ZeonTools
1 Molarity & Solution Concentration
Molarity (M) is the number of moles of solute dissolved per litre of solution — the most universally used concentration unit in analytical and synthetic chemistry. It is defined by M = n / V, where n is moles of solute and V is solution volume in litres. For example, dissolving 58.44 g of NaCl (molar mass 58.44 g/mol) in enough water to make 1.00 L gives exactly 1.00 M NaCl.
Molarity is temperature-dependent because liquid volume expands and contracts with heat. At 25 °C vs 4 °C, a 1 M solution holds slightly different mole counts per litre. For thermodynamic calculations, molality (mol solute per kg solvent) is preferred because it is temperature-invariant. Mass percent and mole fraction are two other key concentration expressions used in industrial contexts and colligative property calculations.
M = n/V = mass/(molar mass × V). For 1 M NaCl: 58.44 g dissolved in 1.00 L gives exactly 1.000 M. Prep a 0.5 M solution by dissolving 29.22 g NaCl in 1.00 L.
C₁V₁ = C₂V₂ is the dilution equation. To make 500 mL of 0.1 M HCl from 12 M stock: V₁ = (0.1 × 500) / 12 = 4.17 mL of concentrated acid, diluted to 500 mL.
Molarity vs Molality: Use molarity (M) for volumetric lab work; use molality (m) for boiling point elevation (ΔTb = Kbm) and freezing point depression (ΔTf = Kfm) calculations.
Industrial Tip: Pharmaceutical solutions are often expressed as mg/mL or % w/v, but pharmacokinetic modelling always converts to molarity for receptor binding calculations.
Fully dissociate; 0.1 M HCl → [H⁺] = 0.1 M exactly
Partially dissociate; 0.1 M CH₃COOH → [H⁺] ≈ 0.00134 M (Ka=1.8×10⁻⁵)
Resist pH change; use Henderson-Hasselbalch for buffer pH
ΔTb, ΔTf, π depend on molality/molarity of solute particles
2 pH Scale & Acid-Base Theory
The pH scale is a logarithmic measure of hydrogen ion concentration: pH = −log₁₀[H⁺]. At 25 °C, pure water auto-ionises to give [H⁺] = [OH⁻] = 10⁻⁷ M, so neutral pH = 7.00. Each unit change represents a 10× change in [H⁺]; pH 3 is 10,000 times more acidic than pH 7. Strong acids (HCl, H₂SO₄, HNO₃) fully dissociate, so pH = −log(c). Weak acids (CH₃COOH, H₂CO₃) only partially dissociate; their equilibrium is characterised by the acid dissociation constant Ka.
For a weak acid HA, [H⁺] ≈ √(Ka × C) when Ka ≪ C, giving pH = ½(pKa − log C). Human blood is maintained at pH 7.35–7.45 by the bicarbonate buffer system (H₂CO₃ / HCO₃⁻, pKa = 6.1). A pH below 7.35 is acidosis; above 7.45 is alkalosis — both life-threatening if uncorrected. The Brønsted-Lowry definition (proton donors/acceptors) and Lewis definition (electron pair acceptors/donors) extend acid-base theory beyond protic solvents.
Strong acids (HCl, H₂SO₄, HNO₃, HClO₄, HBr, HI) fully dissociate: Ka → ∞. Weak acids have finite Ka. Acetic acid Ka = 1.8×10⁻⁵, so 0.1 M solution gives pH = ½(4.74 + 1) = 2.87, NOT 1.0.
H₂SO₄: Ka₁ = ∞ (strong first proton), Ka₂ = 0.012. H₃PO₄: Ka₁=7.5×10⁻³, Ka₂=6.2×10⁻⁸, Ka₃=2.14×10⁻¹³. Each stepwise dissociation is progressively weaker by ~10⁵.
Temperature Effect: The neutral pH at 37 °C (body temp) is ~6.81, not 7.0, because Kw increases with temperature. Clinical blood gas analysers correct for patient temperature.
Safety: Never confuse pH 1 with pH 0. pH 0 means [H⁺] = 1 M (e.g., concentrated HCl). These solutions are highly corrosive and cause severe chemical burns.
HA + H₂O ⇌ H₃O⁺ + A⁻; Ka × Kb = Kw = 10⁻¹⁴ at 25°C
H₂O, HCO₃⁻, HSO₄⁻ act as both acid and base
H⁺ + OH⁻ → H₂O; ΔH = −57.1 kJ/mol for strong acid/base
Change colour at specific pH; phenolphthalein 8.2–10.0, litmus 5–8
3 Buffer Solutions & Henderson-Hasselbalch
A buffer solution resists pH change upon addition of small amounts of strong acid or base. It consists of a weak acid (HA) and its conjugate base (A⁻) in comparable concentrations. The Henderson-Hasselbalch equation describes the pH: pH = pKa + log([A⁻]/[HA]). When [A⁻] = [HA], the ratio is 1, log(1) = 0, and pH = pKa exactly. This also represents the point of maximum buffer capacity, where the buffer resists pH change most effectively.
