How Do Gases Behave?How Do Gases Behave?

What is a solid, liquid or gas?What is a solid, liquid or gas?

Help Marvin the Martian Help Marvin the Martian understand what a solid, understand what a solid, liquid and gas are!liquid and gas are!

Draw what solids, liquids, Draw what solids, liquids, gases look likegases look like

Describe Describe physical/chemical physical/chemical propertiesproperties

What would happen if we What would happen if we changed pressure?changed pressure?

What would happen if we What would happen if we changed temperature?changed temperature?

What is Pressure?What is Pressure?

Pressure = Pressure = Force/AreaForce/Area

1 atmosphere (atm)1 atmosphere (atm) 760 Torr760 Torr 760 mmHg760 mmHg 1.01 Bar1.01 Bar 101,327 Pascal101,327 Pascal 101.3 KPa101.3 KPa Measured with Measured with a barometera barometer

MANOMETERMANOMETER

Column of Column of mercury to mercury to measure measure pressure.pressure.

hh is how much is how much lower or higher lower or higher the pressure is the pressure is than outside. than outside.

PPgasgas = P = Patmatm - h - h PPgasgas = P = Patmatm + h + h

hh

What is Temperature?What is Temperature? Average Kinetic Energy (1/2 mvAverage Kinetic Energy (1/2 mv22) of an atom or molecule) of an atom or molecule Measured in Fahrenheit, Celsius or Kelvin (SI)Measured in Fahrenheit, Celsius or Kelvin (SI) F = (C x 1.8) + 32F = (C x 1.8) + 32 K = C + 273K = C + 273 0 Kelvin: absolute zero (atom stops moving completely)0 Kelvin: absolute zero (atom stops moving completely) Is there a maximum temperature in the universe?Is there a maximum temperature in the universe?

Kinetic Molecular TheoryKinetic Molecular Theory Theory explains why ideal gases behave the way Theory explains why ideal gases behave the way

they do.they do. Assumptions that simplify the theory, but don’t Assumptions that simplify the theory, but don’t

work in real gases.work in real gases.

1.1. The particles are so small we can ignore their volume.The particles are so small we can ignore their volume.2.2. The particles are in constant motion and their collisions The particles are in constant motion and their collisions

cause pressure.cause pressure.3.3. The particles do not affect each other, neither The particles do not affect each other, neither

attracting or repelling.attracting or repelling.4.4. The average kinetic energy is proportional to the The average kinetic energy is proportional to the

Kelvin temperature.Kelvin temperature.5.5. The molecules move in straight path and all The molecules move in straight path and all

collisions are elasticcollisions are elastic

What is an Ideal Gas?What is an Ideal Gas?

An ideal gas or perfect gas is a hypothetical gas An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of:consisting of identical particles of: Negligible volumeNegligible volume With no intermolecular forcesWith no intermolecular forces Atoms or molecules undergo perfectly elastic collisions Atoms or molecules undergo perfectly elastic collisions

with the walls of the containerwith the walls of the container Ideal gas law calculations are favored at low Ideal gas law calculations are favored at low

pressures and high temperatures.pressures and high temperatures. Real gases existing in reality do not exhibit these Real gases existing in reality do not exhibit these

exact properties, although the approximation is exact properties, although the approximation is often good enough to describe real gases.often good enough to describe real gases.

What is What is Boyle’s Law? Law?

In the mid 1600's, Robert Boyle studied the In the mid 1600's, Robert Boyle studied the relationship between the pressure relationship between the pressure P P and the and the volume volume VV of a confined gas held at a constant of a confined gas held at a constant temperature. temperature.

Boyle observed that the product of the Boyle observed that the product of the pressure and volume are observed to be pressure and volume are observed to be nearly constant. nearly constant.

The product of pressure and volume is exactly The product of pressure and volume is exactly a constant for an a constant for an ideal gasideal gas. .

P * V = constantP * V = constant This relationship between pressure and This relationship between pressure and

volume is called volume is called Boyle's LawBoyle's Law in his honor.in his honor.

V

P (at constant T)

BOYLE’S LAW

V

1/P (at constant T)

Slope = k

PV

P (at constant T)

CO2

O2

22.4

1 L

atm

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

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

What is What is Charles’ Law?Law?

The relationship between temperature and The relationship between temperature and volume, at a constant number of moles and volume, at a constant number of moles and pressure, is calledpressure, is called Charles and Gay-Lussac's Charles and Gay-Lussac's Law Law in honor of the two French scientists who in honor of the two French scientists who first investigated this relationship. first investigated this relationship.

