Variable P) Force, created by the collisions of

gas particles against the walls of the container. The units are: mmHg, kPa, Pa, torr, atm

Pressure

• All units of pressure are related to 1 atm, which is known as

Standard Pressure.

• 1 atm = 760 torr = 760 mm Hg = 101.325 kPa = 101,325 Pa • STP = Standard Temperature and Pressure

• P = F/A (force over area) (N/m2 = Pa)

• Example Conversion: Convert 250 mmHg to atm

Answer: 0.33 atm

• Example Conversion: Convert 1.46 atm to torr

Sea level 1 atm

4 miles 0.5 atm

Volume

• Amount of space gases

take up.

• Remember 1 L = 1000 ml • Look for units in mL or L • Example: Convert 500 ml

Temperature

• Never use Celsius in gas law problems! Always give temperature in

Kelvin unless asked otherwise.

• Standard Temperature is a condition defined as 0 ºC or 273 K. • To convert K = 0 ºC + 273

• Remember that temperature and KE are directly related.

• AT THE SAME TEMP, ALL GASES HAVE SAME KE!!

Amount of Gas

• Moles = “n”

• Remember if grams of gas are given, you will

need to convert to moles by using molar mass conversions.

Example: convert

Standard Temperature and Pressure

“STP”

*Must Memorize these parameters, but values are on your equation packet!

P = 1 atmosphere, 760 torr or 1 atm

T = 0°_{C, 273 Kelvins}

Ideal Gas Law

P

V

= nR

T

P = pressure in atm V = volume in liters n = moles

R = proportionality constant (gas constant) = 0.08206 L atm/ mol·K

T = temperature in Kelvins

The conditions 0 0C and 1 atm are called standard

temperature and pressure (STP).

PV = nRT

R = PV

nT = (1 mol)(273.15 K)(1 atm)(22.414L)

R = 0.082057 L • atm / (mol • K)

What is the volume (in liters) occupied by 49.8 g of HCl at STP?

PV = nRT V = nRT_P

T = 0 0C = 273 K P = 1 atm

n = 49.8 g x 1 mol HCl

36.45 g HCl = 1.37 mol

V =

1 atm

1.37 mol x 0.0821 x 273 KL•atm_mol•K

Standard Molar Volume

Equal volumes of all gases at the same temperature and pressure contain the same number of

molecules.

Another use for PV=nRT?

Identification of unknowns.

1. A sample of gas has a mass of 80 grams and is found to occupy 480 L at 1 atm

and 27°C. How many moles of gas are present?

• Mathematical relationship between

pressure, volume, temperature and amount of a gas (moles).

• Only 1 Gas Law given in your equation

packet, might need to derive the others. *Don’t need to know the names of each, just relationship and how to use each.

Should be able to use PV=nRT

This is the only gas law given. Need to be able to derive all other gas laws from this one!

P

V

= P

V

Boyle

’

s Law: The Press – Vol

Relationship

• Pressure is inversely proportional to volume when temperature is held

constant.

P a _1/V

P x V = constant

P₁ x V₁ = P₂ x V₂

Boyle’s Law

V

= V

T

T

Charles

’

s Law: Temp – Vol

Relationship

• The volume of a gas is directly

proportional to temperature when pressure is held

constant.

•

When temperature increases,

As T increases V increases

P

= P

T

T

Gay Lussac

’

s Law: Pres – Temp

Relationship *not in book!

• The pressure and temperature of a gas are directly related, provided that the volume remains constant.

The Combined Gas Law

The combined gas law expresses the

relationship between pressure, volume and temperature of a fixed amount of gas.

Boyle’s law, Gay-Lussac’s law, and Charles’ law

are all derived from this by holding a variable constant.

1 mole O₂ at STP 1 mole He at STP 1 mole NH₃ at STP 6.02x1023 O

2 molecules 6.02x1023 He atoms 6.02x1023 NH3 molecules

Avogadro

’

s Law – Mole and

Volume Relationship

• For a gas at constant temperature and

pressure, the volume is directly proportional to the number of moles of gas.

• As moles are increased, volume increases.

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant

temperature to 154 mL?

P₁ x V₁ = P₂ x V₂ P₁ = 726 mmHg

V₁ = 946 mL

P₂ = ?

V₂ = 154 mL

P₂ = P1 x V1

A sample of carbon monoxide gas occupies 3.20 L at 125

0C. At what temperature will the gas occupy a volume of

1.54 L if the pressure remains constant?

V₁ = 3.20 L

T₁ = 398 K

V₂ = 1.54 L

T₂ = ?

