Gases .

Gases

http://www.chem.leeds.ac.uk/delights/animations/balloons.html

Gas Characteristics

• Based on the Gases lab, what are some of the characteristics of gases?

The three states of matter.

The Structure of a Gas• Gases are composed of

particles that are flying around very fast in their container(s)

• The particles in straight lines until they encounter either the container wall or another particle, then they bounce off

• If you were able to take a snapshot of the particles in a gas, you would find that there is a lot of empty space in there

Gases Pushing

5

• Gas molecules are constantly in motion

• As they move and strike a surface, they push on that surfacepush = force

• If we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exertingpressure = force per unit area

Gas Variables

• Volume (V) - mL, L, kL…• Temperature (T) – oC measured in

lab but K (kelvin) for calculations• Number of particles (n) – moles • Pressure (P) – mmHg, psi…(more to

come)

The Pressure of a Gas

• Gas pressure is a result of the constant movement of the gas molecules and their collisions with the surfaces around them

• The pressure of a gas depends on several factorsnumber of gas particles in a

given volumevolume of the containeraverage speed of the gas

particles

Measuring Air Pressure

gravity

• We measure air pressure with a barometer

• Column of mercury supported by air pressure

• Force of the air on the surface of the mercury counter balances the force of gravity on the column of mercury

Manometer

for this sample, the gas has a larger pressure than the atmosphere, so

Common Units of Pressure

Converting Units of Pressure

PROBLEM: A geochemist heats a limestone (CaCO3) sample and collects the CO2 released in an evacuated flask attached to a closed-end manometer. After the system comes to room temperature, h = 291.4 mm Hg. Calculate the CO2 pressure in atmospheres, and kilopascals.

SOLUTION:

Construct conversion factors to find the other units of pressure.

291.4 torr1 atm

760 torr= 0.3834 atm

0.3834 atm

101.325 kPa1 atm

= 38.85 kPa

Gas Variable Relationships

• To investigate the relationship between 2 gas variables we need to hold the other 2 constant.

• Constant P - same # of collisions/unit area

• Constant V - rigid container• Constant T – thermostat control• Constant n – keep container sealed

Gas Variable Relationships

• P and V n, T = constant• T and V n, P = constant• P and T n , V = constant• n and V T, P = constant

A molecular description of Boyle’s Law – the relationship between P and V

The relationship between the volume and pressure of a gas.

Boyle’s Law

1 1 2 2PV = PV

Boyle’s Law Problems

• What is the volume of gas sample at 750 mmHg if its volume is 4.55 L at 900 mmHg?

• A sample of helium has a volume of 560 mL at standard pressure. What is the pressure if the volume increases to 890 mL?

A molecular description of Charles’s Law – relationship between temperature and volume

The relationship between the volume and temperature of a gas.

Charles’s Law

2 2

1 1

V T =

V T

Charles’s LawJacques Charles (1746–1823)

• Volume is directly proportional to temperatureconstant P and amount of gasgraph of V vs. T is straight line

• As T increases, V also increases

• Kelvin T = Celsius T + 273

• V = constant x Tif T measured in Kelvin

Charles’ Law Problems

• What is the volume of a gas at 75oC if its volume is 780 mL at 25oC?

• What temperature is required to change the volume of a gas to 35 L if its volume is 25 L at 10oC?

Boyle’s Law

n and T are fixedV 1

P

Charles’s Law

V T P and n are fixed

V

T= constant V = constant x T

Amontons’s Law

(Gay-Lusaac’s Law)

P T V and n are fixed

P

T= constant P = constant x T

Combined gas law

V T

PV = constant x

T

P

PV

T= constant

V x P = constant V = constant / P

1 1 2 2

1 2

PV PV =

T T

Combined Gas Law Problems

• What is the volume of a gas at 60oC and 850 mmHg if its volume is 350 L at STP?

• A gas has a volume of 765 mL at 40oC and 1.25 atm. What is the temperature if the sample has a volume of 900 mL with a pressure of 900 mmHg?

An experiment to study the relationship between the volume and amount of a gas.

V n or V = constant x n

Equal volumes of gas under the same conditions contain equal number of particles. If two gases are at the same conditions you can use volumes instoichiometric calculations in place of moles.

IDEAL GAS LAW

Boyle’s Law

V =constant

PV = V =

Charles’s Law

constant X T

Avogadro’s Law

constant X n

fixed n and T fixed n and P fixed P and T

R is the universal gas constant

R = PV

nT=

1atm x 22.414L

1mol x 273.15K

=

0.0821atm*L

mol*K

PV = nRT

Standard Conditions

• Because the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy – we call these standard conditions– STP

• Standard pressure = 1 atm• Standard temperature = 273 K (0 °C)

Standard molar volume.

density = m/V where m = mass

n = m/MM

The Density of a Gas from the Ideal Gas Law

PV = nRT PV = (m/MM)RT

m/V = MM x P/ RT

•The density of a gas is directly proportional to its molar mass.

