gases

Gases:

Gases are composed of particles that are XX

around very XX In their container(s).

- Examples: H2 (g), HF (g), He (g)

• All gases have the following characteristics:

• They take on the XX and XX of their containers.

• They are the most XX the states of matter.

• They will mix XX and completely when confined to the

same container.

• Gases have much lower XX than XX and XX

Gases are composed of particles that are moving

around very fast in their container(s).

- Examples: H2 (g), HF (g), He (g)

• All gases have the following characteristics:

• They take on the volume and shape of their containers.

• They are the most compressible of the states of matter.

• They will mix evenly and completely when confined to the

same container.

• Gases have much lower densities than liquids and solids

Properties of Gases

•Variables to describe a gas sample:

-XX

- XX

- XX

- XX

Properties of Gases

•Variables to describe a gas sample:

- P:PRESSURE

- V:VOLUME

- T:TEMP

- n:MOLES

Basic Assumptions of Kinetic Molecular

Theory

• Gas molecules move XX at various

speeds and in every possible XX.

• The average kinetic energy of gas molecules is

proportional to the XX of the XX in

XX.

• A gas is composed of molecules whose volume

is XX compared to the distance between

them.

• Gas molecules do not exert XX and

XX forces on one another.

• The collisions of gas molecules are XX, i.e.

energy is transferred but not lost in collisions.

Basic Assumptions of Kinetic Molecular

Theory

• Gas molecules move randomly at various

speeds and in every possible direction.

• The average kinetic energy of gas molecules is

proportional to the temperature of the gas in

Kelvin.

• A gas is composed of molecules whose volume

is negligible compared to the distance between

them.

• Gas molecules do not exert attractive and

repulsive forces on one another.

• The collisions of gas molecules are elastic, i.e.

energy is transferred but not lost in collisions.

Pressure and Temperature at Molecular Level

• Pressure is related to the XX of

XX of gas molecules with the surface.

• Temperature is related to the average XX

of gas molecules.

Pressure and Temperature at Molecular Level

• Pressure is related to the frequency of

collision of gas molecules with the surface.

• Temperature is related to the average speed

of gas molecules.

Gas Pressure

• Pressure is force per

unit area.

• lb/in2 (psi)

• N/m2 (pascal)

• mmHg or torr

• atm

• Standard pressure

• 760 mm Hg

• 760 torr

• 1 atm

• 1.01325x105 Pa

Gas Pressure

• Pressure is force per

unit area.

• lb/in2 (psi)

• N/m2 (pascal)

• mmHg or torr

• atm

• Standard pressure

• 760 mm Hg

• 760 torr

• 1 atm

• 1.01325x105 Pa

Boyleʼs Law

•At constant T and amount of gas, the

XX of a gas is inversely proportional

to its XX

•V ∝ 1/P

P × V = constant

As P XX, V XX by the same factor

Boyleʼs Law

•At constant T and amount of gas, the

pressure of a gas is inversely proportional

to its volume.

•V ∝ 1/P

P × V = constant

As P increases, V decreases by the same factor

Boyleʼs Law: Mathematical relationship

•At constant T and amount of gas:

XX

Boyleʼs Law: Mathematical relationship

•At constant T and amount of gas:

P1 × V1 = P2 × V

Charlesʼs Law: XX and XX

The volume of a fixed amount of gas at a constant

pressure is directly proportional to its XX in

XX V ∝ T or

V = constant × T

The volume of a gas XX with increasing XX

Charlesʼs Law: Volume and Temperature

The volume of a fixed amount of gas at a constant

pressure is directly proportional to its temperature in

Kelvin. V ∝ T or

V = constant × T

The volume of a gas increases with increasing temperature.

Charleʼs Law: Mathematical relationship:

XX

Charleʼs Law: Mathematical relationship:

V1/T1=V2/T2

The combined gas law is the

combination of Charle’s and Boyle’s

laws.

