Titrations, Solubility, and Thermodynamics Lecture Review

Comprehensive practice flashcards covering titration concepts, Ksp and solubility, and the laws of thermodynamics based on lecture materials.

Equivalence point (titration)

The point where moles of acid added exactly equal moles of base (stoichiometric neutralization); calculated from stoichiometry, not observed directly.

Endpoint (titration)

The point where the indicator visibly changes color; meant to approximate the equivalence point but is not always identical to it.

Strong acid + strong base equivalence pH

$pH = 7.00$; the salt formed has no acid or base properties.

Weak acid + strong base equivalence pH

$pH > 7$ (basic); all $HA$ has converted to $A^{-}$, which hydrolyzes water as a weak base using $Kb = \\frac{Kw}{Ka}$.

Strong acid + weak base equivalence pH

$pH < 7$ (acidic); all $B$ has converted to $BH^{+}$, which hydrolyzes water as a weak acid using $Ka = \\frac{Kw}{Kb}$.

Half-equivalence point

The volume of titrant where exactly half the original acid (or base) has reacted, so $[HA] = [A^{-}]$; at this point $pH = pKa$.

Henderson-Hasselbalch equation

$pH=pKa+log([A^{-}]/[HA])$ , where of the weak acid, $[A^{-}]$ = concentration (or moles) of conjugate base, and $[HA]$ = concentration (or moles) of remaining weak acid.

Buffer region of a titration curve

The region before equivalence (excluding half-equivalence) where both $HA$ and $A^{-}$ are present in solution; solved with Henderson-Hasselbalch using the current mole ratio.

Past the equivalence point (pH behavior)

pH is controlled entirely by the concentration of leftover EXCESS strong titrant; the weak acid/base component is ignored.

Indicator selection rule

Choose an indicator whose color-change ($pKin$) range is close to the pH AT THE EQUIVALENCE POINT — not close to the $pKa$ of the acid being titrated.

Polyprotic acid titration curve

Has one equivalence point AND one half-equivalence point for each ionizable proton; multiple pH jumps appear on the curve.

pKa trend for successive protons of a polyprotic acid

$pKa$ increases with each proton removed ($Ka$ decreases) because removing $H^{+}$ from an increasingly negative species is increasingly unfavorable.

Back-calculating molar mass from titration data

$MM \\, (g/mol) = \\text{mass of unknown acid (g)} \\div \\text{moles of unknown acid}$ ; moles are found using titrant volume and stoichiometry.

Effect of dilution on % ionization of a weak acid

Increases; diluting shifts the ionization equilibrium toward more particles according to Le Chatelier.

Effect of dilution on pH of a weak acid

Increases (moves toward neutral, $pH \\, 7$) because lower concentration means lower $[H_3O^{+}]$ produced.

Effect of dilution on volume of base needed at equivalence

Unchanged; total moles of weak acid present are unaffected by dilution, only its concentration changes.

Common ion effect

When two sources produce the same species involved in an equilibrium, the added common ion suppresses further ionization from the other source (Le Chatelier).

Buffer response to added strong acid

The conjugate BASE component neutralizes it: $A^{-}+H_3O_{}^{+}\rightarrow HA+H_2O$ .

Buffer response to added strong base

The conjugate ACID component neutralizes it: $HA+OH^{-}\rightarrow A^{-}+H_2O$ .

Ka & Kb for a conjugate acid-base pair

Equals $Kw = 1.00 \\times 10^{-14}$ at $25\\,^{\\circ}C$; only valid for a true conjugate pair like $NH_4^{+}$ and $NH_3$.

pKa + pKb for a conjugate acid-base pair

Equals 14.00 at 25 °C.

Best buffer choice rule

Choose the weak acid (or base) whose $pKa$ (or $pKb$-derived $pKa$ of conjugate acid) is closest to the target buffer pH.

Conjugate of a strong acid

Has essentially no base properties in water (won't reform the acid); examples include $Cl^{-}$, $Br^{-}$, $I^{-}$, $NO_3^{-}$, and $ClO_4^{-}$.

Conjugate of a strong base

Has essentially no acid properties in water; examples include $Na^{+}$, $K^{+}$, $Li^{+}$, and $Ca^{2+}$.

Conjugate of a weak acid

Is itself a weak base; examples include $F^{-}$, $CN^{-}$, and $C_2H_3O_2^{-}$.

Conjugate of a weak base

Is itself a weak acid; example: $NH_4^{+}$.

HSO4− special case

Conjugate of the strong acid $H_2SO_4$ (so it has no base properties), but $HSO_4^{-}$ itself behaves as a weak acid via its own $Ka2$.

