Analytical Chemistry 2 (CH4304

Cheatsheet Content

### Solvent Extraction Basics - **Definition**: Transfer of a solute from one liquid phase to another immiscible liquid phase (e.g., water and organic solvent). Also known as liquid-liquid extraction or partitioning. - **Purpose**: Purify samples, remove interferences, or separate compounds prior to analysis. - **Equilibrium**: $A_{aq} \rightleftharpoons A_{org}$ - **Partition Coefficient (K)**: Equilibrium constant describing solute distribution between two immiscible phases. $$K = \frac{[S]_{phase 2}}{[S]_{phase 1}}$$ - **Extraction Efficiency (q)**: Fraction of solute remaining in the original phase after extraction. $$q = \frac{V_1}{V_1 + KV_2}$$ - $V_1$: volume of original phase - $V_2$: volume of extracting phase - **Multiple Extractions**: More efficient than a single large extraction. After $n$ extractions: $$q_n = \left(\frac{V_1}{V_1 + KV_2}\right)^n$$ ### Effect of pH on Solvent Extraction - **Weak Acids/Bases**: Distribution is pH dependent. - **Distribution Coefficient (D)**: Used when a solute exists in more than one chemical form (e.g., HA and A-). $$D = \frac{\text{total conc. in phase 2}}{\text{total conc. in phase 1}}$$ - **Weak Acid Extraction (HA)**: $HA \rightleftharpoons H^+ + A^-$ - Assuming HA is soluble in the organic phase, and HA and A- are soluble in the aqueous phase. $$D = \frac{K}{1 + \frac{K_a}{[H^+]}} = \frac{K[H^+]}{K_a + [H^+]}$$ - More soluble in organic phase at low pH (HA form). More soluble in aqueous phase at high pH (A- form). - **Weak Base Extraction (B)**: $B + H_2O \rightleftharpoons BH^+ + OH^-$ - Assuming B is soluble in both phases, and BH+ is soluble only in the aqueous phase. $$D = \frac{K}{1 + \frac{[H^+]}{K_a}} = \frac{KK_a}{K_a + [H^+]}$$ - More soluble in organic phase at high pH (B form). More soluble in aqueous phase at low pH (BH+ form). - **General Rule**: To extract a base into water, reduce pH. To extract an acid into water, elevate pH. ### Metal Ion Chelate Extraction - **Principle**: Selectively extract metal ions into an organic solvent by chelation with organic ligands (e.g., oxine, cupferon, dithizone). - **Ligands**: Behave as weak acids (HL), losing a proton when binding to a metal ion: $nL^-_{(aq)} + M^{n+}_{(aq)} \rightleftharpoons ML_{n(aq)}$ - **Assumptions**: - All metal in aqueous phase is $M^{n+}$. - All metal in organic phase is $ML_n$. - **Distribution Coefficient (D)**: $$D = \frac{\text{total metal}_{org}}{\text{total metal}_{aq}} \approx \frac{[ML_n]_{org}}{[M^{n+}]_{aq}}$$ - **Equation for D**: $$D = K_m \beta \left(\frac{K_a}{[H^+]_{aq}}\right)^n \left(\frac{[HL]_{org}}{K_L}\right)^n$$ where: - $K_m$: Partition coefficient for the metal-ligand complex ($ML_n$) - $\beta$: Formation constant of the metal-ligand complex - $K_a$: Acid dissociation constant of the ligand (HL) - $[HL]_{org}$: Concentration of the ligand in the organic phase - $K_L$: Partition coefficient for the ligand (HL) - **Control**: Distribution depends on pH ($[H^+]$) and ligand concentration ($[HL]_{org}$). ### Countercurrent Extraction - **Process**: Serial extraction process involving repeated partitioning of solutes between two liquid phases. - **Objective**: Separate two or more solutes with different distribution coefficients ($D_A \neq D_B$). - **Theoretical Distribution**: After $n$ transfers/equilibration cycles, the fraction of solute $f$ in each tube $r$ is given by the binomial expansion $(q+p)^n$, where $p$ is the fraction in the mobile (upper) phase and $q$ is the fraction in the stationary (lower) phase ($p = D/(1+D)$ and $q = 1/(1+D)$). $$f = \frac{n!}{r!(n-r)!