Charles did the original work, which was verified Charles did the original work, which was verified by Gay-Lussac. They observed that if the by Gay-Lussac. They observed that if the pressure is held constant, the volume pressure is held constant, the volume VV is equal is equal to a constant times the temperature to a constant times the temperature T, T, or: or:

V / T= constant V / T= constant

V (

L)

T (ºC)

He

H2O

CH4

H2

-273.15ºC

CHARLES LAW

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

If the volume of oxygen at 21 °C is 785 L, at what If the volume of oxygen at 21 °C is 785 L, at what temperature would oxygen occupy 804 L?temperature would oxygen occupy 804 L?

Combined Gas LawCombined Gas Law Combining Charles’s Law and Boyle’s Law Combining Charles’s Law and Boyle’s Law

in a single statement:in a single statement: PP11VV11/T/T11 = P = P22VV22/T/T22

39.8 mg of caffeine gives 10.1 mL of 39.8 mg of caffeine gives 10.1 mL of nitrogen gas at 23 C and 746 mmHg. nitrogen gas at 23 C and 746 mmHg. What is the volume of nitrogen at 0 C and What is the volume of nitrogen at 0 C and 760 mmHg?760 mmHg?

Other Gas LawsOther Gas Laws

Gay-Lussac LawGay-Lussac Law At constant volume, pressure and At constant volume, pressure and

absolute temperature are directly related.absolute temperature are directly related. P/T = k (constant)P/T = k (constant)

Avogadro’s LawAvogadro’s Law At constant temperature and pressure, At constant temperature and pressure,

the volume of gas is directly related to the volume of gas is directly related to the number of moles.the number of moles.

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

Gas Law SummaryGas Law SummaryLawLaw StatementStatement EquationEquation ConstantConstant

Boyle’sBoyle’sP inversely P inversely

proportional proportional to Vto V

PV = kPV = k11 T, T, nn

Charle’sCharle’sV directly V directly

proportional proportional to Tto T

V/T = kV/T = k22 P, P, nn

Gay-LussacGay-LussacP directly P directly

proportional proportional to Tto T

P/T = kP/T = k33

V, V, nn

Avogadro’sAvogadro’sV directly V directly

proportional proportional to to nn

V/V/n n = k= k44 P, TP, T

What equation would we get if we combined them all?

What is the Ideal Gas Law?What is the Ideal Gas Law?

Combining Boyle’s Law, Charles’ law & Combining Boyle’s Law, Charles’ law & Avogadro’s Law we derive the Avogadro’s Law we derive the Ideal Gas Law:Ideal Gas Law:

P V = n R TP V = n R T P = Pressure (atm)P = Pressure (atm) V = Volume (L)V = Volume (L) n = # moles (mol)n = # moles (mol) R = Gas Constant (0.0821 L atm /mol K)R = Gas Constant (0.0821 L atm /mol K) T = Temperature (K)T = Temperature (K) Ideal gas law calculations are favored at Ideal gas law calculations are favored at

low pressureslow pressures and and high temperatureshigh temperatures

Let’ Try It!Let’ Try It!

Example: Example: If we had 1.0 mol of gas at 1.0 atm of If we had 1.0 mol of gas at 1.0 atm of

pressure at 0°C (pressure at 0°C (STPSTP), what would be the ), what would be the volume?volume?

PV = nRTPV = nRT V = nRT/PV = nRT/P

D = m/VD = m/V Let Let MM stand for molar mass stand for molar mass MM = m/n = m/n n = m/Mn = m/M PV = nRTPV = nRT PV = (m/M) RTPV = (m/M) RT P = mRT/VM = (mV)(RT/M)P = mRT/VM = (mV)(RT/M) P = d RT/MP = d RT/M PM/RT = d (density)PM/RT = d (density)

Gas Density and Molar MassGas Density and Molar Mass

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

Units must be: atm, KUnits must be: atm, K

Examples Examples

Reactions happen in molesReactions happen in moles At Standard Temperature and At Standard Temperature and

Pressure (STP, 0ºC and 1 atm) 1 Pressure (STP, 0ºC and 1 atm) 1 mole of gas occuppies 22.42 L.mole of gas occuppies 22.42 L.

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

Gases and StoichiometryGases and Stoichiometry

Consider the following reaction:Consider the following reaction:

Suppose you heat 0.0100 mol of Suppose you heat 0.0100 mol of potassium chlorate, KClOpotassium chlorate, KClO33, in a test , in a test tube. How many liters of oxygen can tube. How many liters of oxygen can you produce at 298 K and 1.02 atm?you produce at 298 K and 1.02 atm?

