UCLA Chem 20B Felker Winter 2018

Gas

Anything that expands to occupy the space of its container

Ideal Gas Law

PV=nRT

Pressure x Volume = Number of Moles x Ideal Gas Constant x Temperature

Pressure

Caused by change in momentum that is caused by gas molecules bouncing off container walls

Force/Area

Hydrostatic Pressure

ρgh = Density (Rho, not "p") x Gravity x Height

Units for Pressure

Force/Length^2 or Energy/Volume

Pascals, Bars, Atmospheres, Torrs

Temperature

Proportionate to Kinetic Energy

Thermal Contact

state of two or more objects or substances in contact such that heat can flow from one to the other

0th Law of Thermal Dynamics

If object A is in thermal equilibrium with object B and object B is in thermal equilibrium with object C, then Object A is also in thermal equilibrium with object C

Triple Point Temperature

A temperature where something's (water's) solid, liquid, and gaseous states are all present

Units of Temperature

Kelvin, Celsius, Fahrenheight

Converting from Celsius to Kelvin

C = K - 273.15

Point Mass

Random Velocities, no interaction

How is an ideal gas different from a real gas?

Real gasses interact at a distance

Ideal gas constant

R ; in energy per (mol*temperature) or (pressure x volume)/(mol x temp)

8.314 j/mol x k

8.134 x 10^-2 bar x L/mol x k

8.21 x 10^-2 atm x L/ mol x k

Boyle's Law

P_1 x V_1 = P_2 x V_2

Pressure and volume are inversely proportional (when number of moles and temperature remain constant)

Pressure is proportionate to the #of collisions per time per are...so a smaller volume means there will be more collisions and a higher pressure

Charles Law

Volume is proportionate to temperature (when number of moles and pressure are constant)

Guy-Lussac's Law

Pressure is proportionate to temperature (when number of moles and volume are constant)

STP

Standard Temperature and Pressure (0 degrees celsius and 1 ATM)

Avogadro's Law

Volume is proportionate to number of moles (when temperature and pressure are constant)

Ideal volume

RT/P

24.790 Liter/mol (at STP)

SATP

Standard ambient temperature and pressure

25 degrees celsius and 1 bar

Mole Fraction

x sub i ; number of moles sub i / number of moles total

Dalton's Law

P sub i = (n sub i * RT)/V

Kinetic Theory of Gasses

"gases are made up of tiny particles in random, straight line motion. They move rapidly and continuously and make collisions with each other and the walls."

Boltzmann's Constant

R/Avogadro's Number

Root Mean Speed

V sub(rms) = sqrt(3RT/M)

or Square root of 3 *(Ideal Gas Constant x Temperature in Kelvin )/Molar Mass

Probability that a particle has speeds between v1 and v2

F = probability particle has some speed between v and v + dv

integral from v1 to v2 of f(v)dv

Maxwell-Boltzmann Speed Distribution

Sort of like a bell shaped curve

f(v) = 1/(pi/2 x KbT/M)^(3/2) x v^2((-mv^2)/2KbT)

Note that the first term is normalization

Boltzmann's Factor

-KE/KbT

negative kinetic energy over Boltzmann's constant times temperature

What happens to Maxwell-Boltzmann speed distribution as temperature increases

Max speed increases, peak (most probable speed) is lowered (fewer species) but faster (shifted rightwards)

This is equivalent to having mass decrease

Most Probable Speed from Maxwell-Boltzmann Speed Distribution

At the peak, or critical point.

Where f'(v) = 0

sqrt(2KbT/M)

Square root of 2 x Boltmann's Constant x Temperature / Molar Mass

Average speed of Maxwell-Boltzmann distribution

v-bar = sqrt(8KbT/Pi x m) or sqrt(8RT/pi x M)

Square root of 8 times Boltzmann's constant x temperature over pi x mass

or

square root of 8 times ideal gas constant times temperature over pi time molar mass

Ratio of most probable speed to average speed to root mean square speed

Vmp:V-bar:Vrms =

1 : 1.128 : 1.225

Effusion

df/dv

Rate gas will leave a hole (small hole like a pin hole)

The ratio of the numbers of molecules of the two species effusing

through the hole in a short time interval.

N = Number of Molecules.

M = Molar Mass

B is the heavier molecule (heavier than A)

Diffusion

How quickly a contaminant spreads when introduced

When is PV= nRT not true for real gasses?

When pressure increases

More pressure = more interactions

Energy-Distance Graph

Graph of V(r) where r = distance

Has repulsive wall, where it takes a lot of energy to make molecules get close together due to coulombic forces

Potential Well, where things are stable

Attractive Region; to the right of the potential well

Compression Factor

For ideal gasses, it equals one.

