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  • solubility product constant (\(Ksp\))

    represents the dissolution of an ionic compound at equilibrium

  • solubility

    quantity of a compound that dissolves in a certain amount of liquid

  • molar solubility

    solubility in units of moles/liter

  • relationship between \(Ksp\) and molar solubility

    depends on the stoichiometry of the dissociation reaction

  • effect of a common ion on solubility

    a solution containing a common ion decreases solubility (relative to water), left shift of equilibrium

  • compounds containing basic anions

    more soluble in acidic water

  • precipitation reaction

    occurs when 2 solutions containing ionic compounds are mixed and one of their cross products is insoluble

  • reaction quotient Q (for a reaction involving the dissolution of an ionic compound)

    product of the concentrations of the ionic components raised to their stoichiometric coefficients (not at equilibrium)

  • if Q < \(Ksp\)

    more solid dissolves or the solution remains unsaturated

  • if Q = \(Ksp\)

    reaction is at equilibrium (saturated)

  • if Q > \(Ksp\)

    solid will precipitate out or the solution will become supersaturated

  • selective precipitation

    addition of a reagent that forms a precipitate with 1 of the cations but not the others (they must have different \(Ksp\) values)

  • transition metals

    good electron acceptors / lewis acids

  • complex ions

    central metal ion bound to 1+ ligand

  • ligand

    molecule/ion that donates an electron pair to the central metal ion

  • formation constant (\(K_{f}\))

    eq. constant associated with the formation reaction of a complex ion, determine using law of mass action

  • solubility of an ionic compound with a basic anion

    increases with increasing acidity

  • solubility of an ionic compound containing a metal cation that forms complex ions

    increases in the presence of a lewis base

  • equilibrium constant for a reaction that's the sum of 2 other reactions

    the product of the 2 reaction's eq. constants

  • amphoteric metal hydroxides

    insoluble in water, soluble in solutions with low or high pH

  • nature's heat tax

    energy is dissipated on every energy transaction

  • 2nd law of thermodynamics

    every spontaneous energy transaction requires the dispersal of energy

  • spontaneous process

    occurs without ongoing intervention/work

  • catalysts

    increase the rate of a spontaneous process

  • thermodynamics

    spontaneity, relative chemical potentials of reactants and products

  • S in [\(S=k\ln\left(W\right)\)]

    entropy: thermodynamic function that increases with the number of energetically equivalent ways to arrange the components of a system (to achieve a particular state)

  • k in [\(S=k\ln\left(W\right)\)]

    boltzmann constant: \(1.38\cdot10^{-23}\) J/K

  • W in [\(S=k\ln\left(W\right)\)]

    number of energetically equivalent ways to arrange the components of a system, number of possible microstates that can result in a given macrostate

  • macrostate

    defined by a given set of conditions, energy is constant with constant conditions

  • microstate

    exact internal energy distribution among the particles at any 1 instant (energy distribution is not constant)

  • state with the highest entropy

    greatest dispersal of energy, energy is more randomized and less concentrated

  • for any spontaneous proccess

    the entropy of the universe must increase

  • entropy determines

    the direction of chemical and physical change

  • a chemical system

    proceeds in the direction that leads to the largest value of W

  • entropy of matter (states)

    \(S_{solid}<S_{liquid}<S_{gas}\)

  • energy in a molecular solid (least ways to arrange particles)

    vibrations between molecules

  • energy in a molecular gas (most microstates)

    translational and rotational, straight-line motion and rotations of molecules

  • ΔS > 0

    • solid → liquid

    • solid → gas

    • liquid → gas

    • increase in moles of gas

  • \(q_{rev}\) in [\(\Delta S=q_{rev}\)/\(T\)]

    heat exchanged with the surroundings in a reversible process

  • S (J/K) in [Δ\(S=q_{rev}\)/\(T\)]

    measure of energy dispersal per unit temperature

  • reversible process (constant state of equilibrium and idealized conditions)

    reverses direction upon an infinitesimally small change in some property

  • entropy change of the universe

    \(S_{univ}=\Delta S_{sys}+\Delta S_{surr}\)