T₂ = V2 x T1

V₁ = 1.54 L x 398 K3.20 L = 192 K V₁ /T₁ = V₂ /T₂

Argon is an inert gas used in lightbulbs to slow the vaporization of the filament. A certain lightbulb

containing argon at 1.20 atm and 18 0C is heated to 85 0C

at constant volume. What is the final pressure of argon in the lightbulb (in atm)?

PV = nRT n, V and R are constant

nR

V = _TP = constant P₁

T₁ = TP2₂

P₁ = 1.20 atm

T₁ = 291 K

P₂ = ?

T₂ = 358 K

P₂ = P₁ x T2

AP Practice Question

The pressure, in atm, exerted by 1.85 mol of an ideal gas placed in a 3.00 L container at 35.0°C is given by

which of the following expressions?

Theoretical Understanding?

Suppose we have gas confined to a cylinder w/ movable piston. Consider the following changes and indicate how each change affects the average distance between

molecules, the pressure of the gas, and the number of moles of gas in the cylinder.

1. Heat the gas from 298K to 360K at constant pressure.

Volume will increase

2. Reduce the volume from 1L to 0.5L at constant temperature.

Pressure will increase

3. Inject additional gas, keeping temperature and volume constant.

AP Practice Question

When a sample of oxygen gas in a closed con tainer of constant volume is heated until its abso lute tem pera ture is doubled, which of the follow ing is also dou bled?

A. The density of the gas B. The pressure of the gas

C. The average velocity of the gas molecules D. The number of molecules per cm3

AP Practice Question

A rigid metal tank contains oxygen gas. Which of the following applies to the gas in the tank when additional oxygen is added at constant

temperature?

A. The volume of the gas increases. B. The pressure of the gas decreases.

C. The average speed of the gas molecules remains the same.

D. The total number of gas molecules remains the same.

AP Practice Question

A sample of an ideal gas is cooled from 50.0oC to

25.0oC in a sealed container of constant volume.

Which of the following values for the gas will decrease?

I. The average molecular mass of the gas

II. The average distance between the molecules III. The average speed of the molecules

AP Practice Question

At standard temperature and pressure, a 0.50 mol sample of H₂ gas and a separate 1.0 mol sample of O₂ gas have the same

A. average molecular kinetic energy B. average molecular speed

C. Volume

The volume of a sample of air in a cylinder with a

movable piston is 2.0 L at a pressure P₁, as shown in the diagram above. The volume is increased to 5.0 L as the temperature is held constant. The pressure of the air in the cylinder is now P₂. What effect do the volume and pressure changes have on the average kinetic energy of the molecules in the sample?

A. The average kinetic energy increases. B. The average kinetic energy decreases.

C. The average kinetic energy stays the same.

Which of the following is the most likely cause for the increase in pressure observed in the container as the reaction reaches equilibrium?

A. A decrease in the strength of intermolecular attractions among molecules in the flask

B. An increase in the strength of intermolecular attractions among molecules in the flask

C. An increase in the number of molecules, which increases the frequency of collisions with the walls of the container D. An increase in the speed of the molecules that then collide

Density (

d

) Calculations

d = m_V = PM_RT m _{M is the molar mass of the gas}is the mass of the gas in g

Molar Mass (M ) of a Gaseous Substance

dRT P

M = d is the density of the gas in g/L

M = Molar Mass P = Pressure

R = Gas Constant

T = Temperature in Kelvins

*Density depends on molar

A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0 0C. What is the molar mass of the gas?

dRT P

M = d = m_V 4.65 g

2.10 L

= = 2.21 _Lg

M = 2.21

g L

1 atm

x 0.0821 x 300. KL•atm_mol•K

A.greatest in container A B.greatest in container B C.greatest in container C

Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

P_Total = P₁ + P₂ + P₃ + . . . This is particularly useful in calculating the pressure of gases collected over water.

Dalton

’

s Law of Partial Pressures

V and T

are

constant

Consider a case in which two gases, A and B, are in a container of volume V.

P_A = nART

V

P_B = nBRT

V

n_A is the number of moles of A

n_B is the number of moles of B

P_T = P_A + P_B X_A = nA

n_A + n_B XB =

n_B

n_A + n_B

P_A = X_A P_T P_B = X_B P_T

A sample of natural gas contains 8.24 moles of CH₄, 0.421 moles of C₂H₆, and 0.116 moles of C₃H₈. If the total

pressure of the gases is 1.37 atm, what is the partial pressure of propane (C₃H₈)?

