Science league topic 8: ideal gas law

Standard Pressure Normal atmospheric pressure at sea level is

equal to: 1.00 atm 760 torr or 760 mm Hg 101.325 kPa 14.7 Psi

mm Hg or torr: literally the difference in the heights measured in mm (h) of two connected columns of mercury.

Dalton’s Law of Partial Pressures

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

• In other words,

Ptotal = P1 + P2 + P3 + …

Ideal gas Gases consist of large numbers of molecules that are

in continuous, random motion. The combined volume of all the molecules of the gas

is negligible relative to the total volume in which the gas is contained. V of molecules=0

Attractive forces between gas molecules are negligible. In real life, there is always an attraction force between two

objects having mass. Under standard condition (STP, P= 1 atm, T= room

tempreture 298K), we may assume all the gases as ideal gas.

Ideal Gas LawPV = nRT

P = pressure of gasV = volume of gasn = moles of total gas moleculesR = proportionality constant

= 0.08206 L atm/ mol·KT = temperature in Kelvins

Ideal-Gas Equation

The constant of proportionality is known as R, the gas constant.It’s value depends on the

units of P and V.

Avogadro’s LawIf P and T are fixed, the volume of gas is

directly proportional to the number of moles of the gas.

If all the reactants and products are gas, ratio of coefficients = ratio of V

V = kn

Example of Avogadro’s LawIf reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.

3 H2(g) + N2(g) 2NH3(g)

3 moles H2 + 1 mole N2 2 moles NH3 3 liters H2 + 1 liter N2 2 liters NH3

• How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?

Ideal-Gas Equation

V 1/P (If n and T are constant)

V T (If n and P are constant)V n (If P and T are constant)• Combining these, we get

V nTP

PV = nRT

We know that moles molecular mass = mass

Densities of Gases

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

n = m

PRT

mV

=

nV

PRT

=

Densities of GasesMass volume = density. So,

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

PRT

mV

=d =

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

Becomes

PRT

d =

dRTP =

Page 231: 37, 47, 53, 55, 57, 63, 71, 73,

Homework

Intermolecular Forces

The attractions between molecules are not nearly as strong as the bonds inside of compounds.

But they are strong enough to control physical properties such as boiling and melting points, vapor pressures, and viscosities.

Intermolecular Forces

These intermolecular forces (the attraction forces) as a group are referred to as van der Waals forces.

van der Waals ForcesDipole-dipole interactionsHydrogen bondingLondon dispersion forces

Ion-Dipole InteractionsA fourth type of force, ion-dipole

interactions are an important force in solutions of ions.

The strength of these forces are what make it possible for ionic substances to dissolve in polar solvents.

Dipole-Dipole InteractionsMolecules that have

permanent dipoles are attracted to each other.The positive end of one is

attracted to the negative end of the other and vice-versa.

These forces are only important when the molecules are close to each other.

Dipole-Dipole Interactions

The more polar the molecule, the higher is its boiling point.

London Dispersion Forces

At that instant, then, the helium atom is polar

Another helium nearby, then, would have a dipole induced in it, as the electrons on the left side of helium atom 2 repel the electrons in the cloud on helium atom 1.

London Dispersion Forces

London dispersion forces are attractions between an instantaneous dipole and an induced dipole.

Synonyms: “London forces”, “dispersion forces”, and “dispersion-interaction forces”

London Dispersion Forces

These forces are present in all molecules, whether they are polar or nonpolar. But it plays a major role in the nonpolar molecules.

The tendency of an electron cloud to distort in this way is called polarizability.

Factors Affecting London Forces

The shape of the molecule: long, skinny molecules (like n-pentane tend to have stronger dispersion forces than short, fat ones (like neopentane).

This is due to the increased surface area in n-pentane.

Factors Affecting London Forces

The molecular weight: strength of dispersion forces tends to increase with increased MW.

Larger atoms have larger electron clouds, which are easier to polarize.

