Chemistry 12

Reaction rate is the change in concentration of a reactant or product per unit time: $\text{rate} = \dfrac{\Delta[\text{X}]}{\Delta t}$, and it applies to both homogeneous (one phase) and heterogeneous (multiple phases) reactions.

A potential-energy diagram plots energy along the reaction path: reactants rise to an activated-complex peak (activation energy, $E_a$) before falling to products, tying together potential energy (PE), kinetic energy (KE), and enthalpy (H).

A catalyst provides an alternate reaction pathway with a LOWER activation energy, so a greater fraction of collisions succeed and the rate increases; it is not consumed overall (it's regenerated at the end) and does NOT change $\Delta H$, the reactants, or the products.

Rate increases with higher concentration, higher temperature, greater surface area (for solids), and the presence of a catalyst — these are the levers used to CONTROL reaction rate industrially and in the lab.

$\Delta H$ is the difference between product and reactant energy levels — negative for exothermic, positive for endothermic — while $E_a$ is the height of the climb from reactants to the peak; a catalyst lowers $E_a$ without changing $\Delta H$.

At equilibrium, the forward and reverse reactions are both still happening, but at EQUAL rates — so concentrations of reactants and products stop changing (they reach a plateau, not zero reaction). This reversible nature connects directly to the reaction's potential-energy diagram (the reverse reaction climbs the same hill from the other side).

Le Châtelier's principle: if a system at equilibrium is disturbed — a change in the concentration of reactants/products, in enthalpy and entropy conditions, or the presence of a catalyst — the equilibrium shifts in the direction that partially counteracts the disturbance.

For $a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}$ (homogeneous or heterogeneous), the equilibrium-law expression is $K_{eq}$$= \dfrac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$, using lowest whole-number coefficients and omitting pure solids and liquids.

Equilibrium requires a closed system (nothing escapes or enters) and constant macroscopic properties (colour, concentration, pressure) even though particles keep reacting on the microscopic level.

Real applications show the principle at work: the Haber process shifts conditions to favour ammonia production, and hemoglobin binding oxygen in the blood shifts based on local oxygen concentration.

A saturated solution is a solid ionic compound in dynamic equilibrium with its dissolved ions: $\text{AgCl}_{(s)} \rightleftharpoons \text{Ag}^+_{(aq)} + \text{Cl}^-_{(aq)}$.

The solubility product constant $K_{sp}$ is a specialized $K_{eq}$ expression for this dissolving equilibrium — for the example above, $K_{sp}$$= [\text{Ag}^+][\text{Cl}^-]$, with the solid omitted just like any pure solid in a $K_{eq}$ expression.

$K_{sp}$ can be calculated from molar solubility data (using an ICE-style setup), and the reverse: given $K_{sp}$, you can calculate the molar solubility or the maximum allowable concentration of an ion before precipitation begins.

Comparing the ion product ($Q_{sp}$, calculated the same way as $K_{sp}$ but with the CURRENT concentrations) to $K_{sp}$ predicts behaviour: $Q_{sp} > K_{sp}$ means a precipitate forms; $Q_{sp} < K_{sp}$ means the solution stays unsaturated (no precipitate).

A strong acid or base ionizes essentially completely (100%) in water (e.g. $\text{HCl}$, $\text{NaOH}$); a weak acid or base ionizes only partially, establishing an equilibrium (e.g. $\text{CH}_3\text{COOH}$, $\text{NH}_3$) — this difference shows up as HIGHER electrical conductivity for strong acids/bases at equal concentration, and is ranked on a table of relative acid strength.

Water self-ionizes: $2\text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^-$, an equilibrium like any other, defined by its own equilibrium constant $K_w$$= [\text{H}_3\text{O}^+][\text{OH}^-]$.

A weak acid or weak base only PARTIALLY ionizes in water, establishing a true equilibrium: $\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$ — distinct from a strong acid/base, which dissociates essentially completely (no equilibrium arrow needed).

Titration adds a solution of known concentration (the titrant) to a solution of unknown concentration, drop by drop, until the equivalence point (moles of acid = moles of base, adjusted for stoichiometry) is reached.

A salt's ions can react with water (hydrolysis): the conjugate base of a weak acid makes a solution basic (e.g. $\text{CH}_3\text{COO}^-$ from sodium acetate); the conjugate acid of a weak base makes a solution acidic (e.g. $\text{NH}_4^+$ from ammonium chloride); a salt from a strong acid and strong base (e.g. $\text{NaCl}$) is neutral, since neither ion hydrolyzes.

Oxidation numbers are assigned using a consistent set of rules (elements = 0, monatomic ions = their charge, oxygen usually -2, hydrogen usually +1, etc.), and the sum of oxidation numbers in a neutral compound is 0 (or equals the charge for an ion).

In a voltaic cell, oxidation occurs at the anode and reduction at the cathode ("An Ox, Red Cat"); the salt bridge carries IONS (not electrons) to keep both half-cells electrically neutral, while electrons flow through the external wire.

An electrolytic cell uses an external power supply to force a NON-spontaneous redox reaction to occur, applying at least the minimum voltage needed to drive the half-reactions — the power supply pushes electrons against their natural direction.

$E^0_{\text{cell}}$$= E^0_{\text{cathode}} - E^0_{\text{anode}}$, where BOTH values are read straight off the standard-reduction-potential table as written (for reduction) — you do NOT flip the sign of the anode's tabulated value; the subtraction already accounts for the reversal.

An INCREASE in oxidation number means that species was oxidized (lost electrons); a DECREASE means it was reduced (gained electrons) — comparing oxidation numbers before and after a reaction reveals what's oxidized and reduced even when it isn't obvious from the formulas alone.

In a multi-step calculation (like an ICE table or a log/antilog pH calculation), carry extra guard digits through the INTERMEDIATE steps and only round to the correct number of significant figures at the FINAL answer — rounding too early compounds error.

For a log-based value like pH, the number of decimal places in the answer equals the number of significant figures in the original concentration (since the digits before the decimal point in a log just represent the power of 10, not a measured quantity).

Every measured value carries some uncertainty (from the instrument or technique); when that value is used in a multi-step calculation, its uncertainty propagates forward and can grow, especially through multiplication, division, or exponents (like the squared/cubed terms in a $K_{eq}$ or $K_{sp}$ expression).

Reporting a derived value like $K_{eq}$, $K_{sp}$, $K_a$, or $E^0$ in proper scientific notation with the right number of significant figures reflects HOW confident you can actually be in that final number, given the uncertainty in the original measurements.