The effective buffering range is pKa ± 1 pH unit (ratio 10:1 or 1:10). Outside this range, one component dominates and buffering fails. Common biological buffers: phosphate (pKa 6.86, used in PBS at pH 7.4), HEPES (pKa 7.48, cell culture), Tris (pKa 8.06, DNA/protein work), acetate (pKa 4.76, low-pH applications). Pharmaceutical formulations require precise buffers because ±0.1 pH unit shifts can affect drug ionisation and absorption.
pH = pKa + log([A⁻]/[HA]). For acetate buffer pH 5.0 using pKa 4.76: log([A⁻]/[HA]) = 5.0 - 4.76 = 0.24; [A⁻]/[HA] = 10^0.24 = 1.74. Use 1.74× more sodium acetate than acetic acid.
β = dC/dpH (moles of base per pH unit). Maximum at pH = pKa. Decreases sharply beyond ±1 unit. Total buffer concentration (C_T = [HA]+[A⁻]) proportionally increases capacity; double the concentration, double the capacity.
Biological Buffers (Good's Buffers): MES (pH 5.5–6.7), MOPS (6.5–7.9), HEPES (6.8–8.2), TAPS (7.7–9.1) are zwitterionic and do not interfere with enzyme assays or coordinate metal ions.
Isoelectric Point (pI): Amino acids are amphoteric. Their pI = ½(pKa1 + pKa2). At pI, net charge = 0; no migration in electrophoresis. Crucial for protein purification by isoelectric focusing.
Blood: HCO₃⁻/H₂CO₃; pKa=6.1; kidneys regulate [HCO₃⁻], lungs regulate [CO₂]
Cells: H₂PO₄⁻/HPO₄²⁻; pKa=7.2; ideal near physiological pH
Lab: CH₃COO⁻/CH₃COOH; pKa=4.76; used for low-pH separations
Molecular Bio: pKa=8.06; temperature-sensitive; ΔpKa/°C = −0.028
4 Gibbs Free Energy & Thermodynamics
Gibbs Free Energy (G) determines the spontaneity of a process at constant temperature and pressure. The fundamental equation is ΔG = ΔH − TΔS, where ΔH is enthalpy change (heat), T is absolute temperature, and ΔS is entropy change. A negative ΔG indicates a spontaneous (thermodynamically favourable) process; positive ΔG means non-spontaneous. When ΔG = 0, the system is at equilibrium.
The relationship between standard Gibbs energy and the equilibrium constant K is ΔG° = −RT ln K. At 25°C, RT = 2.479 kJ/mol, so ΔG° = −5.71 kJ/mol for K = 10 (spontaneous), and +5.71 for K = 0.1 (non-spontaneous). Four thermodynamic scenarios exist: (1) ΔH < 0, ΔS > 0 → always spontaneous; (2) ΔH > 0, ΔS < 0 → never spontaneous; (3) ΔH < 0, ΔS < 0 → spontaneous at low T; (4) ΔH > 0, ΔS > 0 → spontaneous at high T.
ΔG = ΔG° + RT ln Q. At equilibrium Q = K, ΔG = 0. Thus ΔG° = −RT ln K. K > 1 means products favoured (ΔG° < 0). K = 10⁶ corresponds to ΔG° = −34.2 kJ/mol at 298 K — strongly product-favoured.
ΔH for a reaction = sum of ΔH of component steps. Since G, H, S are all state functions, Hess's Law applies to ΔG and ΔS too. Allows calculation of ΔG° for any reaction from tabulated standard formation values.
Coupled Reactions: Biological systems drive thermodynamically unfavourable reactions (ΔG > 0) by coupling them to ATP hydrolysis (ΔG° = −30.5 kJ/mol). This is the basis of metabolic energy transduction.
Caution: ΔG° uses standard-state concentrations (1 M, 1 atm, 298 K). Actual cellular ΔG can differ dramatically; [ATP]/[ADP][Pi] in vivo makes ATP hydrolysis far more exergonic (~−50 to −60 kJ/mol).