Break it into 2 problems, one involving Break it into 2 problems, one involving stoichiometry and the other using the stoichiometry and the other using the ideal gas lawideal gas law

ExamplesExamples

(g)3O + 2KCl(s) (s) 2KClO 2heat

3

Using the following reactionUsing the following reaction

Calculate the mass of sodium hydrogen carbonate Calculate the mass of sodium hydrogen carbonate necessary to produce 2.87 L of carbon dioxide at necessary to produce 2.87 L of carbon dioxide at

25ºC and 2.00 atm25ºC and 2.00 atm..

NaCl(aq) + CO (g) +H O(l)2 2

NaHCO (s) + HCl 3

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

The total pressure is the sum of the The total pressure is the sum of the partial pressures.partial pressures.

PPTotalTotal = P = P11 + P + P22 + P + P33 + P + P44 + P + P55 ... ...

For each P = nRT/VFor each P = nRT/V

Dalton’s LawDalton’s Law

PPTotalTotal = = nn11RTRT + + nn22RTRT + + nn33RTRT +... +...

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

same.same.

PPTotalTotal = ( = (nn11+ n+ n22 + n + n33+...)RT+...)RT VV

PPTotalTotal = ( = (nnTotalTotal)RT)RT V V

Dalton's LawDalton's Law

Ratio of moles of the substance to the Ratio of moles of the substance to the total moles.total moles.

symbol is Greek letter chi symbol is Greek letter chi Because pressure of a gas is proportional Because pressure of a gas is proportional

to moles, for fixed volume and to moles, for fixed volume and temperature then,temperature then,

= = nn11 = = PP11

n nTotal Total PPTotalTotal

The Mole FractionThe Mole Fraction

Calculating the Partial Pressure and Calculating the Partial Pressure and Mole Fraction of a Gas MixtureMole Fraction of a Gas Mixture

A 1.00 L sample of dry air at 25°C A 1.00 L sample of dry air at 25°C and 786 mmHg contains 0.925 g Nand 786 mmHg contains 0.925 g N22, , plus other gases including oxygen, plus other gases including oxygen, argon and carbon dioxide.argon and carbon dioxide. What is the partial pressure (in mmHg) What is the partial pressure (in mmHg)

of Nof N22 in the air sample? in the air sample? What is the mole fraction and mole What is the mole fraction and mole

percent of Npercent of N22 in the mixture? in the mixture?

Water evaporates!Water evaporates! When that water evaporates, the vapor When that water evaporates, the vapor

has a pressure.has a pressure. Gases are often collected over water so Gases are often collected over water so

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

Vapor pressure is varies by temperature Vapor pressure is varies by temperature and must be given in the problem or in a and must be given in the problem or in a table.table.

Vapor PressureVapor Pressure

Hydrogen gas is produced by the Hydrogen gas is produced by the reaction of hydrochloric acid, HCl, on reaction of hydrochloric acid, HCl, on zinc metal:zinc metal:

2HCl (aq) + Zn (s) —> ZnCl2HCl (aq) + Zn (s) —> ZnCl22 (aq) + H (aq) + H22 (g)(g)

The gas is collected over water. If The gas is collected over water. If 156 mL of gas is collected at 19 C 156 mL of gas is collected at 19 C and 769 mmHg total pressure, what and 769 mmHg total pressure, what is the mass of hydrogen collected?is the mass of hydrogen collected?

What’s Diffusion and Effusion?What’s Diffusion and Effusion?

Only a few physical properties of gases depends Only a few physical properties of gases depends on the identity of the gas. on the identity of the gas.

DiffusionDiffusion - The rate at which two gases mix. - The rate at which two gases mix. Effusion Effusion - The rate at which a gas escapes - The rate at which a gas escapes

through a pinhole into a vacuum. through a pinhole into a vacuum.

What is Graham’s Law?What is Graham’s Law?

We know that Kinetic energy = 1/2 mvWe know that Kinetic energy = 1/2 mv22

If two bodies of unequal mass have the If two bodies of unequal mass have the same kinetic energy, which moves faster?same kinetic energy, which moves faster?

The lighter one!The lighter one! Thus, for two gases at the same Thus, for two gases at the same

temperature, the one with lower molecular temperature, the one with lower molecular mass will diffuse/effuse faster.mass will diffuse/effuse faster.

The rate of effusion/diffusion of a gas is The rate of effusion/diffusion of a gas is inversely proportional to the square root of inversely proportional to the square root of its mass.its mass.

Calculate the ratio of effusion rates of Calculate the ratio of effusion rates of molecules of carbon dioxide and sulfur molecules of carbon dioxide and sulfur dioxide from the same container and at dioxide from the same container and at the same temperature and pressure:the same temperature and pressure:

Rate of effusion for gas 1

Rate of effusion for gas 2

M

M

2

1