Salt hydrolysis

The reaction of a dissolved ion with water, acting as a weak acid or weak base, producing $H_3O^{+}$ or $OH^{-}$ and shifting solution pH away from neutral.

Cation from a weak base (in a salt)

Acts as a weak acid in water, lowering pH; example: $NH_4^{+}$ from $NH_4Cl$.

Anion from a weak acid (in a salt)

Acts as a weak base in water, raising pH; examples: $F^{-}$, $CN^{-}$, $C_2H_3O_2^{-}$.

Leveling effect

The strongest possible acid (or base) in a given solvent is the conjugate acid (or base) of that solvent itself; any stronger species reacts completely with the solvent.

Higher Ka ↔ pKa relationship

Higher $Ka$ corresponds to lower (less negative-exponent, numerically lower) $pKa$ and a stronger acid.

Net ionic equation

Shows only the species that actually react (e.g. ions forming a precipitate); spectator ions are omitted from the equation.

Rank of Bronsted base strength example logic

Compare conjugate acid strength: the weaker the conjugate acid, the stronger the base (e.g. $OH^{-} > F^{-} > H_2O >> Cl^{-}$, since $Cl^{-}$ is conjugate of strong acid $HCl$).

Ksp (solubility product constant)

Equilibrium constant for the dissolution of a slightly soluble ionic solid into its ions; $Ksp = [cation]^{a} [anion]^{b}$.

Ksp ICE table shortcut

The subscripts in the compound's chemical formula become BOTH the exponents in the Ksp expression AND the coefficients multiplying $x$ for each ion at equilibrium.

Molar solubility

The number of moles of a compound that dissolve per liter of solution before the solution becomes saturated (units $mol/L$).

Converting molar solubility to g/L

Multiply molar solubility ($mol/L$) by the compound's molar mass ($g/mol$).

Ksp direct comparison rule

Ksp values can only be used to directly rank molar solubility between compounds if they produce the SAME total number of ions in the SAME ratio.

Common ion effect on Ksp/solubility

Adding a common ion from another source DECREASES the molar solubility of a salt because it shifts the Ksp equilibrium left.

Buffered-pH Ksp problems

$[H^{+}]$ or $[OH^{-}]$ is FIXED EXTERNALLY by the buffer; plug the fixed $[H^{+}]$ or $[OH^{-}]$ value directly into the Ksp expression.

Selective precipitation

When multiple cations (or anions) could each precipitate with a common added counter-ion, the salt with the LOWEST Ksp reaches saturation and precipitates FIRST.

Maximum concentration of an added ion before a second precipitate forms

The concentration of the added ion at which the SECOND-least-soluble salt just reaches its own Ksp and begins to precipitate.

Minimum pH for hydroxide precipitation

The pH at which $[OH^{-}]$ first reaches the value required to satisfy Ksp for a given metal hydroxide.

Effect of acidity on solubility of a salt with a basic anion

Increasing acidity (lowering pH) INCREASES solubility because $H^{+}$ reacts with and removes the basic anion.

Kf (formation constant)

Equilibrium constant for the formation of a complex ion via the stepwise addition of ligands to a central metal cation.

Combining stepwise Kf values into an overall Kf

If the target (overall) reaction is the sum of given stepwise reactions, MULTIPLY the individual stepwise Kf values together.

Complex ion ICE table approach

Because Kf is typically very large, assume the formation reaction goes nearly to completion.

Ligand

A Lewis base that bonds to a metal cation (a Lewis acid) via a coordinate covalent bond, forming a complex ion.

Coordination number

The number of ligands bonded to the central metal cation in a complex ion; commonly 4 or 6.

Effect of complex ion formation on a salt's solubility

Forming a complex ion removes free metal cation from solution, which shifts the parent salt's Ksp equilibrium to the right and INCREASES its overall solubility.

Effect of root order on solved x value

For the same numeric value under the radical, a HIGHER root yields a LARGER value of x whenever the value under the radical is less than 1.

Net ionic equation for a precipitation reaction

Shows only the ions that combine to form the solid precipitate; spectator ions are left out.

Solubility vs. Ksp (higher water solubility ≠ higher Ksp)

FALSE — if two compounds dissociate into different ratios of ions, a compound with a lower Ksp can still have a higher solubility.

System (thermodynamics)

The part of the universe under study — the matter whose change (Δ) we are considering.

Surroundings

Everything in the universe outside of the system.

System + Surroundings

Equals the Universe.

Δ (delta) convention

Always means final minus initial (final − initial), for any thermodynamic quantity.

Heat (q)

Energy transferred between system and surroundings due to a temperature difference.

Sign convention for q

q > 0 when heat is absorbed BY the system (endothermic); q < 0 when heat is released BY the system (exothermic).