When z is not equal to one, the ideal gas law doesn't work

At intermediate pressures, attractive forces come into play, and z is less than 1 (collision speeds decrease = pressure decreases)

At high pressures, distance decreased and repulsive forces come into play; z is more than 1. (collision speeds increase = pressure increase)

Van der Waal's equation

An upgrade of the ideal gas law

V-nb is accessible volume, the total volume subtracted by the occupied space. As b increases, there is less space, more repulsion, and more pressure

a helps increase the attractive force and decrease the pressure

Volume of Typical Gas

25 Liters per Mol

To find volume when given density and molar mass

Molar Volume = Density/Molar Mass

Typical distance between gas molecules

34 angstroms

Typical distance between liquid molecules

3 angstroms

Distance between neighbors for gas, liquid, and solid

Most distance in gas, appreciable distance in a liquid, and little distance in solid

Compression

Fractional decrease in volume

per unit increase in pressure. Temperature is constant

k = kappa

k = [delta(v)/delta(k)]_t x (-1/V)

in an ideal gas it is 1/P

in a solid it is hard to compress

Thermal Expansion

Fractional increase in the

volume of a substance per degree increase in temperature. Pressure is constant

alpha = [delta(v)/delta(t)]_p x (1/V)

In an ideal gas it is 1/t

Fluidity

The ability of a substance to flow...opposite of rigidity

Rigidity

The physical property of being stiff and resisting bending...opposite of fluidity

Diffusion

Movement of molecules from an area of higher concentration to an area of lower concentration.

Easier in gasses than in liquids. Easier in liquids than in solids.

Surface Tension

Amount of energy required to increase surface area.

To increase surface area, bulk molecules (not in surface) need to go to surface, meaning that bonds will break

Inter vs Intra Molecular forces

Inter = different molecules

Intra = between nuclei within a molecule

Intermolecular forces are weaker and longer range than intramolecular forces. Direction in intermolecular forces are less relevant

Ion-Ion Force

Strong, non-directional, coulumbic interaction.

Happens in both intra and inter molecular contexts

Scales to 1/R (very long range)

Dipole-Ion Force

A neutral molecule (permanent dipole) interacts with a charged molecule.

Strong and directional interaction

Range is 1/R^2 (long range, falls off more rapidly than ion-ion)

Dipole-Dipole Force

Dominant force between polar molecules.

In a dipole, there is a negative and positive part. Sometimes they align and stuff.

Weak, directional, almost always attractive, and short range interactions

Range is 1/R^3

Induced Dipole Force

Approaching charged atoms/molecules can induce a dipole upon a neutral atom

In the pic the blue thing is an Argon

Range is 1/R^4

Weak, directional, attractive, and short range

Polarizability

Electrons respond to electric field.

Scales with number of electrons (more electrons = more polarizeable)

Applies to both atoms and molecules

Dipole Induced Dipole Force

A dipole induces another dipole.

A dipole (like HF) induces a dipole upon a neutral atom.

Range is 1/R^5

Weak, directional, attractive, and short range

London Dispersion Forces (aka van der Waals forces)

Happens momentarily/spontaneously and is very weak. Has a very short range and is directional

A temporary dipole is created when there is a mismatch of electrons

Should be able to happen to anything with electrons, even noble gasses

Range is 1/R^6

Exchange Repulsive Force

Short range and always repulsive.

Originates from Pauli Exclusion principle.

When electrons get too close...they are not supposed to have the same position/spin and stuff

Range is 1/R^16

Boiling

When a liquid escapes to the gas phase.

It needs more energy to break bonds

More attractive interactions/forces = higher boiling point aka harder to boil

Order of intermolecular forces

Ionic > Hydrogen bonding > dipole dipole > Van der Waals dispersion forces

Hydrogen Bond

A dipole-dipole force on steroids, when hydrogen bonds with an extremely electronegative element (F, N, O)

Very strong...

Positive part of a dipole gets close and comfy with a negative part

Phase

One of the three forms--solid, liquid, or gas--which every substance is capable of attaining;

A sample of matter that is uniform throughout, both in its chemical constitution and in its physical state

Vapor Pressure

(P_vap) The pressure of the vapor coexisting with

a confined liquid or solid at any specified temperature.

This is a function of temperature

Achieving Phase Equilibrium (Liquid and Gas)

If we add a liquid into an empty flask (vacuum), eventually both a liquid and a gas will be present. This is because liquid some molecules at the surface will have enough energy to break off, or evaporate.

Once there are gasses in the system, some of them will crash into the surface of the liquid and lose its energy, or condense.

Equilibrium is reached when the rate of evaporation is equal to the rate of condensation

Phase Change (Volume-Temperature Chart @ Constant Pressure)

As temperature decreases, molecules go from a gaseous to a liquid, and to a solid phase.

During the phase changes, the volume will change but the temperature will change. At this time, the two phases will be in equilibrium and coexist.

Volume - Temperature Phase Change Chart for Water

Water expands as it freezes, so after transitioning from water to ice, the volume will increase

Pressure-Volume Phase Change graph (@constant temperature)

We are squeezing a sample and watching as pressure builds up.

We can observe that the flat lines are where the gas and liquid phases are in equilibrium. This is associated with the Vapor Pressure at the temperature.

