Analytical Chemistry and Chromatography Lecture Review

Comprehensive vocabulary flashcards covering basic statistics, signal-to-noise principles, theoretical plates, chromatography fundamentals, GC detectors, and HPLC separation modes.

Precision

How closely replicate measurements agree with one another, commonly assessed using standard deviation.

Accuracy

How close a measurement is to the true or accepted value.

Percent Error

A measure of accuracy calculated using the equation $\% \, \text{error} = \frac{\text{measured} - \text{true}}{\text{true}} \times 100\%$.

Confidence Limit

The estimated range around the sample mean defined by $\bar{x} \pm \frac{t s}{\sqrt{N}}$, where $\bar{x}$ is the sample mean, $s$ is standard deviation, $N$ is the number of measurements, and $t$ is the confidence parameter.

Molarity (M)

A concentration unit expressed as moles of solute per liter of solution ($M = \frac{\text{mol solute}}{\text{L solution}}$), which is directly affected by temperature-related volume changes.

Molality (m)

A concentration unit expressed as moles of solute per kilogram of solvent ($m = \frac{\text{mol solute}}{\text{kg solvent}}$), which is independent of temperature changes.

Weight Percent (% w/w)

Concentration calculated as $\% \, \text{w/w} = \frac{\text{mass solute}}{\text{mass solution}} \times 100\%$.

Volume Percent (% v/v)

Concentration calculated as $\% \, \text{v/v} = \frac{\text{volume solute}}{\text{volume solution}} \times 100\%$.

Mole Fraction ($X_i$)

The fraction of total moles contributed by a particular component, given by $X_i = \frac{n_i}{\sum n}$, where the sum of all mole fractions in a mixture equals $1$.

Parts per Million (ppm)

A concentration unit representing approximately $1$ part analyte per $10^6$ parts mixture, equivalent to $1000\,\text{ppb}$.

Parts per Billion (ppb)

A concentration unit representing approximately $1$ part analyte per $10^9$ parts mixture.

Signal-to-Noise Ratio (S/N)

A parameter indicating measurement quality defined as $\text{S/N} = \frac{\text{mean analyte signal}}{\sigma_{\text{noise}}}$, where a value of $2\text{--}3$ or greater is generally desirable.

Peak-to-Peak Noise Estimation

A visual method to estimate noise standard deviation from a trace using $\sigma_{\text{noise}} \approx \frac{\text{maximum} - \text{minimum}}{5}$, assuming Gaussian noise.

Gaussian Distribution

A normal probability distribution commonly describing random noise, where $\pm 1\sigma$ contains $68.3\%$, $\pm 2\sigma$ contains $95.5\%$, $\pm 2.58\sigma$ contains $99\%$, and $\pm 3\sigma$ contains $99.7\%$ of measurements.

Full Width at Half Maximum (FWHM)

The width of a Gaussian peak measured at half its maximum height, related to standard deviation by $\text{FWHM} = 2.335\sigma$.

Chemical Noise

Noise caused by uncontrollable environmental variables affecting the chemical system, such as temperature and pressure fluctuations or chemical interferences.

Thermal (Johnson) Noise

Instrumental noise caused by the random movement of electrons in electronic components such as resistors and capacitors.

Shot Noise

Instrumental noise caused by random fluctuations in photons reaching a detector or electrons generated in a semiconductor, particularly important in low-signal applications.

Flicker Noise

Low-frequency instrumental noise or drift whose magnitude is inversely proportional to frequency ($1/f$ noise).

Environmental Noise

Instrumental noise arising from external surroundings picked up by instrument components acting like antennas, such as nearby radio frequencies.

Signal Averaging

A noise-reduction technique of taking $N$ independent measurements and averaging them, improving $\text{S/N}$ by a factor of $\sqrt{N}$ while reducing noise standard deviation as $\frac{1}{\sqrt{N}}$.

Ensemble Averaging

A signal-averaging method where successive data sets are co-added point-by-point, averaging the $y$-values at each $x$-value across measurements.

Boxcar Averaging

A smoothing technique where non-overlapping windows of $N$ adjacent data points are averaged into single points, reducing the plotted points to roughly $\frac{1}{N}$ of the original.

Moving Average

A running average technique where a window of $N$ points overlaps and moves through the data set one point at a time.

Instrumental Sensitivity

The quantitative response of an instrument represented mathematically by the slope of the response vs. concentration calibration curve.

Limit of Detection (LOD)

The smallest concentration that can be reliably measured at a specified confidence level, calculated as $\text{LOD signal} = \text{average blank signal} + 3\sigma_{\text{blank}}$.

Limit of Quantification (LOQ)

The smallest amount of analyte that can be reliably quantified, calculated as $\text{LOQ signal} = \text{average blank signal} + 10\sigma_{\text{blank}}$.

Dynamic Range

The concentration region over which a linear calibration curve can be used for quantitative analysis.

