Chem 311 - Titrations

Volumetric Analysis

A chemical procedure that measures the volume of reagent solution needed to react completely with an analyte.

Titration

A type of volumetric analysis where increments of standard reagent solution are added to an analyte solution until the reaction is complete.

Titrant

Reagent solution of known concentration, typically delivered from a buret into the analyte solution.

Quantitative Titration Requirements

The chemical reaction must have a large equilibrium constant, proceed rapidly, and consume the analyte completely.

Types of Titrations

Acid-base reactions, oxidation-reduction reactions, complex formation reactions, and precipitation reactions.

Equivalence Point

The theoretical point in a titration where the quantity of added titrant is exact for stoichiometric reaction with analyte.

End Point

The experimentally observed point in a titration marked by a sudden physical property change in the solution.

Titration Error

The inevitable systematic error resulting from the difference between the observed end point and the true equivalence point.

Blank Titration

Titration carried out on a matrix solution containing no analyte to estimate titration error and correct systematic bias.

Indicator

A compound with a physical property, such as color, that changes abruptly near the equivalence point to signal end point.

Methods for Determining End Point

Observing indicator color change, monitoring light absorbance, or detecting sudden changes in electrode voltage or current.

Primary Standard

A reagent pure enough (greater than or equal to 99.9%) and stable enough to be weighed directly to prepare a solution of known concentration.

Standardization

Procedure where a titrant of approximate concentration is titrated against a primary standard to accurately determine its exact concentration.

Reagent Grades

Commercial purity tiers including Reagent Grade (ACS standard), Trace Metal Grade (sub-ppm impurity), and Primary Standard Grade (certified 100 +/- 0.05%).

Direct Titration

Titration procedure where titrant is added directly to analyte until the reaction reaches completion.

Back Titration

Procedure where a known excess of a standard reagent is added to analyte, and the remaining excess is titrated with a second standard reagent.

Gravimetric Titration

Titration method measuring the mass of titrant solution delivered rather than volume, improving precision from 0.3% to 0.1%.

Titration Calculation Key Step

Relating moles of delivered titrant to moles of analyte using balanced chemical reaction stoichiometry.

Brønsted-Lowry Acids and Bases

Acids are proton donors and bases are proton acceptors.

Conjugate Acid-Base Pair

Two chemical species that differ from each other by the presence or absence of a single transferable proton.

Autoprotolysis of Water

Self-ionization reaction (2 H2O <-> H3O+ + OH-) defined by equilibrium constant Kw, which increases with temperature.

Aqueous Solution pH Range

Typically ranges from 0 to 14 in aqueous media, though extremely concentrated strong acids can reach negative pH values.

Strong Acids and Strong Bases

Substances that completely dissociate in aqueous solution, characterized by pKa < 0 for strong acids and pKa > 14 for strong bases.

Ka and Kb Relationship

For any conjugate acid-base pair in water, Ka * Kb = Kw.

Titration Curve

Graph showing the variation of solution pH as a function of the volume of titrant added.

Strong Base-Strong Acid Titration Curve Regions

Before equivalence point (pH set by excess OH-), at equivalence point (pH = 7.00 set by water dissociation), and after equivalence point (pH set by excess H+).

Weak Acid-Strong Base Titration Curve Regions

Initial point (weak acid equilibrium), buffer region before equivalence point (weak acid + conjugate base), equivalence point (weak base equilibrium), and post-equivalence point (excess strong base).

Half-Equivalence Point Property

In a weak acid-strong base titration, the pH equals pKa of the weak acid at half the equivalence volume (Ve/2).

Weak Acid Titration Inflexion Points

The titration curve exhibits minimum slope at the half-equivalence point (pH = pKa) and maximum slope at the equivalence point.

Factors Affecting End Point Sharpness

Decreasing weak acid strength (higher pKa) or decreasing concentration flattens the break, making the end point less distinct.

Strong Base - Strong Acid Titration Formula (Before Ve)

pH = 14.00 + log[excess OH-], where [OH-] = (moles initial base - moles added acid) / (total volume in L). Used when added acid titrant volume is less than the equivalence volume.

Strong Base - Strong Acid Titration Formula (At Ve)

pH = 7.00 at 25 °C, where pH is determined solely by autoprotolysis of water (Kw = [H+][OH-] = 1.0 x 10^-14). Used at the exact equivalence point of any strong acid-strong base titration.

Strong Base - Strong Acid Titration Formula (After Ve)

pH = -log[excess H+], where [H+] = (moles added acid - moles initial base) / (total volume in L). Used when added acid titrant volume exceeds the equivalence volume.

Weak Acid Titration Initial Formula (V = 0 mL)

[H+] = sqrt(Ka * F) and pH = -log[H+], derived from Ka = x^2 / (F - x) assuming x << F. Used before any strong base titrant is added to a weak acid sample.

Weak Acid Titration Buffer Region Formula (0 < V < Ve)

pH = pKa + log(moles A- formed / moles HA remaining), which is the Henderson-Hasselbalch equation. Used anywhere in the buffer region between the initial volume and the equivalence point.

Weak Acid Titration Half-Equivalence Formula (V = Ve / 2)

pH = pKa, because exactly half of the weak acid (HA) has been converted to its conjugate base (A-), making [A-] / [HA] = 1. Used to easily identify pKa directly from a titration curve.

Weak Acid Titration Equivalence Point Formula (V = Ve)

[OH-] = sqrt(Kb * F') and pH = 14.00 - (-log[OH-]), where Kb = Kw / Ka and F' is the diluted concentration of A- (moles initial HA / total volume). Used at the exact equivalence point where all HA has been converted to weak base A-.

Weak Acid Titration Post-Equivalence Formula (V > Ve)

[OH-] = moles excess strong base / total volume, and pH = 14.00 - (-log[OH-]). Used after the equivalence point where excess strong base overwhelms the weak conjugate base.

Equivalence Volume Formula (Ve)

Ve = (Volume_analyte * Concentration_analyte) / Concentration_titrant. Used to calculate the theoretical volume of titrant required to reach complete stoichiometric reaction with analyte.