• For the same gas sample:

XX

The combined gas law is the

combination of Charle’s and Boyle’s

laws.

• For the same gas sample:

P1V1/T1=P2V2/T2

Avogadroʼs Law

•At constant pressure and temperature, volume

is directly proportional to the number of XX XX(or # of molecules) of a gas.

•Equal volumes of gases contain equal

numbers of moles.

• The gas doesn

ʼt matter. V1/N1=V2/N2

Avogadroʼs Law

•At constant pressure and temperature, volume

is directly proportional to the number of gas

moles (or # of molecules) of a gas.

•Equal volumes of gases contain equal

numbers of moles.

• The gas doesn

ʼt matter. V1/N1=V2/N2

IDEAL GAS LAW:PV=NRT

IDEAL GAS LAW:PV=NRT

Standard temperature and pressure

•Standard temperature and pressure (STP)

• Standard pressure = XX XX

• Standard temperature = XX = XX

• The volume occupied by one mole of a substance

is its molar volume at STP

(T =273 K or 0 °C and P = 1atm).

•Solving the ideal gas equation for the volume

of 1 mol of gas at STP gives XX

Standard temperature and pressure

•Standard temperature and pressure (STP)

• Standard pressure = 1.00 atm

• Standard temperature = 273.15 K = 0.00 °C

• The volume occupied by one mole of a substance

is its molar volume at STP

(T =273 K or 0 °C and P = 1atm).

•Solving the ideal gas equation for the volume

of 1 mol of gas at STP gives 22.4 L.

IDEAL GAS LAW:

By combining the gas laws, we can write a general

equation.

XX

• R is a proportionality constant called the universal

gas constant.

- R = XX atm/mol K

• in ideal gas law

- R = XX

• in thermodynamics

- R = XX

• in gas velocity calculation

By combining the gas laws, we can write a general

equation.

PV = n RT

• R is a proportionality constant called the universal

gas constant.

- R = 0.08206 L atm/mol K

• in ideal gas law

- R = 8.314 J/(mol K)

• in thermodynamics

- R = 8.314 kg m2/(s2 K mol)

• in gas velocity calculation

Gas Laws Problem Solving

•Which gas law to use?

• Is there a change in conditions?

XX XX XX

ØExamples:

Ø….the pressure is decreased from ….

Ø….the volume is increased from ….

Ø….the temperature of the gas is raised to ….

• Does it give you a set of conditions?

XX XX XX

ØExample: P, V and n are given. The problem

asks you to solve for T.

•Watch your units! Especially important in

ideal gas law problems.

Gas Laws Problem Solving

•Which gas law to use?

• Is there a change in conditions?

ØIndividual gas law

ØExamples:

Ø….the pressure is decreased from ….

Ø….the volume is increased from ….

Ø….the temperature of the gas is raised to ….

• Does it give you a set of conditions?

ØIdeal gas law

ØExample: P, V and n are given. The problem

asks you to solve for T.

•Watch your units! Especially important in

ideal gas law problems.

Gas density: XX

Molar mass:XX

Gas density: D=PM/RT

Molar mass:M=dRT/P

Dalton’s Law of Partial Pressures

• The pressure of a single gas in a mixture of

gases is called its XX XX

• The sum of the partial pressures of all the gases

in the mixture equals the total pressure:

–Daltonʼs law of partial pressures

XX

Dalton’s Law of Partial Pressures

• The pressure of a single gas in a mixture of

gases is called its partial pressure.

• The sum of the partial pressures of all the gases

in the mixture equals the total pressure:

–Daltonʼs law of partial pressures

Ptotal = P1 + P2 + P3 + .....

DALTONS LAW OF PARTIAL PRESSURES

Pi = Xi∙Ptotal

where Pi is the partial pressure of gas i

Xi is the mole fraction of gas i

xi=moles of gas i/total moles of gases

The gas with bigger moles will make bigger

contribution to the total pressure.