ΔH < 0; releases heat; reaction vessel warms (combustion, neutralisation)
ΔH > 0; absorbs heat; reaction vessel cools (photosynthesis, dissolving NH₄NO₃)
ΔS > 0 overcomes ΔH > 0 at high T; protein denaturation, dissolution of hydrocarbons
ΔH < 0 overcomes ΔS < 0 at low T; crystallisation, gas condensation
5 Arrhenius Equation & Reaction Kinetics
The Arrhenius equation describes the temperature dependence of rate constants: k = A · e^(−Ea/RT), where A is the pre-exponential (frequency) factor, Ea is activation energy (J/mol), R = 8.314 J/mol·K, and T is temperature in Kelvin. Taking the natural log: ln k = ln A − Ea/RT. Plotting ln k vs 1/T gives a straight line with slope = −Ea/R, allowing Ea to be determined experimentally from two rate measurements at different temperatures.
The two-temperature form is especially practical: ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁). The van't Hoff rule states that most chemical reactions roughly double in rate for every 10 °C rise (Q₁₀ ≈ 2), which corresponds to Ea ≈ 50 kJ/mol. Enzymes lower activation energy dramatically — hexokinase has Ea ≈ 10 kJ/mol vs. 60–80 kJ/mol for uncatalysed glucose phosphorylation, explaining the 10⁶-fold rate enhancement.
Expands Arrhenius: k = (k_B·T/h) · exp(−ΔG‡/RT), where k_B = Boltzmann const, h = Planck const, ΔG‡ = activation Gibbs energy. At 25°C, k_B·T/h = 6.25×10¹² s⁻¹ — the universal frequency for transition state crossing.
0th order: rate = k; [A] = [A]₀ − kt. 1st order: rate = k[A]; t½ = ln2/k (independent of [A]₀). 2nd order: rate = k[A]²; t½ = 1/(k[A]₀). Radioactive decay is always 1st order. Most enzyme-catalysed reactions follow Michaelis-Menten (pseudo-1st order at low [S]).
Catalysis Effect: Catalysts lower Ea without affecting ΔG or K. For Ea = 60 kJ/mol reduced to 40 kJ/mol at 298 K: rate ratio = e^(20000/(8.314×298)) = e^8.07 ≈ 3,200-fold rate increase.
Enzyme Kinetics: Michaelis-Menten: v = Vmax[S]/(Km + [S]). kcat = Vmax/[E]T is the turnover number (reactions/enzyme/second). Catalase: kcat = 4×10⁷ s⁻¹ — among the fastest enzymes known.
Rate = k[A]; t½ constant; radioactive decay, many drug eliminations
Rate = k[A]²; t½ = 1/k[A]₀; NO₂ + CO → NO + CO₂
Rate = k'[A]; excess B makes it appear 1st order; common in hydrolysis
Rate = k; enzyme-saturated reactions; drug metabolism at high dose
6 Ideal Gas Law & Gas Properties
The Ideal Gas Law PV = nRT combines Boyle's Law (PV = const at fixed T), Charles's Law (V/T = const at fixed P), and Avogadro's Law (V ∝ n at fixed P, T). R = 0.08206 L·atm/mol·K or 8.314 J/mol·K. At STP (0°C, 1 atm), 1 mole of ideal gas occupies exactly 22.414 L. This law accurately describes most gases at low pressures (< 10 atm) and moderate temperatures, where intermolecular forces and molecular volumes are negligible.
For real gases, the van der Waals equation corrects for attractive forces (a) and molecular volume (b): (P + an²/V²)(V − nb) = nRT. The compressibility factor Z = PV/nRT = 1 for ideal gases; Z < 1 when attractions dominate (low T, moderate P); Z > 1 when repulsions dominate (high P). Gas density ρ = PM/(RT), where M is molar mass, enabling molar mass determination by gas density measurement — a classic analytical technique.
Dalton's Law: P_total = ΣP_i = Σ(n_i·RT/V). Mole fraction x_i = n_i/n_total = P_i/P_total. Air: 78% N₂ (P=0.78 atm), 21% O₂ (P=0.21 atm), 1% Ar at 1 atm total.
Graham's Law: rate₁/rate₂ = √(M₂/M₁). H₂ effuses √(32/2) = 4× faster than O₂. Used in ²³⁵UF₆ /²³⁸UF₆ isotope enrichment: rate ratio = √(352/349) = 1.0043 per stage.
Van der Waals Constants: CO₂ has a=3.64, b=0.0427 (strong attractions, moderate size). He has a=0.034, b=0.0237 (nearly ideal). NH₃ has a=4.17 (strong H-bonding attractions).
Kinetic Molecular Theory: Average KE = (3/2)RT per mole. Root-mean-square speed: u_rms = √(3RT/M). For N₂ at 25°C: u_rms = √(3×8.314×298/0.028) = 515 m/s.