•The density of a gas is inversely proportional to the temperature.

Molar mass of a gas

PV = nRTm

PV = RTMM

m RTMM =

PV

Mixtures of Gases

• When gases are mixed together, their molecules behave independent of each other– all the gases in the mixture have the same volume

• all completely fill the container each gas’s volume = the volume of the container

– all gases in the mixture are at the same temperature• therefore they have the same average kinetic energy

• Therefore, in certain applications, the mixture can be thought of as one gas– even though air is a mixture, we can measure the

pressure, volume, and temperature of air as if it were a pure substance

– we can calculate the total moles of molecules in an air sample, knowing P, V, and T, even though they are different molecules

Dalton’s Law of Partial Pressures

Ptotal = P1 + P2 + P3 + ...

Mixtures of Gases

•Gases mix homogeneously in any proportions.

•Each gas in a mixture behaves as if it were the only gas present.

Why do we need to know this?

A molecular description of Dalton’s law of partial pressures.

Exchange of O2 and CO2

depends on their partialpressure differencesacross membranes.

Collecting Gas by Water Displacement

Vapor Pressure of Water

P,V,T

of gas A

amount (mol)

of gas A

amount (mol)

of gas B

P,V,T

of gas B

ideal gas law

ideal gas law

molar ratio from balanced equation

Summary of the stoichiometric relationships among the amount (mol,n) of gaseous reactant or product and the gas variables pressure (P), volume (V), and temperature (T).

Stoichiometric Gas Problem

• How many L of CO2 gas at 25oC and 880 mmHg are formed when 15.9 g of gasoline (C8H18) are combusted?

• How many L of O2 at 20oC and 0.95 atm are required to generate 250 mL of CO2 at 1.05 atm and 40oC when gasoline burns?

Kinetic Molecular Theory (KMT) of Gases

• KMT is a model to explain the behavior of gaseous particles and is based on extensive observations of the behavior of gases.

• If a gas follows all the postulates of the the KMT it is said to be an ideal gas.

Postulates of the KMT

• Particles are in constant, random, straight line motion. Collisions with walls of their container generate pressure.

• The actual volume of gas particles is negligible. Particles are far apart. The volume of a gas is effectively the volume the particles occupy, not their particle volume.

Postulates of the KMT

• Gas particles do not attract or repel.

• The average kinetic energy of a collection of gas particles is directly proportional to the Kelvin temperature of the gas.

Diffusion of a gas particle through a space filled with other particles.

distribution of molecular speeds

mean free path

collision frequency

Gas EffusionMovement of a gas through a small opening

What factors affect the effusion of a gas?

Distribution of molecular speeds at three temperatures.

Relationship between molar mass and molecular speed.

Graham’s Law of Effusion

The rate of effusion of a gas is inversely related to the square root of its molar mass.

rate of effusion

1

√MM

Ideal vs Real Gases

• How do gas volumes respond under a range of conditions (such as changing pressures and temperatures)?

• If a gas is ideal, the graph of PV/RT vs P for one mole of gas will have a slope of 1.

• http://intro.chem.okstate.edu/1314F97/Chapter10/RealGas.html

Deviations from Ideality

• For an ideal gas:• PV = nRT or V = nRT/P

• When you actually measure gas volume at high pressures and low temperatures, the Vexperimental often does not match Vtheoretical

Deviations from Ideality

• Why doesn’t Vexp = Vtheor ?

• If Vexp > Vtheor:

• Some gas particles do repel each other so volume is greater than predicted.

• Gas particles do have a volume so volume cannot be reduced beyond a certain point.

Deviations from Ideality

• Why doesn’t Vexp = Vtheor ?

• If Vexp < Vtheor:

• Some gas particles do attract each other so volume is reduced more than expected.

Corrections for Deviations from Ideality

• Johannes van der Waals modified the ideal gas law to account for deviations.

• P x V = nRT

• [Pexp + a(n/V)2] x (V-nb) = nRT

• [Pexp + a(n/V)2] corrects for attractive or repulsive forces (“a” depends on the particle)

• V-nb corrects for particle volume (“b” is a measure of particle volume)

Gas Formula a [(L2 · atm)/mole2] b [L/mole]

Helium He 0.03412 0.02370

Hydrogen H2 0.2444 0.02661

Nitrogen N2 1.390 0.03913

Oxygen O2 1.360 0.03183

Carbon dioxide CO2 3.592 0.04267

Acetylene C2H2 4.390 0.05136

Chlorine Cl2 6.493 0.05622

n - Butane C4H10 14.47 0.1226

n - Octane C8H18 37.32 0.2368

Selected Values for a and b for the van der Waals Equation