chapter 10 gases. characteristics of gases unlike liquids and solids, they unlike liquids and...

Chapter 10Chapter 10GasesGases

Characteristics of GasesCharacteristics of Gases

Unlike liquids and solids, Unlike liquids and solids, theythey Expand to fill their containers.Expand to fill their containers. Are highly compressible.Are highly compressible. Have extremely low densities.Have extremely low densities.

Pressure is the Pressure is the amount of force amount of force applied to an area.applied to an area.

PressurePressure

Atmospheric Atmospheric pressure is the pressure is the weight of air weight of air per unit of area.per unit of area.

P =FA

Units of PressureUnits of Pressure

PascalsPascals 1 Pa = 1 N/m1 Pa = 1 N/m22

BarBar 1 bar = 101 bar = 1055 Pa = 100 kPa Pa = 100 kPa

Units of PressureUnits of Pressure

mm Hg or torrmm Hg or torr These units are These units are

literally the difference literally the difference in the heights in the heights measured in mm (measured in mm (hh) of ) of two connected two connected columns of mercury.columns of mercury.

AtmosphereAtmosphere 1.00 atm = 760 torr1.00 atm = 760 torr

ManometerManometer

Used to measure Used to measure the difference in the difference in pressure between pressure between atmospheric atmospheric pressure and that pressure and that of a gas in a of a gas in a vessel.vessel.

Standard PressureStandard Pressure

Normal atmospheric pressure at Normal atmospheric pressure at sea level.sea level.

It is equal toIt is equal to 1.00 atm1.00 atm 760 torr (760 mm Hg)760 torr (760 mm Hg) 101.325 kPa101.325 kPa

Boyle’s LawBoyle’s Law

The volume of a fixed quantity of gas at The volume of a fixed quantity of gas at constant temperature is inversely constant temperature is inversely proportional to the pressure.proportional to the pressure.

Boyle’s LawBoyle’s Law

As As PP and and VV are areinversely proportionalinversely proportional

A plot of A plot of VV versus versus PP results in a results in a curve.curve.

Since

V = k (1/P)This means a plot of V versus 1/P will be a straight line.

PV = k

Charles’s LawCharles’s Law

The volume of a fixed The volume of a fixed amount of gas at amount of gas at constant pressure is constant pressure is directly proportional directly proportional to its absolute to its absolute temperature.temperature.

A plot of V versus T will be a straight line.

i.e.,i.e., VT

= k

Avogadro’s LawAvogadro’s Law The volume of a gas at constant temperature The volume of a gas at constant temperature

and pressure is directly proportional to the and pressure is directly proportional to the number of moles of the gas.number of moles of the gas.

Mathematically, this meansMathematically, this means V = kn

Ideal-Gas EquationIdeal-Gas Equation

VV 1/ 1/PP (Boyle’s law) (Boyle’s law)VV TT (Charles’s law) (Charles’s law)VV nn (Avogadro’s law) (Avogadro’s law)

So far we’ve seen thatSo far we’ve seen that

Combining these, we getCombining these, we get

V nTP

Ideal-Gas EquationIdeal-Gas Equation

The constant of The constant of proportionality proportionality is known as is known as RR, , the gas the gas constant.constant.

Ideal-Gas EquationIdeal-Gas Equation

The relationshipThe relationship

then becomes

nTP

V

nTP

V = R

or

PV = nRT

Ideal-Gas EquationIdeal-Gas Equation

Densities of GasesDensities of Gases

If we divide both sides of the ideal-If we divide both sides of the ideal-gas equation by gas equation by VV and by and by RTRT, we get, we get

nV

PRT

=

We know thatWe know that moles moles molecular mass = mass molecular mass = mass

Densities of GasesDensities of Gases

So multiplying both sides by the So multiplying both sides by the molecular mass (molecular mass () gives) gives

n = m

PRT

mV

=

Densities of GasesDensities of Gases

Mass Mass volume = density volume = density

So,So,

Note: One only needs to know the Note: One only needs to know the molecular mass, the pressure, and molecular mass, the pressure, and the temperature to calculate the the temperature to calculate the density of a gas.density of a gas.

