Biotechnological Engineering — Revision sheet

Key points

• 01

  Atomic number = protons; mass number = protons + neutrons.

• 02

  Protium, deuterium, tritium = hydrogen's isotopes, with 0, 1, 2 neutrons.

• 03

  Water: 18 daltons, bent at 104.5°, polar. CO₂: linear, symmetrical, nonpolar.

• 04

  Water's unusually high mp/bp/heat of vaporization/surface tension come from intermolecular hydrogen bonding.

• 05

  Hydrophilic = polar = water-soluble. Hydrophobic = nonpolar = water-insoluble. Amphipathic = both, in one molecule.

• 06

  High dielectric constant → weaker ionic attraction → water dissolves salts easily.

• 07

  Water is amphoteric (acts as acid or base) and amphiprotic (donates or accepts H⁺): $H_2O \rightleftharpoons H^+ + OH^-$, and $2H_2O \rightleftharpoons H_3O^+ + OH^-$. $H_3O^+$ → cathode, $OH^-$ → anode.

• 08

  $K_w = [H^+][OH^-] = K_{eq} \times 55.5 = 10^{-14}$ mol²/L² at 25°C ($K_{eq} = 1.8 \times 10^{-16}$ mol/L; $[H_2O]$ held constant at $55.5$ mol/L).

• 09

  Pure water: $[H^+] = 10^{-7}$ mol/L, neutral. Acidic: $[H^+] > 10^{-7}$ M. Basic: $[H^+] < 10^{-7}$ M.

• 10

  $pH = -\log[H^+]$.

• 11

  Brønsted-Lowry: acid donates H⁺, base accepts H⁺. $HCl + H_2O \rightleftharpoons Cl^- + H_3O^+$ — conjugate pairs $HCl/Cl^-$ and $H_3O^+/H_2O$.

• 12

  Strong acids ionize completely; weak acids don't.

• 13

  $K_a = [H^+][A^-]/[HA]$ — an acid's tendency to donate its proton; the equilibrium constant of $HA \rightleftharpoons H^+ + A^-$.

• 14

  $pK_a = -\log K_a$. Larger $K_a$ → lower $pK_a$ → stronger acid. Strong acid ($HCl$): $K_a \sim 10^7$, $pK_a \sim -7$. Weak acid (acetic acid): $K_a = 1.8 \times 10^{-5}$, $pK_a = 4.76$.

• 15

  Henderson-Hasselbalch: $pH = pK_a + \log([A^-]/[HA])$. When $[A^-] = [HA]$, $pH = pK_a$ — the acid is 50% dissociated, the buffer's point of maximum capacity.

• 16

  Titration: titrant (known conc.) added to analyte (unknown conc.) until the reaction is complete. A weak acid is titrated with a strong base; the titration curve plots pH vs. $OH^-$ added.

• 17

  Equivalence point = inflection point (steepest slope): moles titrant added = moles acid originally present. Half-equivalence point ($[HA]=[A^-]$, $pH=pK_a$) sits in the flat buffering zone instead — the two are easily confused but are opposite points on the curve.

• 18

  Curve order (weak acid + strong base, as $OH^-$ is added): start (low pH) → early rise → buffering zone begins → half-equivalence ($pH=pK_a$) → buffering zone ends → equivalence/inflection point ($pH>7$, endpoint detected here) → past equivalence, pH levels off.

• 19

  Mirror case: weak base + strong acid ($NH_3$ + $HCl$) — curve falls instead of rises; equivalence-point pH is $< 7$ (conjugate acid $NH_4^+$ hydrolyzes) instead of $> 7$.

• 20

  Buffer = resists pH change on adding acid/base or on dilution. Acidic buffer (weak acid + conjugate base), $pH<7$; basic buffer (weak base + conjugate acid), $pH>7$. Physiological examples: phosphate buffer ($H_2PO_4^-/HPO_4^{2-}$), bicarbonate buffer ($H_2CO_3/HCO_3^-$ — blood's main buffer, tunable by lungs and kidneys).

• 21

  Buffer range/capacity depend on the conjugate pair's $pK_a$ and on their concentrations. Requires a weak acid + its salt, at reasonably similar concentrations — works via the common ion effect (excess $A^-$ from the salt suppresses the acid's own ionization).

• 22

  Acetic acid/sodium acetate buffer: $CH_3COO^-$ (from the fully dissociated salt) mops up added $H^+$; $CH_3COOH$ mops up added $OH^-$; dilution leaves the $[A^-]/[HA]$ ratio — and so the pH — unchanged.