chem midterm 3

state functions

properties for which only the initial and final values of the system are relevant

• most relevant: pressure, volume, moles, temperature

• internal energy, entropy, enthalpy, Gibbs free energy

Kinetic Molecular Theory

• Gas molecules are in rapid, random motion, and are separated by great atomic distances.

• liquid molecules are in contact with each other and move relative to one another

• solid molecules are in contact with each other and held in place by strong intermolecular forces

ideal gas law

PV = nRT

Kinetic Molecular Theory Assumptions

• particles are in constant motion

• fully elastic collisions (no IMFs)

• large distances between molecules

• speed of particles increases with increasing temperature and decreases with increasing size

Kinetic molecular theory flaws

• gas molecules DO have volume

• gas molecules can stick together through IMFs

  • explains why liquids and solids form

KMT relationships

• Temperature is proportional to kinetic energy

• E_k= ½ kT = ½ mv²

• k is the Boltzmann constant

Boltzmann constant (k)

• explains what happens when there is a collection of gas molecules traveling with varying velocities, depending on collisions with other particles

• average velocity can be found from ½ kT = ½ mv², but there will always be a distribution of velocities in a system of gases

effusion

the rate at which gas escapes through a pinhole into a vacuum

diffusion

the rate at which two gases mix; overall movement of matter in a system

Graham’s law

• the greater the temperature, the faster gases diffuse/effuse

• the greater the size, the slower gases diffuse/effuse

• rate_A/rate_B = sqrt (MW_B / MW_A)

• m₁e₁² = m₂e₂²

• m₁d₁² = m₂d₂²

Boyle’s Law

As volume increases, pressure decreases

• V is proportional to 1/P, when moles and temperature are constant

Charles’ Law

As temperature increases, collisions increase, so volume increases

• V is proportional to T, when moles and pressure are constant

Avogadro’s law

As the number of moles increases, volume increases

• V is proportional to n, when pressure and temperature are constant

combined gas law (charles + boyle)

P₁V₁/T₁n₁ = P₂V₂/T₂n₂

Gay-Lussac’s Law

P = kT → P₁/T₁ = P₂/T₂

Dalton’s Law of Partial Pressures

The total pressure of a vessel of gas is found as the simple addition of partial pressures for all different gases in the mixture

• P_total = ΣP_i

• Partial pressure of a gas = P_b = (X_b)(P_total)

• molar ratio = X_b = moles_b / total moles in mixture

Standard temperature and pressure (STP)

P = 1 atm

T = 273.15 K

Volume of 1 mol of gas at STP is 22.4L

Important unit conversions

molar weight: MW = mass (g)/mol

molarity: M = moles (n)/liters (V)

density: ρ = mass (g)/ Volume (L)

PV = nRT → PV = (g/MW)RT → MW = (gRT)/(PV)

M = n/V → M = nρ/g

ideal gas law constant (R)

fundamental constant that relates temperature to energy

• R = kN = 0.08206 (L*atm)/(mol*K)

• R = (Boltzmann constant)(Avogadro’s number)

Van der Waals equation

(P + n²a/V²)(V-nb) = nRT

• a correction factor fixes attractive forces

• b correction factor fixes gas volumes

• lower a and b correlate with more ideal gases

ideal gases

gases which completely follow KMT and PV = nRT

non-ideal gases

gases that are approximately ideal under certain conditions, but in the real world, are real/non-ideal gases

• PV ≠ nRT

• all gases are actually non-deal, because they are constantly forming instantaneous dipoles, so no collision is completely elastic

conditions to maintain ideal gas conditions

Goal: minimize collisions, and if they do occur, temperature is too hot for sticking to occur

• raise temperature of system

• increase volume of system

• reduce the amount of gas molecules

intramolecular forces

forces within the bonds of an individual molecule, keeps atoms together

• have extremely high bond energies (400-600kJ is common)

intermolecular forces (IMFs)

forces which hold individual molecules together/push them apart

• influence states of matter

• 1-5kJ bond energies

ion-ion bonds

considered both intra- and intermolecular forces because the crystal bond structure of salts makes it less distinct to differentiate where bonds occur in molecules

• typically ~250kJ bond energies

Van der Waals forces

only IMF that is guaranteed to exist in ALL molecules

dispersion forces

attractive forces between molecules and ions that arise due to instantaneous dipoles

• possible because electrons move randomly in molecules, so its possible, for a moment, for the molecule to be polarized and a partial charge forms

• increase as molecule size increases (more electrons, more imbalance)

• examples: Van der Waals, London dispersion

• ~1kJ/mole to break bonds

dipole-dipole interactions

attractive forces between molecules that arise from permanent dipoles

• hydrogen bonding is a special, much stronger variant of a dipole-dipole bond (~20kJ/mole to break bonds)

• ~10kJ/mole to break bonds

general amounts of energy to break bonds

dispersion: ~1 kJ/mole

dipole-dipole: ~10kJ/mole

• hydrogen bond: ~20kJ/mole

ion-dipole: ~100 kJ/mole

single charged ions/double bonds: 400 kJ/mole

doubly charged ions/double bonds: 600kJ/mole

triply charged ions/triple bond: 800kJ/mole

combustion reaction

reactions with O2 that release energy as heat and light, with CO2 and H2O as products

boiling point

• occurs when sufficient energy is imparted to a liquid to break the IMFs that hold molecules together in solution

• tiny pockets of vapor form, and when P_bubble > P_atm, boiling occurs

• increases with increasing IMF

viscosity

• resistance to flow

• property that prompts a molecule to hold onto the molecule “above it”

• increases with increasing IMF

capillary action

• tendency of a liquid to “climb” the walls of a capillary (thin tube)

• increases with increasing IMF

surface tension

• phenomenon that maintains surface interface between a liquid and a gas surrounding the liquid

• increases with increasing IMF

heat of vaporization (ΔH_vap)

the amount of energy required for a liquid to become a gas

• increases with increasing IMF

vapor pressure

pressure of the gas above a liquid in a closed container

• at a given temperature, there is sufficient energy for surface molecules to enter the gas phase

• stronger IMF = less vapor generated, smaller vapor pressure

• decreases with increasing IMF

evaporation

IMFs that hold surface molecules together are overcome by energy (heat), prompting molecules to enter gas phase

• decreases with increasing IMF

order of strength of IMFs

Van der waals < dipole-dipole < hydrogen bonds < ion-dipole < ionic bonding

ionic bonding

charge density (also used to rank lattice energy) applies in ranking melting point

metallic solids

• s- and d- block

• malleable, ductile, lustrous, electrically and thermally conducting, delocalized electrons

• bonds between left and left on periodic table

ionic solids

• bond between left and right of periodic table

• hard, rigid, brittle, high melting point, high boiling point, conductive if soluble in water

network solids

Boron, carbon, black phosphorus

• hard, rigid, brittle, very high melting points, insoluble in water

• non-metals on right

molecular solids

• formed by intermolecular interactions, often at lower temperatures; weak bonds

• ice, glucose, relatively low boiling/melting points, brittle if pure

• held together by IMFs and covalent bonds

covalent network solid

solids consisting of combined units that make up the overall molecule, formed into a large, repeating structure

• ex: wood