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What is a rate law?
Answer: An equation relating reaction rate to the concentrations of reactants, each raised to an experimentally determined power (order): rate = k[A]^m[B]^n.
k is the rate constant; m and n are NOT taken from stoichiometric coefficients — they must be found experimentally.
How is reaction order determined experimentally?
Answer: By the method of initial rates: compare how rate changes when one reactant's concentration is varied while others are held constant.
If doubling [A] quadruples rate, order in A is 2; if rate doubles, order is 1; if rate is unchanged, order is 0.
Zero-order reaction: rate law and units of k?
Answer: Rate = k; units of k are mol·L⁻¹·s⁻¹ (rate is independent of concentration).
First-order reaction: rate law, integrated form, and half-life?
Answer: Rate = k[A]; ln[A] = -kt + ln[A]₀; t₁/₂ = ln2/k. Half-life is constant, independent of concentration.
Units of k: s⁻¹.
What does [A] vs. time look like for a first-order reaction?
Answer: An exponential decay curve — concentration falls by half every constant time interval (t₁/₂).
Example: starting at 1.0 M with t1/2=1 s gives 0.5 M at t=1s, 0.25 M at t=2s, 0.125 M at t=3s.
Second-order reaction: rate law and units of k?
Answer: Rate = k[A]²; units of k are L·mol⁻¹·s⁻¹.
Integrated form: 1/[A] = kt + 1/[A]₀, giving a straight line when 1/[A] is plotted vs t.
What is the rate-determining step (RDS)?
Answer: The slowest elementary step in a multistep reaction mechanism; it controls the overall rate of reaction.
How do you write the overall rate law from a mechanism?
Answer: Use the rate law of the rate-determining step; if it contains an intermediate, substitute using a prior fast equilibrium step.
Example: if RDS is Step2: X + C → D and X is an intermediate from fast Step1 A+B⇌X, express [X] via the equilibrium constant of Step1.
What is activation energy (Ea)?
Answer: The minimum energy required for reactants to reach the transition state and form products.
Higher Ea means a slower reaction at a given temperature.
Identify this diagram: what does it show about catalysts?
Answer: A reaction-coordinate (energy) diagram comparing catalyzed vs. uncatalyzed pathways — the catalyst lowers the activation energy peak but ΔH (start/end energy) is unchanged.
Both curves start and end at the same energy levels; only the height of the peak (Ea) differs.
How do catalysts speed up reactions?
Answer: They provide an alternate mechanism with lower activation energy, without being consumed; they do not change ΔH or the equilibrium position.
Catalysts increase both forward and reverse rates equally, so K is unaffected.
Write the Arrhenius equation.
Answer: k = A·e^(−Ea/RT)
k = rate constant, A = frequency factor, Ea = activation energy, R = gas constant, T = temperature (K). Higher T or lower Ea increases k.
Define enthalpy of reaction (ΔH) and its sign conventions.
Answer: Heat absorbed or released at constant pressure. ΔH < 0 = exothermic (releases heat); ΔH > 0 = endothermic (absorbs heat).
Give the calorimetry equation and define each term.
Answer: q = mcΔT, where q = heat (J), m = mass (g), c = specific heat capacity (J/g·°C), ΔT = temperature change (°C).
Example: 50.0 g water (c=4.18 J/g°C) heated from 20°C to 30°C: q = 50.0×4.18×10 = 2090 J.
What is specific heat capacity?
Answer: The amount of heat required to raise the temperature of 1 gram of a substance by 1°C.
Water's high specific heat (4.18 J/g·°C) makes it resist temperature change.
State Hess's Law.
Answer: The total enthalpy change for a reaction is the same whether it occurs in one step or several steps; ΔH is a state function.
What rules apply when combining reactions by Hess's Law?
Answer: If a reaction is reversed, flip the sign of ΔH; if a reaction is multiplied by a factor, multiply ΔH by that same factor.
Add the adjusted ΔH values of all steps to get the overall ΔH.
What is standard enthalpy of formation (ΔH°f)?
Answer: The enthalpy change when 1 mole of a compound forms from its elements in their standard states; ΔH°f of an element in its standard state = 0.
