How do gases behave under different conditions?

What are the properties and behavior of gases under different conditions such as pressure, volume and temperature?

Gas Particles

Liquid Particles

Solid Particles

An important property of gases is Compressibility◦ Measure of how much the volume of matter

decreases under pressure Why are gases so compressible?

◦ Large spaces between particles

Explains why ideal gases behave the way they do

Assumptions that simplify the theory, but don’t work in real gases:

1.The particles are so small we can ignore their volume

2.The particles are in constant motion and their collisions cause pressure.

3. The particles do not affect each other, neither attracting or repelling.

4. The average kinetic energy is proportional to the Kelvin temperature.

5. The molecules move in a straight path6. All collisions are elastic

We need the formula KE = 1/2 mv2

Force per unit area

Factors Affecting Pressure

◦ Amount of gas

More particles – more pressure

◦ Volume

More volume – less pressure

◦ Temperature

Higher temperature – more pressure

Gas molecules fill container Molecules move around and hit sides Collisions are the force Container is the area

Measures air pressure The pressure of the

atmosphere at sea level will hold a column of mercury 760 mm Hg.

1 atm = 760 mm Hg

1 atm Pressure

760 mm Hg

Vacuum

Column of mercury to measure pressure of a gas

One end has gas, the other is open

h is how much lower the pressure of the gas is than atmosphere

Gas

h

h is how much higher the gas pressure is than the atmosphere.

h

Gas

1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr 1 atm = 101,325 Pascals = 101.325 kPa Occasionally, we must convert between

these Examples:

◦ What is 724 mmHg in torr?◦ in atm?◦ in kPa?

724 torr0.953 atm

96.5 kPa

Unit AbbreviationUnit Equivalent

to 1 atm

Atmosphere Atm 1 atm

Millimeters of Hg

mm Hg 760 mm Hg

Torr Torr 760 torr

Pascal Pa 101,325 Pa

Kilopascal kPa 101.3 kPa

Summary of Units of Pressure

There are several laws we use to quantify the behavior of gases

The laws describe some combination of changes in pressure (P), volume (V), moles/amount of gas (n),or temperature (T)

Standard Temperature and Pressure (STP)◦ 0ºC and 1 atm ◦ 1 mole of gas occupies 22.4 L

BE CAREFUL!!◦ Units are vital to solving these problems◦ Temperature must ALWAYS be in KELVIN

Pressure and volume are inversely related at constant temperature

PV= k, where k is a constant As one goes up, the other goes down P1V1 = P2 V2

V

P (at constant T)

V

1/P (at constant T)

Slope = k

PV

P (at constant T)

CO2

O2

22.4

1 L

atm

Given the volume of gas as 200.mL at 1.05atm pressure, calculate the volume of the same gas at 1.01atm.◦ 208mL

30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa?◦ 4.0kPa

20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume?◦ 2.0L

Volume of a gas varies directly with the absolute temperature at constant pressure.

V = kT (if T is in Kelvin) One goes up, the other goes up

V1 = V2

T1 T2

V (

L)

T (ºC)

He

H2O

CH4

H2

-273.15ºC

What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC , if the pressure is held constant?◦ 311mL

At what temperature would 40.5 L of gas at 23.4ºC have a volume of 81.0 L at constant pressure? ◦ 593K or 320ºC

At constant volume, pressure and absolute temperature are directly related.

P = k T One goes up, the other goes up

P1 = P2

T1 T2

A steel tank contains a gas at 27.0°C and a pressure of 12.0atm. Determine the gas pressure when the tank is heated to 100.°C.

◦ 14.9 atm

At 120°C, the pressure of a sample of nitrogen is 1.07atm. What will the pressure be at 205°C, assuming constant volume?

◦ 1.30 atm

At constant temperature and pressure, the volume of gas is directly related to the number of moles.