How Do We Explain This?

The nonpolar series (SnH4 to CH4) follow the expected trend.

The polar series follows the trend from H2Te through H2S, but water is quite an anomaly.

Hydrogen Bonding

The dipole-dipole interactions experienced when H is bonded to N, O, or F are unusually strong.

We call these interactions hydrogen bonds.

Hydrogen BondingHydrogen bonding arises in part from the high electronegativity of nitrogen, oxygen, and fluorine.

Also, when hydrogen is bonded to one of those very electronegative elements, the hydrogen nucleus is exposed.

Relative Magnitudes of ForcesThe types of bonding forces vary in their strength as measured by average bond energy.

Ionic bonds

Covalent bonds (400 kcal/mol)

Ion- dipole interactions

Hydrogen bonding (12-16 kcal/mol )

Dipole-dipole interactions (2-0.5 kcal/mol)

London forces (less than 1 kcal/mol)

Strongest

Weakest

Summarizing Intermolecular Forces

Intermolecular Forces Affect Many Physical Properties of liquid

Boiling point increases with intermolecular attractive forces

ViscosityResistance of a liquid to flow is

called viscosity.It is related to the ease with which

molecules can move past each other.Viscosity increases with stronger

intermolecular forces and decreases with higher temperature. Higher T faster molecules move

Viscosity of Glycerol as a Function of Temperature

Surface TensionSurface tension results from the net inward force experienced by the molecules on the surface of a liquid.Water surface due to surface

tensionHg surface lack of surface tension

Phase Changes

Energy Changes Associated with Changes of State

Heat of Fusion: Energy required to change a solid at its melting point to a liquid.

Heat of Vaporization: Energy required to change a liquid at its boiling point to a gas.

Energy Changes Associated with Changes of State

The heat added to the system at the melting and boiling points goes into pulling the molecules farther apart from each other.

The temperature of the substance does NOT rise during the phase change.

Page 512: 49, 51, 53

Homework

Vapor pressure and phase diagram

Vapor Pressure

At any temperature, some molecules in a liquid have enough energy to escape. As more molecules escape the liquid, the pressure they exert increases.

The liquid and vapor reach a state of dynamic equilibrium: liquid molecules evaporate and vapor molecules condense at the same rate.

Vapor PressureAs the temperature rises, the fraction of

molecules that have enough energy to escape increases.

VP increases.

Vapor PressureThe boiling point of a

liquid is the temperature at which its vapor pressure = atmospheric pressure.

The normal boiling point is the temperature at which its vapor pressure is 760 torr / 1 atm.

Phase DiagramsPhase diagrams display the state of a substance at various atmosphere pressures and temperatures and the places where equilibria exist between phases.

Phase DiagramsThe AB line is the liquid-vapor

interface.It starts at the triple point (A), the point

at which all three states are in equilibrium.

Phase DiagramsIt ends at the critical point (B); above this critical temperature and critical pressure the liquid and vapor are indistinguishable from each other.Each point along this line is the boiling point of the

substance at that pressure.Supercritical substance

Phase DiagramsThe AD line is the interface between

liquid and solid.The melting point at each pressure can

be found along this line.

Phase DiagramsBelow A the substance cannot exist in

the liquid state.Along the AC line the solid and gas

phases are in equilibrium; the sublimation point at each pressure is along this line.

Phase Diagram of Water

Note the high critical temperature and critical pressure:These are due to the

strong van der Waals forces between water molecules.

Phase Diagram of Water

The slope of the solid–liquid line is negative.This means that as the

pressure is increased at a temperature just below the melting point, water goes from a solid to a liquid.

Phase Diagram of Carbon Dioxide

Carbon dioxide cannot exist in the liquid state at pressures below 5.11 atm; CO2 sublimes at normal pressures.

The low critical temperature and critical pressure for CO2 make supercritical CO2 a good solvent for extracting nonpolar substances (such as caffeine).

Page 513: 83, 85.

Homework