Formula for ΔH°rxn using enthalpies of formation?
Answer: ΔH°rxn = Σ n·ΔH°f(products) − Σ n·ΔH°f(reactants)
n = stoichiometric coefficients. Example: for CH4+2O2→CO2+2H2O, sum products' ΔHf minus reactants' ΔHf (O2=0).
Define entropy (S).
Answer: A measure of the dispersal of energy/matter in a system, often described as the degree of disorder or number of microstates.
List the general sign rules for ΔS in a reaction.
Answer: ΔS > 0 when: gas moles increase, a solid/liquid becomes a gas, a solid dissolves, or particles/complexity increase (e.g., one molecule splits into more).
ΔS < 0 for the reverse trends (gas→liquid/solid, fewer moles of gas).
Formula for ΔS°rxn?
Answer: ΔS°rxn = Σ n·S°(products) − Σ n·S°(reactants)
Unlike ΔH°f, elements have nonzero standard molar entropy (S° ≠ 0).
Write the Gibbs free energy equation.
Answer: ΔG = ΔH − TΔS
ΔG = Gibbs free energy change, ΔH = enthalpy change, T = temperature (K), ΔS = entropy change.
How does the sign of ΔG indicate spontaneity?
Answer: ΔG < 0: spontaneous (forward, favored); ΔG > 0: nonspontaneous (reverse favored); ΔG = 0: system at equilibrium.
When is a reaction spontaneous at all temperatures vs. temperature-dependent?
Answer: ΔH<0,ΔS>0: always spontaneous. ΔH>0,ΔS<0: never spontaneous. ΔH<0,ΔS<0: spontaneous at low T. ΔH>0,ΔS>0: spontaneous at high T.
Determined by the sign of ΔG = ΔH − TΔS across temperatures.
How does ΔG° relate to the equilibrium constant K?
Answer: ΔG° = −RT ln K
R = 8.314 J/mol·K, T in Kelvin. Large K (products favored) gives a very negative ΔG°; K=1 gives ΔG°=0.
How does ΔG° relate to standard cell potential E°?
Answer: ΔG° = −nFE°
n = moles of electrons transferred, F = Faraday's constant (96,485 C/mol e⁻). Positive E° gives negative ΔG° (spontaneous).
How are K and E°cell linked (combining the two Gibbs relations)?
Answer: Setting −nFE° = −RT ln K gives E° = (RT/nF) ln K — a larger K corresponds to a larger (more positive) E°.
This connects thermodynamics (K), free energy (ΔG°), and electrochemistry (E°) into one consistent framework.
What is a galvanic (voltaic) cell?
Answer: An electrochemical cell that uses a spontaneous redox reaction (ΔG<0, E°>0) to generate electrical energy.
What is an electrolytic cell?
Answer: An electrochemical cell that uses an external electrical energy source to drive a nonspontaneous redox reaction (ΔG>0, E°<0).
Used in electroplating and electrolysis (e.g., decomposing water).
Compare electrode charge/sign in galvanic vs. electrolytic cells.
Answer: Galvanic: anode is negative, cathode is positive. Electrolytic: anode is positive, cathode is negative (power source reverses polarity).
In both cell types, oxidation always occurs at the anode and reduction always at the cathode.
Mnemonic for anode/cathode and oxidation/reduction?
Answer: "An Ox, Red Cat": Anode = Oxidation; Cathode = Reduction.
Electrons flow from anode to cathode through the external circuit.
Formula for standard cell potential E°cell?
Answer: E°cell = E°cathode − E°anode (using standard reduction potentials for both).
A positive E°cell indicates a spontaneous galvanic reaction.
Faraday's law: How many grams of Cu are deposited by 2.00 A of current for 965 s in electroplating (Cu²⁺ + 2e⁻ → Cu)?
Answer: ≈0.636 g Cu.
Charge q=It=2.00×965=1930 C. Moles e⁻=1930/96485=0.0200 mol. Moles Cu=0.0200/2=0.0100 mol. Mass=0.0100×63.5 g/mol=0.635 g.
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