} p^r q^{n-r}$$ - **Maximum Amount (rmax)**: For large $n$, the tube containing the maximum amount of solute is $r_{max} = np$. - **Bandwidth and Resolution**: - **Bandwidth**: How broadly each solute is distributed. - **Resolution**: How well $r_{max,A}$ and $r_{max,B}$ are separated. - **Gaussian Approximation**: For large $n$, the distribution approximates a Gaussian curve with standard deviation $\sigma = \sqrt{npq}$. $$f \approx \frac{1}{\sqrt{2\pi npq}} e^{-(r-np)^2 / (2npq)}$$ ### Continuous Extraction - **Purpose**: Efficiently remove solutes when many extractions are needed, or when a solute is difficult to extract. - **Advantages**: Uses small amount of solvent, high percent recovery, can run unattended. - **Soxhlet Extractor**: Example for continuous extraction of solids. ### Solid Phase Extraction (SPE) - **Purpose**: Sample preparation method for removing interfering matrices, selective enrichment, and isolation of analytes. - **Enrichment**: 100 to 5000 possible. ### Supercritical Fluid Extraction (SFE) - **Supercritical Fluid**: Substance above its critical temperature and pressure, exhibiting properties between a gas and a liquid. - **Critical Point**: Point on a phase diagram where liquid and gas phases become indistinguishable. - **Triple Point**: Point where solid, liquid, and gas phases coexist in equilibrium. - **Supercritical CO2**: Common SFE solvent (Critical Point: 31.25 °C; 73.9 bar). ### Chromatography Introduction - **Definition**: Physical method of separation where components distribute between a stationary phase (solid or liquid bonded to solid) and a mobile phase (liquid or gas). - **Principle**: Solutes separate based on differential interaction/affinity with stationary and mobile phases. - **Types**: - **Column Chromatography**: Stationary phase packed in a column. - **Planar Chromatography (TLC)**: Stationary phase on a flat surface. - **Theoretical Plate (N)**: Each section of the column where equilibrium is assumed to be achieved. - **Height Equivalent of Theoretical Plate (HETP or H)**: Length of column corresponding to one theoretical plate. Smaller H means more efficient separation. - **Distribution Coefficient (D)**: The larger D, the longer the solute spends in the stationary phase. - **Chromatogram**: Graph showing detector response vs. elution time. - **Retention Time ($t_R$)**: Time for a compound to elute. - **Void Time ($t_M$)**: Time for an unretained solute (or mobile phase) to travel through the column. - **Adjusted Retention Time ($t'_R$)**: $t'_R = t_R - t_M$ (additional time spent in stationary phase). - **Capacity Factor (k')**: Measure of solute retention. $$k' = \frac{t'_R}{t_M} = \frac{\text{moles of solute in stationary phase}}{\text{moles of solute in mobile phase}} = K \frac{V_S}{V_M}$$ - $K$: Partition coefficient, $V_S$: volume of stationary phase, $V_M$: volume of mobile phase. - Good separation generally requires $k'$ between 0.5 and 20. - **Separation Factor ($\alpha$)**: Measure of efficiency in separating two solutes. $$\alpha = \frac{k'_2}{k'_1} = \frac{t'_{R2}}{t'_{R1}}$$ - $\alpha > 1$ for separation. Greater $\alpha$ means better separation. ### Chromatography Sorption Mechanisms 1. **Adsorption Chromatography**: Solute and solvent molecules compete for active sites on an adsorbent (solid stationary phase). 2. **Partition Chromatography**: Solute partitions between a liquid stationary phase and a mobile phase (gas or liquid). - **Normal Phase**: Polar stationary phase, non-polar mobile phase. Separates polar compounds. - **Reverse Phase**: Non-polar stationary phase, polar mobile phase. Separates non-polar compounds (most common). 3. **Ion Exchange Chromatography**: Involves substitution of one ionic species for another. Stationary phase is a rigid matrix with charged sites. 4. **Size Exclusion Chromatography**: Separates molecules by molecular weight/size. Large molecules elute first. 5. **Affinity Chromatography**: Specific binding between a solute and a ligand immobilized on the stationary phase. ### Chromatography Efficiency & Resolution - **Separation Efficiency**: How well solutes are separated, influenced by peak shapes/widths and difference in elution times ($\Delta t_R$). - **Resolution (R)**: Quantitative measure of separation. $$R = \frac{\Delta t_R}{w_{av}} = \frac{2(t_{R2} - t_{R1})}{w_{b2} + w_{b1}}$$ - $\Delta t_R = t_{R2} - t_{R1}$ - $w_{av}$: average peak width (at base, $w_b$). - Baseline resolution ($R \ge 1.5$) means peaks are well separated. - **Band Spreading/Broadening**: Major cause of poor resolution. Analyte band expands as it travels through the column. - Caused by diffusion (Fick's Law). - $D$: Diffusion coefficient. - **Column Efficiency (N)**: Number