Analytical Chemistry

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### Chemical Equilibrium - **Equilibrium Constant ($K$):** For $aA + bB \rightleftharpoons cC + dD$, $$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$ $$K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b}$$ - $K_p = K_c(RT)^{\Delta n}$, where $\Delta n = (c+d)-(a+b)$ - **Reaction Quotient ($Q$):** Same form as $K$, but uses current concentrations/pressures. - If $Q K$, reaction proceeds reverse (left). - If $Q = K$, system is at equilibrium. - **Le Chatelier's Principle:** A system at equilibrium, when subjected to a stress, will shift in a direction that alleviates the stress. - **Concentration:** Adding reactant shifts right; removing reactant shifts left. - **Temperature:** For endothermic reactions, increasing T shifts right. For exothermic, increasing T shifts left. - **Pressure/Volume:** Increasing P (decreasing V) shifts to side with fewer gas moles. - **Solubility Product ($K_{sp}$):** For $M_x A_y (s) \rightleftharpoons xM^{y+}(aq) + yA^{x-}(aq)$, $$K_{sp} = [M^{y+}]^x[A^{x-}]^y$$ - **Common Ion Effect:** Solubility of a sparingly soluble salt decreases in the presence of a common ion. ### Acid-Base Chemistry - **Arrhenius Definition:** - Acid: Produces $H^+$ in water. - Base: Produces $OH^-$ in water. - **Brønsted-Lowry Definition:** - Acid: Proton ($H^+$) donor. - Base: Proton ($H^+$) acceptor. - Conjugate Acid-Base Pairs: $HA \rightleftharpoons H^+ + A^-$. $HA$ (acid), $A^-$ (conjugate base). - **Lewis Definition:** - Acid: Electron pair acceptor. - Base: Electron pair donor. - **pH & pOH:** - $pH = -\log[H^+]$ - $pOH = -\log[OH^-]$ - $pH + pOH = 14$ (at 25°C) - **Acid/Base Dissociation Constants:** - Weak Acid: $HA \rightleftharpoons H^+ + A^-$, $$K_a = \frac{[H^+][A^-]}{[HA]}$$ - Weak Base: $B + H_2O \rightleftharpoons BH^+ + OH^-$, $$K_b = \frac{[BH^+][OH^-]}{[B]}$$ - $K_a \cdot K_b = K_w = 1.0 \times 10^{-14}$ (for conjugate pairs at 25°C) - **Buffer Solutions:** Resist changes in pH upon addition of small amounts of acid or base. - Composed of a weak acid and its conjugate base, or a weak base and its conjugate acid. - **Henderson-Hasselbalch Equation:** $$pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)$$ $$pOH = pK_b + \log\left(\frac{[BH^+]}{[B]}\right)$$ - **Titration:** - **Equivalence Point:** Moles of acid = Moles of base. - **Indicators:** Weak organic acids/bases that change color over a specific pH range. - **Titration Curves:** Plot pH vs. volume of titrant. - Strong Acid-Strong Base: Equivalence point at pH 7. - Weak Acid-Strong Base: Equivalence point at pH > 7. Buffer region before equivalence. - Strong Acid-Weak Base: Equivalence point at pH ### Volumetric Analysis - **Titrimetry:** Quantitative chemical analysis by measuring the volume of a solution of known concentration (titrant) required to react completely with an analyte. - **Molarity (M):** Moles of solute per liter of solution. $$M = \frac{\text{moles of solute}}{\text{liters of solution}}$$ - **Dilution Equation:** $M_1V_1 = M_2V_2$ - **Standard Solution:** A solution of accurately known concentration. - **Primary Standard:** High purity, stable, soluble, high molar mass compound used to prepare standard solutions or standardize other solutions. - **Types of Titrations:** - **Acid-Base Titration:** Determines concentration of acid or base. - **Redox Titration:** Involves an oxidation-reduction reaction. - **Complexometric Titration:** Involves formation of a soluble complex (e.g., EDTA titrations). - **Precipitation Titration:** Involves formation of an insoluble precipitate (e.g., Mohr method for halides). - **Calculations:** At equivalence point, moles of analyte = moles of titrant (stoichiometrically). $$(\text{Concentration of A}) \times (\text{Volume of A}) = (\text{Concentration of B}) \times (\text{Volume of B})$$ (Adjust for stoichiometry if reaction is not 1:1) ### Gravimetric Analysis - **Definition:** A quantitative method where the amount of an analyte is determined by measuring the mass of a pure substance to which the analyte is chemically related. - **Steps:** 1. **Preparation of Solution:** Dissolve sample, adjust conditions (pH, temperature, etc.). 