PV = k at constant T, n; P₁V₁ = P₂V₂; explains syringe compression
V/T = k at constant P, n; V₁/T₁ = V₂/T₂; hot air balloon rises
V/n = k at constant T, P; adding gas increases volume proportionally
P/T = k at constant V, n; P₁/T₁ = P₂/T₂; tyre pressure vs temperature
7 Electrochemical Cells & Reduction Potentials
Electrochemical cells convert chemical energy to electrical energy (galvanic/voltaic cells) or vice versa (electrolytic cells). The standard cell potential is E°cell = E°cathode − E°anode (both written as reduction potentials from the standard reduction potential table). The SHE (standard hydrogen electrode, E° = 0.000 V exactly by definition) serves as the reference. A positive E°cell means the reaction is spontaneous: ΔG° = −nFE°cell, where F = 96,485 C/mol (Faraday's constant).
The Nernst equation corrects E°cell for non-standard concentrations: E = E° − (RT/nF) ln Q. At 25°C this simplifies to E = E° − (0.05916/n) log Q. The Daniel cell (Zn|ZnSO₄||CuSO₄|Cu) gives E°cell = 0.34 − (−0.76) = 1.10 V, producing 212 kJ/mol of electrical work (n=2). Concentration cells have identical electrodes but different concentrations; their E° = 0 but E ≠ 0 due to the Nernst term — the basis of biological membrane potentials and pH electrodes.
Mass deposited in electrolysis: m = (M×I×t)/(n×F). Electroplating 10 g Cu (M=63.5) with I=2 A, n=2: t = (10×2×96485)/(63.5×2) = 15,156 s ≈ 4.2 hours. Used in copper refining, electroplating, chlor-alkali process.
Cathode (discharge): LiCoO₂ + Li⁺ + e⁻ → Li₂CoO₂, E° ≈ +1.0 V. Anode (discharge): C (graphite) → LiC₆, E° ≈ −0.1 V. Overall: E_cell ≈ 3.7 V. Energy density ~150–250 Wh/kg. Solid-state batteries target >400 Wh/kg.
Electrolysis of Water: 2H₂O → 2H₂ + O₂. E° = −1.23 V (non-spontaneous; requires at least 1.23 V applied + overpotential ≈1.6–1.8 V total). PEM electrolysers operate at 80°C to reduce overpotential.
Corrosion Prevention: Zinc is sacrificial anode for steel (galvanic protection). Cathodic protection uses external current to reverse corrosion direction. Passivation: Al₂O₃ film on aluminium provides kinetic barrier despite thermodynamic instability.
Spontaneous: ΔG < 0, E°cell > 0; converts chemical → electrical energy
Driven: ΔG > 0, E°cell < 0; converts electrical → chemical energy
Same electrodes, different [ion]; E° = 0; E driven by Nernst term
Continuous: H₂ + ½O₂ → H₂O; E° = 1.23 V; 40–60% efficiency
8 Radioactive Decay & Nuclear Chemistry
Radioactive decay is a first-order kinetic process: N(t) = N₀ × e^(−λt) = N₀ × (½)^(t/t½), where N is number of atoms remaining, λ = ln2/t½ is the decay constant, and t½ is the half-life. Activity A = λN (in Becquerels: 1 Bq = 1 decay/second; 1 Curie = 3.7×10¹⁰ Bq). The key property of first-order decay: half-life is independent of initial amount, making it a reliable chronometer for geological and archaeological dating.
Decay modes: α decay (emits ⁴₂He, mass decreases by 4, Z by 2), β⁻ decay (neutron → proton + e⁻ + antineutrino), β⁺ decay (proton → neutron + e⁺ + neutrino), γ decay (nucleus relaxes from excited state, no Z or A change), electron capture. Nuclear binding energy is calculated from the mass defect: ΔE = Δm·c² (Einstein). ²³⁵U fission releases ~200 MeV per event — ~10⁸ × a typical chemical reaction energy.
¹⁴C (t½ = 5,730 yr) is produced in the atmosphere and maintained at ~1.2×10⁻¹² relative abundance. Living organisms exchange C; after death, ¹⁴C decays. Age = (t½/ln2) × ln(A₀/A). Accurate for 0–50,000 yr; calibrated against dendrochronology.
¹³¹I (t½=8 days): thyroid cancer treatment. ⁹⁹ᵐTc (t½=6 h): most used diagnostic (SPECT imaging). ¹⁸F-FDG (t½=110 min): PET scan glucose analogue; reveals metabolic activity in tumours, brain, heart.
