Friday 4/27. An Introduction to Gases Chapter 13.

Friday4/27

An Introduction to Gases

Chapter 13

Kinetic Molecular Theory

• Postulate #1– Gases consist of tiny particles (atoms or

molecules)

• Postulate #2– These particles are so small, compared

with the distances between them, that the volume (size) of the individual particles can be assumed to be negligible (zero).

– Gases are COMPRESSIBLE

Kinetic Molecular Theory

• Postulate #3– The particles are in constant random

motion, colliding with the walls of the container. These collisions with the walls cause the pressure exerted by the gas.

Kinetic Molecular Theory

• Postulate #4– The particles are assumed not to

attract or to repel each other.

• Postulate #5– The average kinetic energy of the gas

particles is directly proportional to the Kelvin temperature of the gas.

Pressure

What is pressure?What is pressure?

How is it measured?How is it measured?1.1.mmHg (or Torr)mmHg (or Torr)2.2.Atmospheres (atm)Atmospheres (atm)3.3.Pascals (used in physics: Pascals (used in physics:

1 pascal = 1 newton per square meter)1 pascal = 1 newton per square meter)4. 4. psi psi

Equivalences:Equivalences:1 atm = 760 mmHg1 atm = 760 mmHg1 atm = 101,325 Pa = 101.325 kPa1 atm = 101,325 Pa = 101.325 kPa1 atm = 14.7 psi

Pressure

Pressure of air is Pressure of air is measured with a measured with a BAROMETERBAROMETER(developed by Torricelli in (developed by Torricelli in 1643)1643)

Pressure Calculation

What is 475 mm Hg expressed in atm?

475 mm Hg=

1 atm

760 mm Hg0.625 atm

Dalton’s Law

“The Law of Partial Pressure”

• The total pressure of a mixture of gases is the sum of the partial pressures of the gases in the mixture.

Ptotal = PA + PB + PC

Temperature ScalesTemperature Scales

Notice that 1 kelvin = 1 degree Celsius

Boiling point of water

Freezing point of water

CelsiusCelsius

100 ˚C100 ˚C

0 ˚C0 ˚C

100˚C100˚C

KelvinKelvin

373 K373 K

273 K273 K

100 K100 K

Calculations Using Temperature

ALL gas calculations require temperature in Kelvin

T (K) = T(˚C) + 273.15

Body temp = 37 ˚C + 273 = 310 K

Liquid nitrogen = -196 ˚C + 273 = 77 K

ALL gas calculations require temperature in Kelvin

T (K) = T(˚C) + 273.15

Body temp = 37 ˚C + 273 = 310 K

Liquid nitrogen = -196 ˚C + 273 = 77 K

Relationships

How are temperature and volume related?

How are volume and pressure related?

How are pressure and temperature related?

Reminders

Homework:Gases WS 1

Reminders:Extra Credit Due 5/11

Test Corrections due 5/1

Monday and Tuesday4/30 and 5/1

Warm Up

When you increase the temperature in a container, do the particles of gas move faster or slower? Would this increase or decrease the pressure?

What would happen if you put a balloon in the freezer?

What would happen if you put a balloon in the oven?

Is it possible to compress a gas?

Put a few drops of water in a can. Heat the can until the water boils. What is happening to the gas inside? Now flip the can over

into cold water. Predict what do you predict will happen?

Demo

On a Larger Scale

On a Larger Scale

Gas Laws Calculations

Get out a calculator!!!

The Gas Law

PV=nRT

P = pressure ( atm or kPa )V= volume ( L )

n= number of moles (mol)T= temperature (K)

R – The Proportionality Constant

Value depends on units

8.314L (kPa)mol (K)

0.0821L (atm)mol (K)

Or

The Gas Law – Problem If 7.0 moles of an ideal gas has a volume

of 12.0 L with a temperature of 300. K, what is the pressure in kPa?

P (12.0 L) =(7.0 mol)(300

K)8.31

4

L (kPa)

mol (K)

PV = nRT

P = 1454.95 kPa P = 1500 kPa

The Gas Law – Problem If 4.00 moles of a gas has a volume of

10.0 L with a temperature of 303. K, what is the pressure in atm?

P (10.0 L)

=(4.00 mol)

(303 K)0.082

1

L (kPa)

mol (K)

PV = nRT

9.95 atm

Combined Gas Law

fff

iii

ff

ii

TRn

TRn

VP

VP

Let’s say we have a balloon full of O2 gas AND we change some conditions. Would there be anything similar between the two gases?

Combined Gas Law – Problem

You have 3.0 moles of a solution at 300. K and 15 atm in a 2.0 L container. If the container is heated to 350. K and the volume decreased to 1.0 L, what will the new pressure be?