DALTONS LAW OF PARTIAL PRESSURES

Pi = Xi∙Ptotal

where Pi is the partial pressure of gas i

Xi is the mole fraction of gas i

xi=moles of gas i/total moles of gases

The gas with bigger moles will make bigger

contribution to the total pressure.

Kinetic-Molecular Theory

• Different gases at the same T have the same

average XX XX

• At the same T, the heavier the gas molecule, the

slower its XX XX

Kinetic-Molecular Theory

• Different gases at the same T have the same

average kinetic energy.

• At the same T, the heavier the gas molecule, the

slower its average speed.

Molecular Velocities

rms=square root 3rt/molar mass

• The root-mean square velocity:

• The heavier the molecule, the slower the speed.

• To calculate rms velocity correctly:

- R = 8.314 kg m2/(s2 K mol)

- The molar mass must be in kg/mol.

Molecular Velocities

rms=square root 3rt/molar mass

• The root-mean square velocity:

• The heavier the molecule, the slower the xx

• To calculate rms velocity correctly:

- R = 8.314 kg m2/(s2 K mol)

- The molar mass must be inxx/xx

Diffusion and Effusion of Gases

• Diffusion is the xx of gases.

• Effusion is the XX of gases through XX XX

Diffusion and Effusion of Gases

• Diffusion is the intermingling of gases.

• Effusion is the escape of gases through tiny holes

Graham’s Law of Effusion Rate

•The rate of effusion is inversely proportional to

the square roots of the molar mass.

XX

Graham’s Law of Effusion Rate

•The rate of effusion is inversely proportional to

the square roots of the molar mass.

Rate 1/Rate 2=square root MM2/MM1

It’s explaining WHEN real gases stop acting like ideal gases.

Normal conditions → gases act IDEAL ✅

At normal/moderate temperature and pressure, gas molecules are pretty far apart.

So:

• Their actual size doesn’t really matter.

• Their attractions to each other don’t really matter.

• We can safely use \(PV=nRT\) and the other gas laws.

But LOW temperature + HIGH pressure → NON-IDEAL ⚠

Think about what each one does:

HIGH pressure → molecules get pushed close together.

When they're close together, suddenly their actual size matters. You can no longer pretend they're tiny points with zero volume.

LOW temperature → molecules move more slowly.

Because they're moving slowly and are close together, intermolecular attractions have a bigger effect. Molecules can pull on each other instead of behaving like completely independent particles.

So memorize this:

Ideal behavior:

\[ \boxed{\text{HIGH T + LOW P}} \]

Particles are fast + far apart → attractions and particle size don't matter much.

Non-ideal behavior:

\[ \boxed{\text{LOW T + HIGH P}} \]

Particles are slow + close together → attractions and particle size DO matter.

And that's exactly why we need the van der Waals equation under those condition

vIt’s explaining WHEN real gases stop acting like ideal gases.

Normal conditions → gases act IDEAL ✅

At normal/moderate temperature and pressure, gas molecules are pretty far apart.

So:

• Their actual size doesn’t really matter.

• Their attractions to each other don’t really matter.

• We can safely use \(PV=nRT\) and the other gas laws.

But LOW temperature + HIGH pressure → NON-IDEAL ⚠

Think about what each one does:

HIGH pressure → molecules get pushed close together.

When they're close together, suddenly their actual size matters. You can no longer pretend they're tiny points with zero volume.

LOW temperature → molecules move more slowly.

Because they're moving slowly and are close together, intermolecular attractions have a bigger effect. Molecules can pull on each other instead of behaving like completely independent particles.

So memorize this:

Ideal behavior:

\[ \boxed{\text{HIGH T + LOW P}} \]

Particles are fast + far apart → attractions and particle size don't matter much.

Non-ideal behavior:

\[ \boxed{\text{LOW T + HIGH P}} \]

Particles are slow + close together → attractions and particle size DO matter.

And that's exactly why we need the van der Waals equation under those condition