Radiation Safety: Dose units: Gray (Gy) = 1 J/kg absorbed. Sievert (Sv) = Gy × quality factor (1 for γ/β, 20 for α). Annual background dose ≈ 2.4 mSv. Lethal dose LD₅₀ ≈ 4 Sv whole-body acute exposure.
Nuclear Transmutation: Bombarding ²⁷Al with α particles: ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ¹₀n. Curie/Joliot discovery of artificial radioactivity (1934). Particle accelerators create hundreds of artificial nuclides for medical, industrial, research use.
A decreases by 4, Z by 2; low penetration (paper stops); ²³⁸U → ²³⁴Th + ⁴He
Z increases by 1; medium penetration (Al stops); ¹⁴C → ¹⁴N + e⁻
No change in A or Z; high penetration (Pb/concrete shields); ⁶⁰Co → γ
Heavy nucleus splits; ²³⁵U + n → ⁹²Kr + ¹⁴¹Ba + 3n + 200 MeV
9 Dilution Calculations & Serial Dilutions
Dilution calculations are governed by conservation of moles of solute: C₁V₁ = C₂V₂. To prepare 500 mL of 0.050 M HCl from 12.0 M stock: V₁ = (0.050 × 500) / 12.0 = 2.08 mL. Always add concentrated acid to water (not reverse) to dissipate heat safely. The dilution factor (DF) = V_final / V_initial = C_initial / C_final. Serial dilutions multiply the dilution factor at each step: a 1:10 dilution repeated 6 times gives a total DF of 10⁶.
Serial dilutions are fundamental in microbiology (colony counting), immunology (antibody titres), and pharmacology (dose-response curves). A 2-fold dilution series (1:2, 1:4, 1:8...) is used in minimum inhibitory concentration (MIC) testing for antibiotics. Beer-Lambert Law (A = εcl) connects absorbance to concentration for spectrophotometric quantification — calibrated using a dilution series of known standards. Standard curves typically span 3–5 orders of magnitude concentration.
Primary standards (high purity, stable): KHP (potassium hydrogen phthalate, FW 204.22), Na₂CO₃, K₂Cr₂O₇. Used to standardise secondary standards (NaOH, HCl) by titration. NIST Standard Reference Materials guarantee traceability to SI units.
A = ε·c·l. ε = molar absorptivity (L/mol·cm). l = path length (typically 1 cm). Absorbance A = −log(I/I₀). Linear range: A = 0.1–1.0. NADH: ε₃₄₀ = 6,220 L/mol·cm; protein assay (Bradford): ε₅₉₅.
Lab Technique: When making very dilute solutions (nM–pM range), use serial dilutions rather than one large dilution to minimise pipetting errors. Each 1:100 serial step has much better accuracy than a single 1:10,000 dilution.
Environmental Analysis: Environmental samples often need 1000–1,000,000× concentration or dilution before analysis. Solid-phase extraction (SPE) concentrates trace contaminants; isotope dilution mass spectrometry measures even fg/mL concentrations.
Add 1 mL sample to 9 mL diluent; final volume 10 mL; DF=10
Antibody titre: 1:2, 1:4, 1:8, 1:16... endpoint is last tube showing activity
96-well: 12 serial 2-fold dilutions across 8 rows; tests 8 samples simultaneously
Weigh solute/solution for highest accuracy; used in primary standard preparation
10 Stoichiometry & Mole Concept
Stoichiometry uses molar ratios from balanced equations to relate amounts of reactants and products. The mole (mol) is the SI unit of amount: 1 mol = 6.022×10²³ entities (Avogadro's number). Molar mass (g/mol) numerically equals atomic/molecular weight. To find moles: n = mass/molar mass. For gases at STP (0°C, 1 atm): n = V/22.414 L. For solutions: n = M × V (in litres). Converting: 1 mol NaCl (58.44 g) contains 6.022×10²³ formula units and dissolves to give 6.022×10²³ Na⁺ and 6.022×10²³ Cl⁻ ions.
The limiting reagent is the reactant that is completely consumed first and determines the theoretical yield. Identify it by dividing moles of each reactant by its stoichiometric coefficient — the smallest ratio gives the limiting reagent. Percent yield = (actual yield / theoretical yield) × 100%. Industrial syntheses aim for >85% yield; pharmaceutical processes must achieve >95% for economic viability. Atom economy = (molar mass of desired product / sum of molar masses of all reactants) × 100% — a Green Chemistry metric.
Determine from combustion analysis: burn compound, collect CO₂ and H₂O. If 0.261 g compound gives 0.457 g CO₂ and 0.187 g H₂O: C = 0.457/44 = 0.01039 mol, H = 2×0.187/18 = 0.02078 mol. Ratio C:H = 1:2 → CH₂. Use molar mass to get molecular formula.