P_propane = X_propane P_T

X_propane = _{8.24 + 0.421 + 0.116}0.116

P_T = 1.37 atm

= 0.0132

A flask contains 2.00 moles of O₂ and 8.00 moles of N₂ gas. The total pressure of the flask is 200. kPa. What are the partial pressures of each gas?

P_O2 = X_O2P_T

X_oxygen = _{2.00 moles + 8.00 moles}2.00 moles

P_T = 200. kPa

=

PO2 = x 200 kPa = 40. kPa

X_nitrogen = _{2.00 moles + 8.00 moles}8.00 moles = P_N2 = X_N2P_T

PN2 = x 200 kPa = 160. kPa

0.2

0.8

AP Practice Question

A flask contains 0.25 mole of SO₂(g), 0.50 mole of CH₄(g), and 0.50 mole of O₂(g). The total

pressure of the gases in the flask is 800 mm Hg. What is the partial pressure of the SO₂(g) in the flask?

AP Practice Question

A 2 L sample of N₂(g) and a 1 L sample of Ar(g), each originally at 1 atm and 0°C, are combined in a 1 L tank. If the temperature is held constant,

what is the total pressure of the gases in the tank?

How can you collect gas?

2KClO₃ (s) 2KCl (s) + 3O₂ (g)

Bottle full of oxygen gas and water vapor

Gas of interest is not the only gas

collected, water vapor is also present. Must be accounted for using Dalton’s Law of Partial Pressures.

Example: Collecting gas over

water

A common way to make hydrogen gas in the lab is to place a metal such as zinc in

hydrochloric acid. The HCl reacts with Zn to produce H₂ gas, which is then collected over water. Suppose a student carries out this experiment and collects a total of 154.4

Ex Cont’d

First find the P_H2 from: P_T = P_H2 + P_H2O

Then use PV = nRT to find n

Diagram 1 above shows equimolar samples of two

gases inside a container fitted with a removable barrier placed so that each gas occupies the same volume.

The reaction between NO(g) and O₂(g) to produce

NO₂(g) in a rigid reaction vessel is represented in the diagram above. The pressure inside the container is recorded using a pressure gauge. What would be a

AP Practice Question

When 6.0 L of He(g) and 10. L of N₂(g), both at 0oC and 1.0 atm, are pumped into an evacuated

4.0 L rigid container, the final pressure in the container at 0oC is

Interpret the Graph?

Make a prediction. What would happen if temperature was to decrease? Draw this as a dotted (----) line on your graph.

What did you draw?

Why? As Temp increases, KE increases, causes speed (or velocity) to increase, higher speeds able to be achieved (x-axis) area under curve larger and wider.

Lower T

The distribution of speeds for nitrogen gas molecules

at three different temperatures

The distribution of speeds of three different gases at the same temperature

5.7

u_rms = 3RT

M

Maxwell-Boltzmann Distribution

These graphs show the probability of the amount of gas particles that will travel at different speeds at a given temperature.

Lower mass, more possibility for speed

(lower, but longer peak)

The Meaning of Temperature

Kelvin temperature is an index of the

random motions of gas particles (higher T

means greater motion.)

(KE)

3

2

Kinetic Energy of Gas Particles

At the same conditions of temperature, all gases have the same average kinetic energy.

KE = 1

2

mv

Root Mean Square μ

Good approximation of the speed at which molecules travel (not their KE). This is a velocity, units are m/s.

R = 8.314 J / mol K 1 J = 1 kg m2 / s2

Example:

Calculate the rms speed of the molecules in a sample of N₂ gas at 25°C.

Diffusion vs. Effusion

Effusion - how gases escape through a small pore or opening (balloons deflating)

When NH₃ and HCl gases are mixed a white cloudy ppt of NH₄Cl forms. If NH₃ and HCl are placed on either side of a sealed tube, where would you expect the ppt to form?

NH₃(g)

HCl(g)

Graham’s Law

Rates of Effusion and Diffusion

r₁ r₂ =

M₂ M₁



You may need to derive this formula from the KE formula!

Rate of effusion for gas 1

Rate of effusion for gas 2



Example:

What is the rate of diffusion of ammonia gas compared to hydrogen chloride gas?

ANSWER: ammonia:~1.5 faster

Another Example:

Two gases are contained in a balloon. The rate of effusion of neon gas is 4.35 mol/min, while the rate of effusion of an unknown gas is 9.76

mol/min. Calculate the molar mass and identify the unknown gas inside the balloon.

You Try:

An unknown gas effuses 1.66 times more

rapidly than CO₂. What is the molar mass of the unknown gas?