P1 15 atm P2 want

V1 2.0 L V2 1.0 L

n1 3.0 moles n2 3.0 moles

R1 constant R2 constant

T1 300. K T2 350. K

Combined Gas Law – Problemc

P1V1=

n1R1T1

P2V2 n2R2T2

P1V1=

T1

P2V2 T2

If we know that R1 = R2 and the mass is constant then

(15 atm)(2.0 L) =(300. K)

P2(1.0L) (350. K)

Replace with numbers

Combined Gas Law – Problem

(15 atm)(2.0 L) = (300. K)

P2(1.0 L) (350. K)

(15 atm)(2.0 L)(350. K) =

P2(1.0L)(300. K)

P2 = 35 atm

Pressure & Volume• At constant Temperature• Pressure and Volume vary inversely.

– Why? – More collisions More pressure

P1V1 = P2V2

P1V1=

n1R1T1

P2V2 n2R2T2

P & V – Example Problem If you start with 0.500 L of a gas at 7.0 atm and you move the gas to a container with 3.5 L available, how much pressure will the gas exert?

7.0 atm (0.500 L) = P2

3.5 L

P1 (V1) = P2 (V2)

7.0 atm (0.500 L) = P2 (3.5 L)

1.0 atm = P2

Temperature & Volume

At constant PressureVolume & Temperature vary directly.– Why?– More collisions More Volume

V1=

V2

T1 T2

P1V1=

n1R1T1

P2V2 n2R2T2

T & V – Example Problem

If a gas is in a balloon with a volume of 12.0 L and at a temperature of 300. K, what will the volume be if you place the balloon in a freezer at 250. K?

V1=

V2

T1 T2

12.0 L=

V2

300. K250.

K

12.0 L (250. K) = V2

300. K

10.0 L = V2

S.T.P.

• Standard Temperature and PressureStandard Temperature and Pressure

These are conditions that are universalThese are conditions that are universal

Standard Temperature: Standard Temperature:

0ºC or 273.15 K0ºC or 273.15 K

Standard Pressure: Standard Pressure:

1atm or 101.325kPa1atm or 101.325kPa

S.T.P. – Example Problem

What is the volume What is the volume of 1 mole of a gas of 1 mole of a gas at STP?at STP?

P 1 atm

V want

n 1 mole

R 0.0821 (L)(atm)/(K)(mole)

T 273 KPV = nRT

(1atm)V = (1 mole)(0.0821 [Latm/Kmole])(273K)

V= 22.4 L

Practice Problems

The pressure of a sample of gas is 5.00 atm and the volume is 30.0 L. If the volume is changed to 50.0 L, what is the new pressure?

Practice Problems

A sample of gas has a volume of 50.0 L at a temperature of 300.K. What temperature would be needed for this sample to have a volume of 60.0 L if its pressure remains constant?

Practice Problems

A 3.68g sample of a certain diatomic gas occupies a volume of 3.00 L at 1.00 atm and a temperature of 45°C. Identify this gas.

Quiz Time

Have out a pencil and a calculator

Cage of Death Lab

•Determine the volume of one mole of gas at STP

•Do prelab before class

•Lab write up due

Reminders

Homework:Gases WS 2Cage of Death Pre-lab

Reminders:Extra Credit Due 5/11

Wednesday and Thursday5/2 and 5/3

Warm Up

A sample of gas has a volume of 90.0 L at a temperature of 303.K. What temperature would be needed for this sample to have a volume of 70.0 L if its pressure remains constant?

Cage of Death Lab

•Determine the volume of one mole of gas at STP

Gas collection tubeBalancing pressureMaking cage

Cage of Death Lab

2.

Why is the length of the magnesium ribbon important? Think back to stoichiometry.

3. Be careful with the HCl – 3.0 M is very corrosive

Cage of Death Lab

4.

5.

Why is it important that the HCl and H2O don’t mix?

Not too tightNot too loose

Cage of Death Lab6.

8. (F) Today’s atmospheric pressure is…

Cage of Death Lab

9.

10.

Allow reaction to happen…

How would a bubble effect your results?

Too lowToo highJust right

Cage of Death Lab

Repeat the lab for a second trial.

CLEAN UPLiquids down drain

Solids return to container

After Lab

Done in lab? Work on Homework:Cage of Death Write UpGases WS 3

Reminders:Extra Credit due 5/11

Friday5/4

Warm Up

A sample of gas is in a 13.0 L container with 1.26 atm of pressure on it at 23.5 ˚C. How many moles of gas are in the sample?

If the gas in the problem above is released from its container into a 56.0 L container but the temperature remains constant, what will the new pressure be?

Demos

How does atmospheric pressure affect gas particles?

Reminders

Homework:Study for your test

Reminders:Extra Credit Due 5/11Gases Test 5/7 or 5/8