V = k n (n is the number of moles)

V1 = V2

n1 n2

Combines Boyles’, Charles’ and Gay-Lussac’s laws

Describes the relationship between pressure, temperature, and volume

If the moles of gas remains constant, use this formula and cancel out the other things that don’t change

P1 V1 = P2 V2

. T1 T2

A sample of gas has a volume of 4.18 L at 29ºC and 732 torr. What would its volume be at 24.8ºC and 756 torr?◦ 3.99L

5.00L of air at a temperature of -50ºC has a pressure of 107kPa. What is its pressure if the temperature is raised to 102ºC and its volume to 7.00L◦ 129kPa

The volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa pressure.What would the volume be at standard temperature and pressure (STP)?◦ 39.5 L

PV = nRT An Equation of state

◦ Independent of how you end up where you are at◦ Does not depend on the path

An Empirical Equation◦ Based on experimental evidence

Tells you about current state of gas◦ The other laws tell you about a gas when it

changes Given 3 factors you can determine the

fourth

PV = nRT R is the ideal gas constant V = 22.41 L at P = 1 atm, T = 0ºC, n = 1

mole What is R?

◦ R = 0.08206 (L·atm)/(mol·K)◦ With different units: R = 8.31 (L·kPa)/(mol·K)

Ideal gases are hypothetical substances Think of it as a limit Gases only approach ideal behavior at low

pressure (< 1 atm) and high temperature Use the laws anyway, unless told to do

otherwise They give good estimates

A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature?◦ 658K

Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at 24.8ºC What is the mass of Kr?◦ 546g Kr

Real gas particles have volume and there are attractions between the particles (especially polar molecules)

A real gas behaves ideally at low pressure and high temperature.

Under conditions of high pressures and low temperatures, deviations from the expected results of the ideal gas law will occur.

Need to add correction factors to the ideal gas law to account for these.

D = m/V Let M stand for molar mass M = m/n n= PV/RT M = m

PV/RT M = mRT = mRT = DRT

PV VP P

What is the density of ammonia at 23ºC and 735 torr?

M = DRT P D = MP / RT D = (17.04g/mol)(735torr/760 torr/atm)

(0.08206 (L·atm)/(mol·K)(296K) D = 0.678g/L

Reactions happen in moles At Standard Temperature and Pressure

(STP),◦ 0ºC and 1 atm ◦ 1 mole of gas occupies 22.4 L

If not at STP, use the ideal gas law to calculate moles of reactant or volume of product.

Consider the following reaction:4NH3(g) + 5O2(g) 4NO(g) +6H2O(g)

What volume of NO at STP will be produced from 23.7L of NH3?◦ 23.7L

What volume of O2 measured at STP will be

consumed when 10.0L NH3 is reacted?

◦ 12.5L

Mercury can be produced by the following reaction:

2HgO 2Hg +O2

What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP?◦ 0.229L

At 400.ºC and 740 torr?◦ 0.580L

Using the following reaction:NaHCO3(s)+ HCl(aq)NaCl(aq) +CO2(g)

+H2O(l) Calculate the mass of sodium hydrogen

carbonate necessary to produce 2.87 L of carbon dioxide at 25ºC and 2.00 atm◦ 19.7g NaHCO3

The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container.

The total pressure is the sum of the partial pressures.

PTotal = P1 + P2 + P3 + P4 + P5 ... For each P = nRT/V

PTotal = n1RT + n2RT + n3RT +...

V V V In the same container R, T and V are the

same.

PTotal = (n1+ n2 + n3+...)RT

V

PTotal = (nTotal)RT

V

Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen at 101.30 kPa of total pressure if the partial pressures of nitrogen, carbon dioxide,and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?◦ 21.22kPa

Ratio of moles of the substance to the total moles.

Symbol is Greek letter chi

= n1 = P1

nTotal PTotal

The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen?◦ 0.787

What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm?◦ 4.13 atm

When these valves are opened, what is each partial pressure and the total pressure?

3.50 L

O2

1.50 L

N2

2.70 atm

4.00 L

CH4

4.58 atm 0.752 atm

Water evaporates! When that water evaporates, the vapor has

a pressure. Gases are often collected over water so the

vapor. pressure of water must be subtracted from the total pressure.

It must be given.

N2O can be produced by the following

reaction

what volume of N2O collected over water at

a total pressure of 94 kPa and 22ºC can be produced from 2.6 g of NH4NO3? ( the vapor

pressure of water at 22ºC is 21 torr)

NH NO NO (g) + 2H O4 heat

23 2( ) ( )s l

Passage of gas through a small hole, into a vacuum.

The effusion rate measures how fast this happens.

Graham’s Law the rate of effusion is inversely proportional to the square root of the mass of its particles.

The spreading of a gas through a room. Slow considering molecules move at 100’s

of meters per second. Collisions with other molecules slow down

diffusions. Best estimate is Graham’s Law.