of theoretical plates. $$N = \frac{L}{H} = 16 \left(\frac{t_R}{w_b}\right)^2 = 5.54 \left(\frac{t_R}{w_{1/2}}\right)^2$$ - $L$: column length, $w_b$: peak width at base, $w_{1/2}$: peak width at half-height. - A higher N (or lower H) indicates better column efficiency. - **Purnell Equation (Resolution & N)**: $$R = \frac{\sqrt{N}}{4} \left(\frac{\alpha - 1}{\alpha}\right) \left(\frac{k'_2}{1 + k'_2}\right)$$ - Doubling column length improves resolution by $\sqrt{2}$. - **Asymmetric Peaks**: Efficiency can be estimated using Foley-Dorsey equation for tailed peaks. ### Van Deemter Equation - **Purpose**: Relates plate height (H) to mobile phase flow rate ($u_x$), explaining band broadening. $$H = A + \frac{B}{u_x} + C u_x$$ - **A (Eddy Diffusion)**: Due to multiple paths through packed bed. Minimized by uniform, small packing particles. - **B (Longitudinal Diffusion)**: Solute diffuses from high to low concentration. Minimized by faster flow rates. - **C (Mass Transfer Resistance)**: Solute equilibrates slowly between mobile and stationary phases. Minimized by slower flow rates and small particle sizes. - **Optimum Flow Rate**: There is an optimum flow rate for maximum efficiency (minimum H). - **Conclusions**: Uniformly packed columns with small particles reduce A and C terms. ### Gas Chromatography (GC) - **Principle**: Separates volatile organic compounds. Sample must be thermally stable and volatile. - **Components**: 1. **Carrier Gas**: Inert (N2, He, Ar, H2). Influences separation efficiency and detector. H2 is good due to low viscosity and low HETP over wide flow rates. 2. **Injector**: Heats, vaporizes, and mixes sample with carrier gas before column. - **Flash Vaporizer Port**: Common injection method using microsyringe. - **Split/Splitless Injection**: For capillary columns with low flow rates. - **Split Mode**: For high concentration analytes (>0.1%), a fraction enters column, rest vented. - **Splitless Mode**: For trace analytes ( $250,000 theoretical plates). - **Types**: WCOT (wall coated open tubular), SCOT (support coated open tubular), PLOT (porous layer open tubular). - **Advantages**: Higher resolution, shorter analysis time, greater sensitivity. - **Film Thickness**: Decreasing thickness increases plate height, shortens retention, reduces capacity. - **Stationary Phase Selection**: "Like dissolves like." Polar stationary phases for polar solutes, non-polar for non-polar. 4. **Detectors**: Measure eluates. - **Requirements**: High sensitivity, rapid response, wide linear range, stable, insensitive to T/P/flow. - **Thermal Conductivity Detector (TCD)**: Universal, responds to all analytes. Less sensitive. Based on differences in thermal conductivity of gas mixtures. - **Flame Ionization Detector (FID)**: Universal for organic compounds. High sensitivity. Eluate burned, producing ions that generate current. - **Nitrogen Phosphorous Detector (NPD)**: Specific for N or P containing compounds. Modified FID. - **Electron Capture Detector (ECD)**: Selective for electronegative compounds (halogens, nitriles). High sensitivity (ppt range). Uses radioactive source. ### GC: Developing a Chromatogram - **Factors Affecting Retention**: - **Column Temperature**: Increased temperature reduces retention times. - **Temperature Programming**: Changing column temperature during separation optimizes separation, especially for complex mixtures with wide boiling point ranges. - **Film Thickness & Column Diameter**: Affect relative amount of phases. - **Column Length**: Affects number of plates ($N$), $R \propto \sqrt{N}$. - **Qualitative Analysis**: Direct comparison of retention time with standards. - **Retention Indices (Kovats Index)**: Assigns standard retention value for compound identification using n-alkanes as standards. $$KI = 100\left\{n + (N-n) \frac{\log t'_R(\text{unknown}) - \log t'_R(n)}{\log t'_R(N) - \log t'_R(n)}\right\}$$ - $n$: # C atoms in smaller alkane, $N$: # C atoms in larger alkane. - **Quantitative Analysis**: - **Peak Area Normalization**: %A = (Peak area A / Sum of all peak areas) * 100. - **Response Factor ($F_x$)**: Corrects for detector response differences. - **Internal Standard