12 Principles: atom economy, prevent waste, safer solvents, catalysis, renewable feedstocks. E-factor = kg waste / kg product. Fine chemicals: E-factor 5–50; pharmaceuticals: 25–100. Green chemistry targets E-factor < 5 by designing reactions with minimal byproducts.
Titration Calculation: n_acid × Molarity_acid × Volume_acid = n_base × Molarity_base × Volume_base. For H₂SO₄ (diprotic, n=2): 25.00 mL × M × 2 = 1 × 0.1000 × 35.40 mL. M(H₂SO₄) = 0.07080 M.
Yield Optimisation: Le Chatelier's Principle guides industrial conditions. Haber process N₂ + 3H₂ ⇌ 2NH₃ (ΔH < 0): high pressure (200 atm, favours fewer moles), moderate temperature (450°C, balance kinetics vs equilibrium), Fe catalyst, continuous removal of NH₃.
From balanced equation coefficients; N₂ + 3H₂ → 2NH₃: 1:3:2 molar ratio
Calculated from limiting reagent; maximum possible amount of product
Measured; always ≤ theoretical; losses from incomplete reaction, separation
MW product / Σ MW reactants × 100%; SN2 reactions often 100% atom economy
11 Chemical Equilibrium & Le Chatelier's Principle
Chemical equilibrium is reached when the rate of forward reaction equals the reverse, giving a constant ratio of product to reactant concentrations. The equilibrium constant Kc = Π[products]^coeff / Π[reactants]^coeff (pure solids and liquids omitted). For N₂ + 3H₂ ⇌ 2NH₃: Kc = [NH₃]² / ([N₂][H₂]³). A large K (>>1) means products are strongly favoured; small K (<<1) means reactants dominate. K is temperature-dependent (van't Hoff equation: d(ln K)/dT = ΔH°/RT²).
Le Chatelier's Principle states that a system at equilibrium responds to a perturbation by shifting to partially counteract it. Adding a reactant shifts equilibrium right (more products); removing a product shifts right. Increasing pressure shifts towards fewer moles of gas. For exothermic reactions (ΔH < 0), increasing temperature shifts left (reduces K). Industrial application: Haber process uses 200 atm, 450°C, Fe catalyst. High pressure and moderate temperature (not too high to prevent K from being too small) balance yield and rate.
Q uses current (non-equilibrium) concentrations. Q < K: reaction proceeds forward (produces more products). Q > K: reaction goes backward (produces more reactants). Q = K: system is at equilibrium. Q is identical in form to K, but evaluated at any time point.
For slightly soluble salts: AgCl ⇌ Ag⁺ + Cl⁻; Ksp = [Ag⁺][Cl⁻] = 1.77×10⁻¹⁰. Molar solubility s = √Ksp = 1.33×10⁻⁵ M. Common ion effect: add NaCl → [Cl⁻] increases → Q > Ksp → more AgCl precipitates.
Temperature vs K: For endothermic reactions (ΔH > 0), K increases with T (high T favours products). For exothermic (ΔH < 0), K decreases with T. The exact relationship: ln(K₂/K₁) = −(ΔH°/R)(1/T₂ − 1/T₁) — the van't Hoff equation.
Solubility Rules: All nitrates and ammonium salts are soluble. Most chlorides are soluble (except AgCl, PbCl₂, Hg₂Cl₂). Most sulphates soluble (except BaSO₄, PbSO₄, SrSO₄). All carbonates insoluble (except Na, K, NH₄).
Kp = Kc(RT)^Δn; Δn = moles gaseous products - moles gaseous reactants
Pure solids/liquids have constant activity=1; not included in K expression
Extraction: K_D = [A]_org/[A]_aq; used in liquid-liquid extraction separations
Metal-ligand: Zn²⁺ + 4NH₃ ⇌ [Zn(NH₃)₄]²⁺; Kf = 2.9×10⁹; very stable
12 Intermolecular Forces & States of Matter
Intermolecular forces (IMFs) determine physical properties: boiling/melting points, solubility, viscosity, and surface tension. Types in increasing strength: (1) London dispersion (all molecules; temporary dipoles; scales with molar mass and surface area); (2) Dipole-dipole (polar molecules, permanent dipoles); (3) Hydrogen bonding (N−H, O−H, or F−H with lone pairs; 10–40 kJ/mol); (4) Ion-dipole (dissolved salts). The anomalously high boiling point of water (100°C vs −61°C expected from analogues) results from its extensive hydrogen-bonding network (each water makes up to 4 H-bonds).
