# Chem

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### Gas Laws

• gas laws are equations relating Volume, moles, temperature and pressure of gases
• `V = f(n,T,P)`
• Ideal gas law states `PV = nRT`, R is a gas constant, which can be expressed in many combinations of units
• pressure is force per area, the collision of gas against a wall of a container
• measured in Newtons per m^2 (Pascal)
• Boyle's Law is the relationship between pressure and volume for fixed amount of gas ( constant `nRT`)
• Law of Charles
• absolute temperature (Kelvin) is used for gas relationships

### Dalton's Law

• different types of gases in a mixture act independently from each other
• this introduces partial pressures, each gas has it's own mol value and pressure value for constant V and T
• partial pressures are additive, the pressure exerted on a container by the gas independently
• partial pressure can be used for molar fractions (what percentage of the mixture does the given gas make up for?)

### Kinetic Theory of Gases

• a model for gas behaviour, provides theoretical justification for ideal gas law
• states a gas is composed of lots of particles in constant, random motion
• gas is mostly empty space
• molecules collide with others or walls
• no intermolecular forces, other than collisions
• molecules gain or lose energy during elastic collisions, but net energy remains constant
• translational kinetic energy: `ek = (1/2)• m • u^2` (`u` is velocity)
• frequency of collision: `f ∝ u • (N / V)`
• momentum transfer to wall: `µ ∝ m • u`
• Gas pressure: `P ∝ µ • f ∝ (m•u)•u•(N/V) ∝ mu^2•(N/V)`
• then, assuming all molecules have the same speed, we can approximate: `P = (1/3)mu^2(N/V)`, where u is the rms speed

### Liquids and Solutions

• phase is a region of uniform properties
• at phase equilibrium there is no net conversion from one phase to another
• vapour pressure is the pressure at phase equilibrium, independent of the size of the system and correlative with temp/boiling point
• h2o forms partial dipoles and water forms tetrahedral shapes of 5 molecules, O is partial negative
• vapour pressure
• Antoine's equation for Pvap: `log Pvap = A - B/(C+T)`, where A, B, C are constants; properties of a substance
• heat is necessary to accomplish phase transition
• the heat is measured at constant pressure called enthalpy
• Clausius-Clapeyron equation for Pvap is correlation between Pvap to tempurature
• `ln(Pvap2/Pvap1) = delta Hvap/R • (1/T1 - 1/T2)`
• phase diagrams graph Pressure vs. Temperature, showing the state of a compound for a given temp and pressure

### Henry's Law

Ideal solutions are ones where solvent and solute do not interact with each other

Henry's law applies to gas-liquid solutions

• relates partial pressure of gas (solute) to its molar fraction in the liquid (solvent):
• `Pi = ki•xi`, ki is Henry's law constant, and depends on solute,solvent,temp
• important for calculating solubility, `xi`

### Ideal Solutions and Raoult's Law

Relates partial pressure of a gas to its vapour pressure in liquid/liquid and liquid/solid solutions: `Pi = xi•Pvap,i`

• a solution of dissolved non-volatile solute (sugar) in water is an ideal solution, obeys Raoult's Law and Henry's Law
• 4 colligative properties:
• vapour pressure lowering
• boiling point elevation
• freezing point depression
• osmotic pressure

#### Vapour-pressure lowering

• Raoult's Law: P = Pliquid + Psolid = x1•Pvap,1 + x2•Pvap,2
• for non-volatile solids, Pvap,2 = 0
• P = Pliquid = x1 • Pvap,1
• since x1 < 1 (theres dissolved solid) and P < Pvap (by dalton's law of partial pressures) then vapour pressure lowering is calculated by:
• delta P1 = P - Pvap,1 = x1 • Pvap,1 - Pvap,1

#### Boiling Point Elevation

Normal boiling point of a pure liquid is the temp at which Pvap = 1atm

• according to Raoult's Law, vapour pressure of liquid/solid solution is less than that of the pure liquid
• temperature of the solution might be increased to make it boil
• `delta Tb = Kb•m`, m is the molality of the solution
• if a solution dissociates, the number of solute particles increases
• since colligative properties depend on number of dissolved particles, the equation adjusts
• the required change is hte insertion of `i`, the van't Hoff factor
• parameter `i` equals number of particles released into solution per formula unit of solute

#### Freezing Point Depression

`delta Tf = -i•Kf•m`, Kf depends only on solvent type

### Chemical Equilibrium

Dissociation to ions (including oxidation and reduction)

• Equilibrium Constant Kc = Π[products]/Π[reactants] where [] denotes conceptration in mol/L
• chemical equilibrium is when concentration of reactants and products remain constant
• dynamic process, forward rate = backwards rate
• for solving chemical equilibrium questions, try to find concentrations or partial pressures for the compounds in the equation, then get Kc and Kp

• Ksp is the solubility product constant, for solid ionic solute and a liquid solvent
• Ksp = [C]c • [D]d
• the solubility of a solid in a solvent in the concentration of the dissolved salt in a saturated solution for a given temperature

### Common Ion Effect

If NaCl dissociates in AgCl solution, then theres extra [Cl-]; Q = [Ag+][Cl-] > Ksp. So the extra [Cl-] ions precipitate to restore [Ag+][Cl-] to equilibrium Ksp.

### Electrochemistry

Oxidation state is related to the number of electrons that an atom gains or loses when combining with outher atoms

• O.S. is the number of valance electrons needed to make a complete valence
• break reaction into two half reactions
• acidic medium: add H+ to hydrogen-deficient side
• basic medium: add H2O to the hydrogen-deficient side and OH- to the other

### Galvanic Cell

Oxidation occurs at the anode, electrons flow from the anode, it shows negative charge

• reduction occurs at the cathode, electrons flow to the cathode, it shows positive charge
• salt bridge allows ions to diffuse from one side to the other

• cell dies if it reaches equilibrium, or if you run out of solid reactant
• they are not in the equilibrium equation

Faraday's Law says the mass of a given substance produced or consumed at an electrode is proportional to the quantity of electric charge passed through the cell

### Chemical Kinetics

Describe how fast a reaction takes place

• think change in concentration with respect to time
• for 2 SO2 + O2 -> 2 SO3, reaction rate r = - 1/2 d[SO2]/dt = -d[O2]/dt = 1/2 d[SO3]/dt
• r = -1/a d[A]/dt = k[A]n[B]m, r as a function of reactants aA + bB -> ------
• n and m are given, determined through experiment. n and m are the order of the reaction with respect to A and B

### Integrated Rate Law

Concentration is represented by linear functions f([A]) = -kt + [A0], with the following:

• 0 order, [A] vs time is linear, with slope -k
• 1st order, ln[A] vs time is linear, with slope -k
• 2nd order, 1/[A] vs time is linear, with slope -k

### Activation Energy

k = A * e^(-Ea/RT), where A and Ea are constants that depend on the reaction type

# Useful Examples

• 10-2 for relating phase pressures to temperatures
• 13-1 for raoult's law