Method**: Adds a known amount of internal standard to sample and standards to correct for injection volume variations. ### Liquid Chromatography (HPLC) - **Principle**: Separates compounds based on partitioning between stationary and mobile liquid phases. No vaporization needed. - **HPLC vs. GC**: - **Sample Volatility**: HPLC (no volatility req.), GC (volatile). - **Sample Polarity**: HPLC (polar/non-polar/ions), GC (volatile non-polar/polar). - **Thermal Lability**: HPLC (can be analyzed at/below room T), GC (must survive high T). - **Molecular Weight**: HPLC (no theoretical upper limit), GC ( ### HPLC Method Development - **Attributes of a New Method**: Adequate resolution, short run times, robust/rugged. - **Criteria for Separation**: - $0.5 \le k' \le 20$. If $k'$ too high, use gradient elution. - Resolution ($R$) > 2 (minimum 1.5 for adequate quantitation). - Operating pressure $\le$ 15 MPa. - Peak asymmetry factor ### Ion Exchange Chromatography (IC) - **Principle**: Separates ionic compounds using an ion exchange resin as stationary phase. - **Mechanism**: Reversible exchange between analyte ions and counterions in the mobile phase. Retention depends on charge density. - **Stationary Phase**: Polystyrene resins (styrene and divinylbenzene copolymer). - **Anion Exchangers**: Contain bound positive groups (e.g., $-NR_3^+$). Binds anions. - **Cation Exchangers**: Contain bound negative groups (e.g., $-SO_3^-$). Binds cations. - **Selectivity**: Ion exchangers favor binding of ions with higher charge, decreased hydrated radius, and increased polarizability. Selectivity increases with crosslinking. - **Elution**: A buffer with countercharged ions is used to displace and elute the molecule of interest. - **Instrumentation**: Similar to HPLC, but components are inert to corrosive mobile phases. - **Detectors**: UV-Vis, but most commonly conductivity detectors (measure electrical resistance changes). - **Ion Suppressors**: Devices (e.g., membranes) used to reduce high mobile phase conductivity, improving detector signal. ### Thermal Analysis - **Definition**: Group of methods where a physical property of a sample is measured as a function of temperature under a controlled temperature change. - **Types of Thermal Events**: Phase transition, adsorption/desorption, sublimation, melting/freezing, thermal decomposition, glass transition, dissolution, oxidation/combustion. - **General Instrument**: Temperature programmer (X-axis) and property measurement (Y-axis). - **Techniques Covered**: - **Thermogravimetric Analysis (TGA)**: Measures weight loss. - **Differential Thermal Analysis (DTA)**: Measures temperature difference. - **Differential Scanning Calorimetry (DSC)**: Measures heat flow difference. ### Thermogravimetric Analysis (TGA) - **Principle**: Measures mass of a substance as a function of temperature (or time) under a controlled temperature program. - **Instrumentation**: 1. **Balance**: Electronic microbalance. 2. **Heating Device**: Furnace. 3. **Temperature Programmer**: Controls heating/cooling rate (linear, isothermal, combined). 4. **Measurement Device**: Records mass changes and temperature. 5. **Atmosphere Control**: Inert (He, N2) for decomposition, oxidative (air, O2) for combustion. - **What TGA Detects**: Physical changes (sublimation, vaporization, adsorption, desorption) and chemical changes (decomposition, gas evolution). - **Optimum Conditions**: Few mg sample, thin layer, open container, inert gas flow, slow heating rate. - **Factors Affecting Results**: Sample mass, particle size, packing, heating rate, atmosphere, furnace geometry, pan material. - **Applications**: - Evaluate thermal decomposition and stability of materials. - Determine bulk composition: thermal oxidation, heat resistance, residual water/solvents, ash content, inorganic filler quantity. - **Derivative Thermogravimetry (DTG)**: Plots rate of change in mass ($dM/dt$) vs. temperature. Resolves changes more clearly. ### Differential Thermal Analysis (DTA) - **Principle**: Measures temperature difference ($\Delta T$) between a sample and an inert reference material as they are subjected to a controlled temperature program. - **Instrumentation**: Sample and reference (typically 0$, peak upwards/downwards depending on convention). - **Endothermic Processes**: Absorb heat ($\Delta T ### Differential Scanning Calorimetry (DSC) - **Principle**: Measures differences in heat flow into a sample and a reference as a function of sample temperature under a controlled temperature program. - **Difference from DTA**: DSC is calorimetric (measures energy differences/heat flow), DTA measures temperature differences. - **Types of Instruments**: - **Heat Flux Device**: More common, stable baseline. Measures difference in heat flow directly. - **Power Compensation Device**: Better resolution, faster heating/cooling. Supplies power to sample/reference heaters to maintain identical temperatures. - **Heat Capacity Measurement**: Baseline change in DSC indicates changes in heat capacity ($h \propto C_p$). - **Other Uses**: Oxidation temperatures, phase diagrams of liquid crystals, thermal conductivity, purity of pharmaceuticals. ### Multiple Techniques in Thermal Analysis - **Evolved Gas Detection (EGD) / Evolved Gas Analysis (EGA)**: When interfaced with TGA/DSC, identifies and quantifies gases evolved during heating. - **Modular Instruments**: Most thermal analysis instruments are modular, allowing simultaneous measurement of multiple properties (e.g., TG-DTG-DTA, TGA-DSC). ### Mass Spectrometry Basics - **Principle**: Measures mass-to-charge ratio ($m/z$) of ions to identify and quantify compounds. - **Components**: 1. **Ionization Source**: Creates ions from sample (e.g., MALDI, Electron Impact, Chemical Ionization). 2. **Mass Analyzer**: Separates ions based on $m/z$. 3. **Detector**: Measures abundance of separated ions. - **Key Specifications**: Resolution, mass measurement accuracy, sensitivity. - **Resolution (R)**: Ability to separate two ions with similar $m/z$. $R = m / \Delta m$. Higher R means better separation. - High resolution spectrometers can distinguish molecules with similar nominal masses but different exact masses (e.g., N vs. O). ### Magnetic Sector Analyzer (MSA) - **Principle**: Ions are accelerated by a voltage (V), then deflected by a magnetic field (B). Only ions with a specific $m/z$ ratio follow a curved path of radius (r) to reach the detector. - **Equations**: 1. **Kinetic Energy**: $\frac{1}{2}mv^2 = zV$ 2. **Magnetic Force**: $Bzv = \frac{mv^2}{r}$ 3. **Mass Spectrometer Equation**: $\frac{m}{z} = \frac{B^2 r^2}{2V}$ - **Operation**: Can vary V (voltage scanning) or B (magnetic scanning) to scan $m/z$. - **Limitations**: Single focusing MSAs have limited resolution (up to ~5000) because not all ions of the same $m/z$ have identical kinetic energies (due to thermal energy, source inhomogeneity). ### Double Focusing Mass Analyzer - **Purpose**: To improve resolution by focusing ions w.r.t. their velocities. - **Components**: 1. **Electrostatic Analyzer (ESA)**: Filters ions based on kinetic energy. Only ions with a specific kinetic energy pass through. - Ions are deflected by an electric field (E). Radius of curvature (R) is $R = \frac{2V}{E}$. - For constant V and E, only ions of a single kinetic energy can exit the ESA. 2. **Magnetic Sector**: Separates the kinetic-energy-filtered ions based on $m/z$. - **Result**: Achieves very high resolution (up to 100,000). ### Quadrupole Mass Analyzer (QMA) - **Principle**: Uses oscillating electric fields to stabilize/destabilize ions, allowing only ions within a narrow $m/z$ range to pass through to the detector. - **Components**: Four parallel rods. Opposite rods are electrically connected (DC voltage + variable RF AC potentials). - **How it Works**: - Ions are accelerated (5-15V) into the space between rods. - The AC potential preferentially oscillates lighter ions. - The DC potential preferentially stabilizes heavier ions. - The combination of AC and DC potentials acts as a narrow mass-pass filter. - **Advantages**: - Cheap, rugged, light, compact (benchtop instruments). - Fast scanning (suitable for GC-MS, LC-MS). - Linear mass scale. - Microprocessor control. - **Limitations**: Lower resolution compared to magnetic sector (~5000), but sufficient for most volatile GC-MS analytes (MW