The Clausius-Clapeyron equation relates vapour pressure to temperature: ln(P₂/P₁) = −(ΔH_vap/R)(1/T₂ − 1/T₁). At high altitude (low P), water boils below 100°C — food takes longer to cook. Phase diagrams show the stability regions of solid, liquid, and gas as functions of T and P. The triple point (water: 273.16 K, 0.006 atm) is where all three phases coexist and is used as a thermometric fixed point for SI temperature definition.
"Like dissolves like": polar solvents (water, methanol) dissolve polar/ionic solutes; nonpolar solvents (hexane, CCl₄) dissolve nonpolar solutes. Soap/detergent: amphiphilic (polar head, nonpolar tail) — forms micelles to emulsify grease in water.
Depend on particle number, not identity. ΔTb = Kb·m·i; ΔTf = Kf·m·i (i = van't Hoff factor: NaCl i=2, glucose i=1). Kb(water)=0.512°C/m, Kf(water)=1.86°C/m. Osmotic pressure: π = iMRT. Blood plasma ~7.5 atm (310 K, ~0.3 M total solutes).
Surface Tension: Water has high surface tension (72.8 mN/m at 25°C) due to H-bonding. Surfactants reduce surface tension: detergent lowers it to ~25 mN/m, enabling wetting and emulsification. Lung surfactant (DPPC) reduces surface tension to near 0 during exhalation, preventing alveolar collapse.
Crystal Structures: NaCl (face-centred cubic, coordination number 6:6), CsCl (simple cubic, 8:8), ZnS (tetrahedral, 4:4). Metallic bonds: electrons delocalised in conduction band. Band gap determines electrical conductivity: conductors (0 eV), semiconductors (Si: 1.1 eV), insulators (SiO₂: 9 eV).
All molecules; weak (1-10 kJ/mol); increases with MW and surface area
Polar molecules: HCl, SO₂; 5-25 kJ/mol; determines boiling points in series
O-H, N-H, F-H; 10-40 kJ/mol; responsible for DNA base pairing, enzyme specificity
Electrons delocalised; explains electrical conductivity, malleability, metallic lustre
14 Frequently Asked Questions
Explore these detailed answers to some of the most common questions in general chemistry, thermodynamics, and physical chemistry. Each explanation is designed to deepen your conceptual understanding.
Use the accordion below to quickly find answers to your specific questions.
Perfect for exam preparation or refreshing your foundational chemistry knowledge.
Molarity (M) is defined as the number of moles of solute dissolved in one liter of solution. It is temperature-dependent because the volume of the solution can expand or contract with temperature changes. Molality (m), on the other hand, is the number of moles of solute per kilogram of solvent. Because it is based on mass rather than volume, molality is completely independent of temperature, making it preferable for precise thermodynamic measurements like boiling point elevation.
A pH of 7 implies that the concentration of hydrogen ions ([H+]) in the solution is 10^-7 moles per liter (M). At 25°C, this is considered exact neutrality because pure water auto-ionizes into equal amounts of [H+] and [OH-], both being 10^-7 M. If the temperature changes, the neutral pH also changes; for instance, at human body temperature (37°C), pure water has a neutral pH of about 6.81. Thus, a pH of 7 is only definitively 'neutral' under standard conditions of 298 K.
The Henderson-Hasselbalch equation describes the pH of a buffer based on the pKa and the ratio of conjugate base to weak acid. An effective buffer neutralizes both added acids and bases, which requires significant amounts of both conjugate components. When the ratio exceeds 10:1 or drops below 1:10 (which corresponds to pH = pKa ± 1 due to the log10 function), one component is largely depleted. Therefore, outside this ±1 pH range, the buffer capacity drastically falls, leaving the solution vulnerable to rapid pH shifts.
ΔH represents the change in enthalpy (heat content), determining whether a process is exothermic (releases heat) or endothermic (absorbs heat). ΔS is the change in entropy, which measures the degree of disorder or randomness introduced to the system. ΔG is the change in Gibbs Free Energy, which combines both enthalpy and entropy to predict the overall spontaneity of a reaction at constant temperature and pressure. A negative ΔG signifies a spontaneous reaction, whereas a positive ΔG indicates a non-spontaneous process.
A negative ΔG guarantees spontaneity only at the specific temperature where it is calculated, according to the equation ΔG = ΔH - TΔS. Since T (temperature) is always positive in Kelvin, the balance between ΔH and TΔS can shift across different temperatures. For instance, an endothermic reaction (positive ΔH) with an increase in entropy (positive ΔS) is spontaneous at high temperatures (where TΔS > ΔH) but non-spontaneous at lower temperatures. Thus, ΔG must be continuously evaluated across the temperature range of interest.