Work (w, thermodynamics)

Energy transferred by a force acting through a distance, such as the expansion or compression of a gas.

First Law of Thermodynamics

\Delta U = q + w, where $\Delta U$ = change in internal energy; energy cannot be created or destroyed, only transferred.

Work formula for gas expansion/compression

$w = -P_{external} \times \Delta V$.

Sign of w during gas expansion

Negative — the system does work ON the surroundings.

Sign of w during gas compression

Positive — the surroundings do work ON the system.

State function

A property that depends only on the initial and final states, not on the path taken; examples: $U, H, T, P, V$.

Path function

A property that depends on the specific path or process by which a change occurs; examples: $q$ and $w$.

Zeroth Law of Thermodynamics

If object A is in thermal equilibrium with object B, and B is in thermal equilibrium with object C, then A is in thermal equilibrium with C.

Thermal contact

Two objects or systems positioned so that heat can flow between them.

Thermal equilibrium

Two objects in thermal contact have reached the same temperature; net heat flow between them is zero.

Heat capacity (C)

The amount of energy needed to change the temperature of a substance by 1°; depends on the total amount of substance present.

Specific heat capacity (Cs)

The amount of energy needed to change the temperature of 1 gram of a substance by 1°; units $J \\cdot °C^{-1} \\cdot g^{-1}$.

Molar heat capacity (Cn)

The amount of energy needed to change the temperature of 1 mole of a substance by 1°; units $J \\cdot °C^{-1} \\cdot mol^{-1}$.

q = m·Cs·ΔT

Formula relating heat to specific heat, where q = heat (J), m = mass (g), Cs = specific heat capacity (J·°C⁻¹·g⁻¹), ΔT = temperature change.

q = n·Cn·ΔT

Formula relating heat to molar heat capacity, where q = heat (J), n = moles, Cn = molar heat capacity (J·°C⁻¹·mol⁻¹), ΔT = temperature change.

Specific heat of liquid water

$4.184 \\, J \\cdot °C^{-1} \\cdot g^{-1}$.

Why coastal regions have smaller temperature swings

Water's high specific heat moderates the temperature of nearby air.

Calorimetry heat balance

$q_{lost} = -q_{gained}$; heat lost by the hotter object equals the heat gained by the cooler object.

q_{reaction} (calorimetry) formula

$q_{reaction} = -(q_{solution} + q_{calorimeter})$.

q_{solution} formula (calorimetry)

$q_{solution} = m·Cs·ΔT$.

q_{calorimeter} formula

$q_{calorimeter} = C_{calorimeter}·ΔT$.

Determining exo/endothermic from calorimetry ΔT

If $ΔT_{solution}$ is positive, the reaction is exothermic; if negative, it is endothermic.

Finding ΔH per mole from calorimetry data

Divide $q_{reaction}$ by the moles of the LIMITING REAGENT.

Hess's Law

The total enthalpy change for a reaction is independent of the number of steps; heats of reaction are ADDITIVE.

Hess's Law — reversing a reaction

$ΔH_{reverse} = -ΔH_{forward}$.

Hess's Law — scaling a reaction

Multiplying every coefficient in a balanced equation by X also multiplies its $ΔH$ by X.

Hess's Law — adding reactions

$ΔH_{total} = \text{sum of the individual }ΔH \text{ values}$.

Hess's Law vs. Keq manipulation

$ΔH$ values ADD when reactions are combined; $K_{eq}$ values MULTIPLY.

Standard Enthalpy of Formation (ΔH°_f)

The enthalpy change to form exactly ONE mole of a substance from its elements in their standard states.

ΔH°_f = 0 condition

True for any element in its standard state.

Standard state exceptions to memorize

All metals as solids EXCEPT $Hg(l)$; carbon as $C(s, graphite)$ not diamond.

ΔH°_rxn from ΔH°_f values

$ΔH°_{rxn} = ΣΔH°_f,products - ΣΔH°_f,reactants$.

Standard state conditions (definition)

1 M concentration for all aqueous species, 1 atm pressure for all gases, typically evaluated at 25 °C (298 K).

Isobaric process

Occurs at constant pressure (ΔP = 0); $q = ΔH$.

Isochoric process

Occurs at constant volume (ΔV = 0); $w = 0$, $ΔU = q_v$.

Isothermal process

Occurs at constant temperature (ΔT = 0); $ΔU = 0$.

Adiabatic process

Occurs with no heat transfer between system and surroundings (q = 0).

ΔU formula (constant volume)

$ΔU = q_v = n·C_v·ΔT$.

ΔH formula (constant pressure)

$ΔH = q_p = n·C_p·ΔT$.

Why q ≠ 0 during a phase change

Energy must still be absorbed or released to break or form intermolecular attractive forces.