16.0 g/mol

Can you make a reasonable guess as to its identity? (It is suspected to be a

hydrocarbon)

AP Challenge Problem! r₁ r₂ M₂ M₁



Nickel forms a gaseous compound of the formula Ni(CO)_x. What is the value of x given that under the same

conditions methane (CH₄) effuses 3.3 times faster than the compound?

r₁ = 3.3 x r₂

M₁ = 16 g/mol

M₂ = r1 r₂

( )

AP Sample Question

A 0.5 mol sample of He(g) and a 0.5 mol sample of Ne(g) are placed separately in two 10.0 L rigid containers at 25°C.

Each container has a pinhole opening. Which of the gases, He(g) or Ne(g), will escape faster through the pinhole and why?

A. He(g) will escape faster because the He(g) atoms are moving at a higher average speed than the Ne(g) atoms. B. Ne(g) will escape faster because its initial pressure in the

container is higher.

C. Ne(g) will escape faster because the Ne(g) atoms have a higher average kinetic energy than the He(g) atoms.

The diagram below shows the distribution of speeds for a sample of N₂(g) at 25°C. Which of the following graphs shows the distribution of speeds for a sample

of O₂(g) at 25°C (dashed line) ?

Ideal Gases(What you learned 10th grade)

Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular Theory (KMT).

 Gases consist of tiny particles that are far apart

relative to their size, a lot of empty space.

 Collisions between gas particles and between

particles and the walls of the container are

elastic collisions (No KE lost in elastic collisions)

* Gas molecules exert neither attractive nor repulsive forces on one another.

 Temperature proportional to KE of gas particles.

Kinetic Molecular Theory of Gases Details

1. A gas is composed of molecules that are separated from each other by distances far greater than their own

dimensions. The molecules can be considered to be

points; that is, they possess mass but have negligible volume.

2. Gas molecules are in constant motion in random directions, and they frequently collide with one

another. Collisions among molecules are perfectly elastic.

3. *Gas molecules exert neither attractive nor repulsive forces on one another.

4. The average kinetic energy of the molecules is

proportional to the temperature of the gas in Kelvins.

Can Real Gases Behave

Ideally?

• _{Under conditions of high}

Temperature (high KE) and low Pressure

• _{High T keeps gas}

particles spread away from one another

(minimizes

attractive/repulsive forces)

• _{Low P keeps gases}

moving and able to spread out, less

• 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.

• We need to add correction factors to the ideal gas law to account for these factors.

Van der Waals equation

•

The actual volume the molecules

are free to move in, is less

because of particle size.

•

More molecules will have more

effect.

•

Because the molecules are

attracted to each other, the

pressure on the container will be

less than ideal.

Real Gases

­ ­

corrected pressure corrected volume

P_ideal Videal

Must correct ideal gas behavior when at

high pressure (smaller volume) and low temperature (attractive forces become important), collisions become inelastic.

Real vs. Ideal

This graph shows how real gases deviate from Ideal behavior.

Both water and Xe have extremely negative

deviations due to their

stronger IM forces. (Ideals do not have IM forces)

(water: H-bonding

Can you make predictions?

Which gas would produce the lowest

pressure with moles, T, and V constant?

H₂O or CH₄

A. The gas in sample 1 would deviate more from ideal behavior because the average distance an Xe atom travels before

colliding with another Xe atom is greater.

B. The gas in sample 2 would deviate more from ideal behavior because the Xe atoms are closer together, leading to an

increase in intermolecular attractions.

C. The gas in sample 2 would deviate more from ideal behavior because the average speed of the Xe atoms is less, leading to an increase in intermolecular attractions.

AP Practice Question

Which of the following best helps explain why the pressure of a sample of CH₄(g) (molar mass 16g/mol) is closer to the pressure predicted by the ideal gas law than a sample of NH₃(g) (molar mass 17g/mol) ?

A. NH₃ molec are polar while CH₄ molec are not, and the greater attractions between NH₃ molec cause the molec to collide

with the walls of the container with less force.

B. NH₃ molec have a greater molar mass than CH₄ molec so the NH₃ molec collide with the walls of the container with more force.

C. CH₄ molec have more hydrogen atoms than NH₃ molec so CH₄ molec have more hydrogen bonding and greater intermolecular forces.

D. CH₄ molec are larger than NH₃ molecules, so the

AP Practice Question

The ideal gas law best describes the

properties of which of the following gases at 0°C and 1 atm?

Under which of the following conditions of temperature and pressure would 1.0 mol of the real gas CO₂(g)

behave most like an ideal gas?