2. **Precipitation:** Add precipitating agent to form an insoluble compound. 3. **Digestion:** Heat the precipitate in contact with mother liquor to improve crystal size and purity. 4. **Filtration:** Separate precipitate from mother liquor. 5. **Washing:** Remove impurities from precipitate. 6. **Drying/Ignition:** Convert precipitate to a stable, weighable form. 7. **Weighing:** Measure the mass of the pure precipitate. 8. **Calculation:** Determine the amount of analyte based on the precipitate's mass and stoichiometry. - **Factors Affecting Precipitation:** - **Solubility:** Should be very low. - **Purity:** Precipitate should be free from co-precipitated impurities. - **Filterability:** Precipitate should be easily filterable. - **Calculations:** - **Gravimetric Factor (GF):** Ratio of molar mass of analyte to molar mass of precipitate, multiplied by stoichiometric coefficients. $$GF = \frac{\text{Molar Mass of Analyte}}{\text{Molar Mass of Precipitate}} \times \frac{\text{Stoichiometric Coeff. of Analyte}}{\text{Stoichiometric Coeff. of Precipitate}}$$ - **Mass of Analyte = Mass of Precipitate $\times$ GF** - **Percent Analyte = $\frac{\text{Mass of Analyte}}{\text{Mass of Sample}} \times 100\%$** ### Electrochemistry - **Electrochemical Cells:** Devices that convert chemical energy into electrical energy (voltaic/galvanic) or electrical energy into chemical energy (electrolytic). - **Components:** - **Anode:** Electrode where oxidation occurs (electron loss). - **Cathode:** Electrode where reduction occurs (electron gain). - **Salt Bridge:** Maintains charge neutrality in voltaic cells. - **Standard Electrode Potentials ($E^\circ$):** - Measured relative to the Standard Hydrogen Electrode (SHE), $E^\circ = 0.00 V$. - More positive $E^\circ$ indicates stronger oxidizing agent (more easily reduced). - More negative $E^\circ$ indicates stronger reducing agent (more easily oxidized). - **Cell Potential ($E_{cell}$):** - **Standard Cell Potential:** $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$ (using standard reduction potentials). - For a spontaneous reaction (voltaic cell), $E^\circ_{cell} > 0$. - **Gibbs Free Energy and Cell Potential:** - $\Delta G^\circ = -nFE^\circ_{cell}$ - $n$: number of moles of electrons transferred. - $F$: Faraday's constant ($96485 C/mol\ e^-$). - If $\Delta G^\circ 0$). - **Nernst Equation:** Relates cell potential under non-standard conditions to standard potential and reaction quotient ($Q$). $$E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q$$ At 25°C (298 K): $$E_{cell} = E^\circ_{cell} - \frac{0.0592}{n} \log Q$$ - **Electrolysis:** Using electrical energy to drive a non-spontaneous reaction. - **Faraday's Laws of Electrolysis:** 1. The mass of substance produced at an electrode is proportional to the quantity of electricity passed. 