PRT

mV

=d =

Molecular MassMolecular Mass

We can manipulate the density We can manipulate the density equation to enable us to find the equation to enable us to find the molecular mass of a gas:molecular mass of a gas:

Becomes

PRT

d =

dRTP =

Dalton’s Law ofDalton’s Law ofPartial PressuresPartial Pressures

The total pressure of a mixture of The total pressure of a mixture of gases equals the sum of the gases equals the sum of the pressures that each would exert if it pressures that each would exert if it were present alone.were present alone.

In other words,In other words,

PPtotaltotal = = PP11 + + PP22 + + PP33 + … + …

Partial Pressures of Partial Pressures of GasesGases

Partial PressuresPartial Pressures

When one collects a gas over water, there When one collects a gas over water, there is water vapor mixed in with the gas.is water vapor mixed in with the gas.

To find only the pressure of the desired gas, To find only the pressure of the desired gas, one must subtract the vapor pressure of one must subtract the vapor pressure of water from the total pressure.water from the total pressure.

Kinetic-Molecular TheoryKinetic-Molecular Theory

This is a model This is a model that aids in our that aids in our understanding of understanding of what happens to what happens to gas particles as gas particles as environmental environmental conditions change.conditions change.

Main Tenets of Kinetic-Main Tenets of Kinetic-Molecular TheoryMolecular Theory

Gases consist of large Gases consist of large numbers of molecules that numbers of molecules that are in continuous, random are in continuous, random motion.motion.

Main Tenets of Kinetic-Main Tenets of Kinetic-Molecular TheoryMolecular Theory

The combined volume of all the The combined volume of all the molecules of the gas is negligible molecules of the gas is negligible relative to the total volume in relative to the total volume in which the gas is contained.which the gas is contained.

Attractive and repulsive forces Attractive and repulsive forces between gas molecules are between gas molecules are negligible.negligible.

Main Tenets of Kinetic-Main Tenets of Kinetic-Molecular TheoryMolecular Theory

Energy can be Energy can be transferred between transferred between molecules during molecules during collisions, but the collisions, but the averageaverage kinetic kinetic energy of the energy of the molecules does not molecules does not change with time, as change with time, as long as the long as the temperature of the temperature of the gas remains constant.gas remains constant.

Main Tenets of Kinetic-Main Tenets of Kinetic-Molecular TheoryMolecular Theory

The average The average kinetic energy of kinetic energy of the molecules is the molecules is proportional to proportional to the absolute the absolute temperature.temperature.

EffusionEffusion

The escape of The escape of gas molecules gas molecules through a tiny through a tiny hole into an hole into an evacuated evacuated space.space.

DiffusionDiffusion

The spread of one The spread of one substance substance throughout a throughout a space or space or throughout a throughout a second second substance.substance.

Boltzmann DistributionsBoltzmann Distributions

Effect of Molecular Mass Effect of Molecular Mass on Rate of Effusion and on Rate of Effusion and

DiffusionDiffusion

Real GasesReal Gases

In the real world, In the real world, the behavior of the behavior of gases only gases only conforms to the conforms to the ideal-gas ideal-gas equation at equation at relatively high relatively high temperature and temperature and low pressure.low pressure.

Deviations from Ideal Deviations from Ideal BehaviorBehavior

The assumptions made in the kinetic-The assumptions made in the kinetic-molecular model break down at high molecular model break down at high pressure and/or low temperature.pressure and/or low temperature.

Real GasesReal Gases

Corrections for Nonideal Corrections for Nonideal BehaviorBehavior

The ideal-gas equation can be The ideal-gas equation can be adjusted to take these deviations adjusted to take these deviations from ideal behavior into account.from ideal behavior into account.

The corrected ideal-gas equation The corrected ideal-gas equation is known as the is known as the van der Waals van der Waals equation.equation.

The van der Waals The van der Waals EquationEquation

) (V − nb) = nRTn2aV2(P +