The Arrhenius equation (k = A * e^(-Ea/RT)) mathematically models how reaction rates accelerate with rising temperatures. The exponential term represents the fraction of molecular collisions possessing energy equal to or greater than the activation energy (Ea). As temperature (T) increases, this exponential term grows significantly, implying a vast increase in successful, energetic collisions. Consequently, the rate constant (k) grows exponentially, elucidating why even modest heating can drastically accelerate chemical reactions.
The ideal gas law assumes that gas molecules occupy negligible volume and exhibit zero intermolecular attractive or repulsive forces. However, at extremely high pressures, the physical volume of the molecules themselves becomes significant compared to the total container volume. At very low temperatures, molecular kinetic energy drops, allowing intermolecular forces (like van der Waals forces) to pull molecules closer together. In these conditions, gases deviate sharply from ideal behavior, necessitating more complex models like the Van der Waals equation.
To calculate the standard cell potential (E°cell), you subtract the standard reduction potential of the anode from the standard reduction potential of the cathode (E°cell = E°cathode - E°anode). Both potentials are typically provided as reduction potentials in standard tables. It is critical not to reverse the sign of the anode potential before subtracting, as the subtraction inherently accounts for the oxidation process. A positive overall E°cell indicates a spontaneous galvanic (voltaic) cell reaction.
The Nernst equation enables the calculation of cell potential under non-standard conditions, where reactant and product concentrations are not 1 M or pressures are not 1 atm. It adjusts the standard cell potential (E°cell) based on the temperature, the number of moles of electrons transferred, and the reaction quotient (Q). You need it whenever dealing with real-world batteries or cells, as concentrations deplete and Q changes continuously as the electrochemical reaction progresses toward equilibrium (where cell potential becomes zero).
Radioactive decay is an inherently random, probabilistic process occurring at the level of individual atomic nuclei independently of external conditions like temperature or pressure. Because the probability of any single nucleus decaying per unit time is constant, the overall rate of decay is strictly proportional to the number of unstable nuclei currently present. This direct proportionality (Rate = k * N) is the exact definition of first-order kinetics, resulting in the characteristic constant half-life observed for radioactive isotopes.
Activity refers to the overall rate at which unstable nuclei undergo radioactive decay in a given sample. The Becquerel (Bq) is the SI unit for activity, representing exactly one decay event per second. The Curie (Ci) is a traditional, much larger unit historically based on the activity of one gram of Radium-226, equivalent to 3.7 × 10^10 decays per second. Thus, while activity is the physical quantity, Bq and Ci are merely different scales used to quantify that identical measurement.
A serial dilution is a stepwise, sequential process where a small aliquot of a highly concentrated solution is repeatedly transferred into successive volumes of diluent. By keeping the dilution factor constant at each step (e.g., 1:10), researchers can rapidly span multiple orders of magnitude of concentration without requiring massive quantities of solvent. This technique is indispensable for generating standard curves for spectrophotometry, plating bacterial cultures to achieve countable colonies, and creating extremely low-concentration assay standards.
Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions—such as concentration, pressure, or temperature—the position of equilibrium will shift to counteract the change. For example, adding more reactant will push the reaction forward to consume the excess, while increasing pressure will shift the system toward the side with fewer moles of gas. This principle allows chemists to manipulate conditions artificially to maximize the yield of desired industrial products like ammonia.
Endothermic reactions fundamentally absorb thermal energy from their surroundings in order to proceed (Reactants + Heat -> Products). According to Le Chatelier's principle, adding heat acts identically to increasing the concentration of a reactant. The system responds by consuming this excess thermal energy, thereby shifting the equilibrium toward the right to generate more products. Consequently, higher temperatures dramatically favor product formation and increase the equilibrium constant (K) for all endothermic processes.
Strong electrolytes undergo complete dissociation (100% ionization) into constituent ions when dissolved in water, resulting in highly conductive solutions. Examples include strong acids like HCl, strong bases like NaOH, and highly soluble salts like NaCl. Weak electrolytes, conversely, only partially ionize, establishing an equilibrium between intact molecules and dissociated ions. Because they generate far fewer charge carriers, weak electrolytes like acetic acid or ammonia produce solutions with significantly lower electrical conductivity.
Electronegativity quantifies an atom's tendency to attract shared electrons in a chemical bond. When the difference in electronegativity between two atoms is essentially zero, electrons are shared equally, forming a pure nonpolar covalent bond. A moderate difference (typically 0.4 to 1.7) causes unequal sharing, resulting in a polar covalent bond with partial electrical charges. If the difference is very large (greater than 1.7), one atom effectively steals the electron from the other, producing separate ions held together by an ionic bond.