  • a process can be spontaneous when \(\Delta S_{sys}<0\) if

    \(\Delta S_{surr}>-\Delta S_{sys}\)

  • exothermic process

    increases the entropy of the surroundings

  • endothermic process

    decreases the entropy of the surroundings

  • greater surrounding temperature

    smaller entropy increase

  • \(\Delta S_{surr}\) (constant pressure and temp)

    \(=-\Delta H_{sys}\)/\(T\)

  • gibbs free energy equation

    \(G=H-TS\)

  • change in gibbs free energy (constant T and P)

    \(\Delta G=-T\Delta S\)

  • chemical potential

    chemical systems tend towards lower GFE

  • \(\Delta G<0\)

    spontaneous

  • \(\Delta G>0\)

    nonspontaneous

  • -ΔH, +ΔS

    spontaneous at all T

  • +ΔH, -ΔS

    nonspontaneous at all T

  • -ΔH, -ΔS

    spontaneous at low T only

  • +ΔH, +ΔS

    spontaneous at high T only

  • standard entropy change for a reaction (\(\Delta S_{rxn}^{^{o}}\))

    change in entropy for a process where all reactants and products are in their standard states

  • third law of thermodynamics

    the entropy of a perfect crystal at absolute 0 is 0

  • increased molar mass = increased entropy at 25 ºC (noble gas)

    the energy states associated with the motion of heavy atoms are more closely spaced than those of lighter atoms (more closely spaced energy states allow for greater dispersal of energy)

  • number of places to put energy within a substance depends on

    • substance state and molar mass

    • particular allotrope and molecular complexity

    • extent of dissociation

  • allotropes

    elements that exist in 2+ forms with different structures (different standard molar entropies)

  • the dissociation of a crystalline solid into solution

    increase in entropy (thermal energy in the crystal disperses throughout the solution)

  • determine standard change in free energy

    \(\Delta G^{^{o}}_{rxn}=\Delta H_{rxn}^{^{o}}-T\Delta S_{rxn}^{^{o}}\) (around 25 ºC)

  • free energy of formation: \(\Delta G^{^{o}}_{f}\)

    change in \(G^{^{o}}_{f}\) when 1 mole of a compound (standard state) forms from its constituent elements in their standard states

  • compounds with negative \(G^{^{o}}_{f}\)

    spontaneously form from their elements

  • change in free energy of a chemical reaction represents

    the max amount of energy available to do work

  • positive \(\Delta G^{^{o}}_{f}\)

    the minimum amount of energy required

  • all real reactions

    irreversible and do not achieve the theoretical limit of available free energy

  • predict spontaneity for nonstandard states

    \(\Delta G_{rxn}=\Delta G_{rxn}^{^{o}}+RT\ln Q\)

  • equilibrium conditions (\(\Delta G_{rxn}=\Delta G_{rxn}^{^{o}}+RT\ln Q\))

    \(RT\ln Q\) is equal but opposite in sign to \(\Delta G_{rxn}^{^{o}}\)

  • when \(Q=K\) and \(\Delta G_{rxn}=0\)

    \(\Delta G_{rxn}^{^{o}}=-RT\ln K\)

  • when \(K<1\)

    \(\ln K\) is negative and \(\Delta G_{rxn}^{^{o}}\) is positive

    spontaneous reaction in the reverse direction

  • when \(K>1\)

    \(\ln K\) is positive and \(\Delta G_{rxn}^{^{o}}\) is negative

    spontaneous reaction in the forward direction

  • how K depends on temp

    \(\ln K=-\Delta H_{rxn}^{^{o}}\)/\(R\)\(\left(\frac{1}{T}\right)\)\(+\Delta S_{rxn}^{^{o}}\)/\(R\)

  • driving force for lightning and batteries

    electrons flow away from negative charge and towards positive charge

  • oxidation

    loss of electrons

  • reduction

    gain of electrons

  • electrical current

    flow of electrons through wire or solution

  • voltaic cell

    electrochemical cell that produces electrical current from a spontaneous reaction

  • electrolytic cell

    electrochemical cell that consumes electrical current to drive a nonspontaneous reaction