2. The masses of different substances produced by the same quantity of electricity are proportional to their equivalent weights. - **Quantity of Charge (Q):** $Q = I \times t$ (Coulombs = Amperes $\times$ seconds) - **Moles of electrons:** $\text{moles } e^- = \frac{Q}{F}$ - **Concentration Cells:** Voltaic cells composed of two half-cells with the same electrodes but different concentrations of ions. Drive current to equalize concentrations. ### Spectroscopy Introduction - **Definition:** Study of the interaction between matter and electromagnetic radiation. - **Electromagnetic Spectrum:** Regions of radiation (Gamma, X-ray, UV, Visible, IR, Microwave, Radio) correspond to different types of molecular transitions. - **Beer-Lambert Law:** $A = \epsilon bc$ - $A$: Absorbance (unitless) - $\epsilon$: Molar absorptivity (L mol$^{-1}$ cm$^{-1}$) - $b$: Path length (cm) - $c$: Concentration (mol L$^{-1}$) - **Transmittance (%T):** $\%T = \frac{I}{I_0} \times 100\%$, where $I$ is transmitted intensity and $I_0$ is incident intensity. - $A = -\log T = \log \frac{I_0}{I}$ - **UV-Vis Spectroscopy:** - **Principle:** Absorption of UV or visible light by molecules, causing electronic transitions. - **Applications:** Quantitative analysis (using Beer-Lambert Law), identification of functional groups (qualitative). - **Chromophore:** Part of a molecule responsible for absorbing light. - **Infrared (IR) Spectroscopy:** - **Principle:** Absorption of IR radiation causes molecular vibrations (stretching and bending). - **Applications:** Identification of functional groups in organic and inorganic compounds. - **Fingerprint Region:** Below 1500 cm$^{-1}$, unique to each compound. - **Atomic Absorption Spectroscopy (AAS):** - **Principle:** Ground state atoms absorb light at specific wavelengths, causing electronic transitions. - **Applications:** Quantitative analysis of metal ions in solutions. Highly selective and sensitive. ### Chromatography Basics - **Definition:** A separation technique based on the differential distribution of components between a stationary phase and a mobile phase. - **Key Terms:** - **Stationary Phase:** Fixed bed or layer over which the mobile phase passes. - **Mobile Phase:** Solvent that carries the sample through the stationary phase. - **Analyte:** Substance being separated. - **Eluent:** Mobile phase entering the column. - **Eluate:** Mobile phase exiting the column. - **Separation Mechanism:** - **Adsorption:** Solutes adsorb onto the surface of the stationary phase. - **Partition:** Solutes distribute between stationary and mobile phases based on solubility. - **Ion Exchange:** Solutes interact with charged sites on the stationary phase. - **Size Exclusion (Gel Filtration):** Solutes are separated by size as they pass through pores in the stationary phase. - **Chromatographic Parameters:** - **Retention Time ($t_R$):** Time taken for an analyte to pass from injection to detection. - **Dead Time ($t_M$ or $t_0$):** Time taken for an unretained component to pass through the system. - **Retention Factor ($k'$):** $k' = \frac{t_R - t_M}{t_M} = \frac{\text{moles in stationary phase}}{\text{moles in mobile phase}}$ - **Resolution ($R_s$):** Measures the extent of separation between two peaks. $$R_s = \frac{2(t_{R2} - t_{R1})}{w_1 + w_2}$$ where $w$ is the peak width. A resolution of 1.5 or greater indicates baseline separation. - **Plate Height (H) / Plate Number (N):** Measure of column efficiency. $$N = 16\left(\frac{t_R}{w}\right)^2$$ $$H = \frac{L}{N}$$ where $L$ is column length. Smaller $H$ and larger $N$ mean better efficiency. - **Types of Chromatography:** - **Gas Chromatography (GC):** Mobile phase is a gas, stationary phase is liquid or solid. Used for volatile compounds. - **Liquid Chromatography (LC):** Mobile phase is a liquid. - **High-Performance Liquid Chromatography (HPLC):** Uses high pressure to push mobile phase through column. - **Normal Phase:** Polar stationary phase, non-polar mobile phase. - **Reverse Phase:** Non-polar stationary phase, polar mobile phase (most common). - **Detectors:** UV-Vis, Refractive Index (RI), Mass Spectrometry (MS), Flame Ionization Detector (FID).