If we had a higher constant temperature, the vapor pressure will increase

Pressure-Temperature Phase Diagram

Shows areas where the temperature and pressure combination will incur a solid, liquid, or gas phase.

The boundary lines are where two phases are present.

The triple point is a unique pressure and temperature where three phases coexist.

The critical point is where the distinction between liquid and gas cannot be made.

Note that it is possible to go around the critical point to seamlessly transition from gas to liquid (or vise-versa) without having both phases present at the same time

Pressure-Temperature Phase Diagram for Water and other Anamolous Molecules

Notice that the equilibrium line between the solid and gas phase curves slightly to the left, which means that the melting point will DECREASE as the pressure increases

Solution

A homogeneous (like, evenly distributes) mixture of two or more substances

Concentration

Basically how much of a solvent is in a solution

Molarity

It is the moles of solute over the volume of solution. Units are mol/liter

Molality

It is the moles of solute over the mass of the solvent (a bit more accurate than using volume because unlike mass, volume changes with temperature)

Binary Solution

Has one solute and one solvent

To go from a pure solute to a dissolved solute...

Solute-Solute bonds have to break

Solute-Solvent bonds are formed

Since there is more disorder in a solution than the independent solute/solvent, nature...likes it

Nonelectrolyte

Substance that does not ionize in water and cannot conduct electricity (ex: acetone)

Undergoes intact solvation; solute species don't have any bonds broken.

Strong Electrolyte

A substance that completely dissociates into ions when dissolved into water (ex: NaCl breaks up to Na+ and Cl-)

Weak Electrolyte

A substance that partially dissociates into ions when dissolved into water (ex: Acetic Acid --> gives up a H+ to the water)

Solution Stoichiometry

Basically a load of balancing equations, finding moles, volume, etc...

Pro tip: always convert to number of mols to make life easier.

Titration

A solution of known concentration is used to determine the concentration of another solution.

End Point Indicator

A physical property that tells us that all of a reactant got consumed (ex: dye changes color)

Acid-Base Titration

A titration process where one solution is a base and another is an acid.

Requirements of acid-base titration

Strong acid and strong base

or

Strong acid and weak base

or

Weak acid and strong base

Strong Acid and Weak Base

A strong acid and a weak base will create an acidic solution. Some base will be left over because the acid will completely react. Will basically create a weak acid

The reaction goes to completion

Strong Acid and Strong Base

Will neutralize each other and create water

Weak Acid and Strong Base

A weak acid and a strong base will create a basic solution. Some acid will be left over because the base will completely react. Will basically create a weak base

The reaction goes to completion

Weak Acid and Weak Base

The reaction will not go to completion because neither the base nor the acid will completely react.

Please don't titrate with this

pH

The negative of the logarithm to base 10 of the concentration of hydrogen ions, measured in moles per liter; a measure of acidity or alkalinity of a substance, which takes numerical values from 0 (maximum acidity) through 7 (neutral) to 14 (maximum alkalinity).

Oxidation-Reduction (Redox) Titrations

electrons are transferred between reacting species as they combine to form products.

Reduced species gains electrons

Oxidized Species gives up electrons

Steps to Balance Redox Equations

1. Write two unbalanced half equations (one for the reduced and one for the oxidized)

2. Insert coefficients to balance all elements except for O and H

3. Balance oxygen by adding H2O to one side of each half-equation.

4. Balance hydrogens by adding H2O to one side and H3O+ (for acidic solutions) or OH- (for basic solutions to the other

5. Balance charges of equations by adding electrons

6. Multiply equations to balance electrons then add them together

Oxidation Number

a number assigned to an element in chemical combination that represents the number of electrons lost (or gained, if the number is negative) by an atom of that element in the compound.

Colligative properties

The properties of a liquid that may be altered by the presence of a solute:

vapor pressure lowering

boiling point elevation

freezing point depression

osmotic pressure

Raoult's Law

the vapor pressure of a solution is directly proportional to the mole fraction of solvent present

Psolution = Xsolvent x Psolvent

Vapor Pressure Lowering

The lowering of vapor pressure of a solvent by the addition of a nonvolatile solute to the solvent.

Note that adding more nonvolatile solution will always lower the vapor pressure

Boiling Point Elevation

The temperature difference between a solution's boiling point and a pure solvent's boiling point

Change in Tb = Kb x m

Note that Kb is a constant, and is not Boltzmann's constant. The little m is molality, measured in mol/kg

Freezing Point Depression

The difference in temperature from the freezing point of a solution (solute added to solvent) and the freezing point of the pure solvent

Change in Tf = -Kf x m

Kf is a constant that depends on the solvent and m is the total molality

Osmotic Pressure

the external pressure that must be applied to stop osmosis

Osmosis

Diffusion of a solvent through a selectively permeable membrane

Henry's Law

direct relationship between pressure and solubility

S1/P1 = S2/P2

Bascially the pressure of molecule 2 is the ratio of the vapor pressures of molecule 2 and 1 (k) multiplied by the mole fraction of molecule 2 (moles of 2 over total moles)