  • the continuous flow of electrical current in a voltaic cell requires

    a pathway counterions can flow through to neutralize charge buildup

  • electrons flow towards the electrode

    with lower potential energy

  • charge difference between electrodes is due to

    differences in ionization tendencies

  • potential difference (V)

    measure of the difference in potential energy (J) per unit charge (C)

  • cell potential (\(E_{cell}\))

    emf difference between 2 electrodes in a voltaic cell

  • standard emf (\(E_{cell}^{^{o}}\))

    1 M concentration, 1 atm for gas, 25 ºC

  • anode (blue electrode)

    • oxidation occurs

    • more negatively charged

    • electrons flow away

    • positive ions form

  • cathode (red electrode)

    • reduction occurs

    • more positively charged

    • electrons flow towards

    • positive ions get reduced

  • salt bridge

    contains a strong electrolyte, causing a flow of ions that neutralize charge buildup

  • \(E_{cell}=E_{catode}^{^{o}}-E_{anode}^{^{o}}\)

    voltage difference between the final state (reduction) and the initial state (oxidation)

  • reduction tendency

    increases with increasing standard electrode potential (Eº)

  • oxidation tendency

    increases with decreasing standard electrode potential (Eº)

  • positively charged electrode

    greater tendency to undergo reduction

  • negatively charged electrode

    lower tendency to undergo reduction

  • Q in terms of partial pressures

    \(P_{prdct}\)/\(P_{rctnt}\)

  • \(+E_{cell}^{^{o}}\)

    spontaneous reaction

  • \(-E_{cell}^{^{o}}\)

    nonspontaneous reaction

  • half reactions at the top of the standard electrode potential table

    large positive standard electrode potentials, cathode for voltaic cells, good oxidizer

  • half reactions at the bottom of the standard electrode potential table

    large negative standard electrode potentials, anode for voltaic cells, good reducer

  • any reduction half reaction is spontaneous when paired with

    the reverse of a half reaction below it in the table

  • oxidizing agent

    causes the oxidation of another substance, gets reduced

  • reducing agent

    causes the reduction of another substance, gets oxidized

  • metals that dissolve in acid

    have reduction half reactions listed below the reduction of H⁺

  • spontaneous redox

    • \(-\Delta G^{^{o}}\)

    • \(+E_{cell}^{^{o}}\)

    • \(K>1\)

  • nonspontaneous redox

    • \(+\Delta G^{^{o}}\)

    • \(-E_{cell}^{^{o}}\)

    • \(K<1\)

  • faraday's constant (\(F\))

    the charge of 1 mole of electrons

  • nernst equation (\(E_{cell}^{^{o}}\) in volts)

    \(E_{cell}=E_{cell}^{^{o}}-\frac{0.0592}{n}\log_{}\left(Q\right)\)

  • Q < 1 (nernst equation)

    greater reactant molarity drives forward reaction

  • Q > 1 (nernst equation)

    greater product molarity drives backwards reaction

  • Q = K (equilibrium)

    \(E_{cell}=0\)

  • Q < K

    \(+E_{cell}\)

  • Q > K

    \(-E_{cell}\)

  • electrons spontaneously flow from the cell with the ___ ion concentration to the cell with the ___ ion concentration

    lower, higher

  • electrolysis (in an electrolytic cell)

    the process by which an electrical current is used to drive an otherwise nonspontaneous redox reaction

  • power source producing > 1.10 V in a voltaic cell

    forces electrons to flow in the opposite direction; reverses which half cell is the anode/cathode

  • in a voltaic cell

    (-) anode

    (+) cathode

  • in an electrolytic cell

    (+) anode

    (-) cathode

  • the cation that gets reduced first

    has the more positive electrode potential

  • the anode that gets oxidized first

    has the more negative electrode potential

  • cations of active metals can't be reduced in aqueous solutions by electrolysis because

    the water in the solution is reduced at a lower voltage

  • total charge depends on

    current magnitude and time current runs

  • corrosion

    the gradual oxidation of metals that are exposed to oxidizing agents in the environment