MCAT

• When analysing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• The Wealth of Nations was written

  1776
• Rational


  (in classical economic theory) economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Workers act rationally by


  Balancing welfare at work with consideration of both pay and benefits
• Governments act rationally by


  Placing the interests of the people they serve first in order to maximise their welfare
• Groups assumed to act rationally


  • Consumers
  • Producers
  • Workers
  • Governments
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• A firm increases advertising

  Demand curve shifts right
• Demand curve shifting right

  Increases the equilibrium price and quantity
• Marginal utility


  The additional utility (satisfaction) gained from the consumption of an additional product
• If you add up marginal utility for each unit you get total utility
• Order Reaction


  • Zeroth order
  • First order
  • Second order
• [A]


  Concentration of reactant A
• ln [A]


  Natural logarithm of the concentration of reactant A
• 1/[A]


  Reciprocal of the concentration of reactant A
• m


  Order of the reaction
• Rate Law


  Equation that describes the relationship between the rate of a reaction and the concentrations of the reactants
• Integrated Rate Law


  Equation that describes the relationship between the concentration of a reactant and time for a given reaction order
• Half Life


  Time required for the concentration of a reactant to decrease to half of its initial value
• Units of Rate


  Units used to express the rate of a reaction
• Constant


  Value that determines the rate of a reaction
• Zeroth order reaction


  1. R = k

  2. [A] = [A]0 - kt

  3. t1/2 = [A]0/2k
• First order reaction


  1. R = k[A]

  2. [A] = [A]0 * e^(-kt)

  3. t1/2 = ln(2)/k
• Second order reaction


  1. R = k[A]^2

  2. [A] = 1/(1/[A]0 + kt)

  3. t1/2 = 1/k[A]0
• At low substrate concentrations, the reaction is approximately first-order
• At very high substrate concentration, the reaction approximates zero-order since the reaction ceases to depend on substrate concentration
• Equivalence point


  When equivalent amounts of acid and base have reacted
• pH at equivalence point

  • Strong acid + strong base, pH = 7
  • Weak acid + strong base, pH > 7
  • Weak base + strong acid, pH < 7
  • Weak acid + weak base, pH > or < 7 depending on the relative strength of the acid and base
• Indicators


  Weak acids or bases that display different colors in the protonated and deprotonated forms. The indicator's pKa should be close the pH of the equivalence point.
• Indicators


  • Litmus: Acid = red; Base = blue; Neutral = purple
  • Phenolphthalein: pH < 8.2 = colorless; pH > 8.2 = purple
  • Methyl Orange: pH < 3.1 = red; pH > 4.4 = yellow
  • Bromophenol Blue: pH < 6 = yellow; pH > 8 = blue
• Endpoint


  When indicator reaches full color
• Polyvalent acid/base titrations


  • Multiple buffering regions and equivalence points
• Buffer


  • Weak acid + conjugate salt
  • Weak base + conjugate salt
• Buffering capacity


  The ability of a buffer to resist changes in pH. Maximum buffering capacity is within 1 pH point of the pKa.
• When [A-] = [HA] at the half equivalence point, log(1) = 0, so pH = pKa
• Burette, conical flask, titrant (strong acid), analyte/titrand (weak base) are used in a titration setup
• At the midpoint, pOH = pKb
• Oxidation number rules


  • Any free element or diatomic species = 0
  • Monatomic ion = the charge of the ion
  • Group 1A metals = +1 in compounds, group 2A metals = +2 in compounds
  • Group 7A elements = -1 in compounds, unless combined with a more electronegative element
  • H = +1 unless paired with a less electronegative element, then = -1
  • O = -2 except in peroxides (-1) or compounds with more electronegative elements
• The sum of all oxidation numbers in a compound must equal the overall charge