Selectivity

The extent to which an analytical technique can distinguish and quantify a target analyte in the presence of interfering compounds.

Distribution Coefficient ($K_c$)

The equilibrium ratio describing analyte distribution between stationary and mobile phases, given by $K_c = \frac{[X]_{\text{stationary}}}{[X]_{\text{mobile}}}$.

Dead Time ($t_m$)

The time required for the mobile phase (or an unretained solute) to traverse the chromatographic column.

Adsorption Chromatography

A separation technique where the stationary phase is a solid and analytes adsorb onto its surface (e.g., TLC, column chromatography).

Partition Chromatography

A separation technique where the stationary phase is a liquid supported on a solid, and analytes dissolve/partition into it.

Ion-Exchange Chromatography

A separation technique using a liquid mobile phase and a stationary resin with charged side groups to separate ionic analytes.

Size-Exclusion Chromatography

A chromatographic method using a porous polymer stationary phase that separates analytes based on molecular size/weight, where larger molecules elute first.

Theoretical Plate Number ($N$)

A measure of chromatographic column efficiency given by $N = 16\left(\frac{t_r}{w_b}\right)^2$, where $t_r$ is retention time and $w_b$ is baseline peak width.

Height Equivalent to a Theoretical Plate (HETP)

A column-length normalized measure of separation efficiency defined as $H = \frac{L}{N}$, where a smaller $H$ represents a more efficient column.

Van Deemter Equation

An equation modeling plate height as a function of average linear velocity $\bar{u}$: $H = A + \frac{B}{\bar{u}} + C\bar{u}$.

Eddy Diffusion ($A$ Term)

Band broadening caused by analyte molecules taking multiple different paths through packed stationary-phase material, independent of flow velocity.

Longitudinal Diffusion ($B$ Term)

Band broadening caused by axial diffusion of analyte molecules along the length of the column from high to low concentration regions, represented as $\frac{B}{\bar{u}}$.

Mass-Transfer Broadening ($C$ Term)

Band broadening resulting from finite equilibration times between mobile and stationary phases, represented as $C\bar{u}$.

Retention Factor ($k$)

A measure of analyte retention relative to mobile phase given by $k = \frac{t_r - t_m}{t_m} = \frac{t_r'}{t_m}$.

Chromatographic Resolution ($R_s$)

Quantitative degree of separation between two adjacent peaks, defined as $R_s = \frac{t_{r,2} - t_{r,1}}{\frac{1}{2}(w_1 + w_2)}$, where $R_s \approx 1.5$ indicates baseline resolution.

Selectivity Factor ($\alpha$)

The ratio of adjusted retention times or retention factors of two compounds, given by $\alpha = \frac{t_{r,2}'}{t_{r,1}'} = \frac{k_2}{k_1}$.

Gas Chromatography (GC)

An analytical separation technique requiring volatile compounds and a gas mobile phase (carrier gas) with purity $\ge 99.99\%$.

Open Tubular Column

A fused-silica capillary GC column without solid packing, having stationary phase coated directly on its inner wall, offering high efficiency due to minimal eddy diffusion ($A \approx 0$).

Thermal Conductivity Detector (TCD)

A universal, non-destructive GC detector with poor sensitivity that measures resistivity changes in a heated wire.

Flame Ionization Detector (FID)

The most widely used GC detector, which burns analytes in an $H_2/\text{air}$ flame to produce measurable ion currents; it is sensitive, destructive, and nearly universal for organic compounds.

Electron Capture Detector (ECD)

A selective, destructive GC detector using a $^{63}\text{Ni}$ radioactive source to detect electronegative compounds such as halogens, $NO_2$, and phosphorus.

Flame Photometric Detector (FPD)

A selective, destructive GC detector that measures photon emissions from flame combustion products, highly selective for sulfur ($S$) and phosphorus ($P$).

Mass Spectrometric Detector (MS)

A destructive GC detector that ionizes analytes via electron impact (EI) and separates them by mass-to-charge ratio ($m/z$), providing qualitative structural information.

Temperature-Programmed GC

A GC separation mode where oven temperature is deliberately ramped during the run to elute less volatile compounds efficiently.

Normal-Phase LC

Liquid chromatography featuring a polar stationary phase (e.g., $SiO_2$) and a nonpolar mobile phase (e.g., hexane), where nonpolar analytes elute first.

Reverse-Phase LC

Liquid chromatography featuring a nonpolar stationary phase (e.g., $C18$) and a polar mobile phase (e.g., $H_2O$, $CH_3CN$), where polar analytes elute first.

Gradient Elution

Deliberately changing mobile-phase solvent composition during an LC run to optimize separation time and resolution.

Refractive Index Detector (RI)

The most universal HPLC detector, which measures refractive index changes non-destructively but cannot be used with solvent gradients.

UV-Visible Absorption Detector

A sensitive, non-destructive HPLC detector that measures light absorption governed by Beer-Lambert's law ($A = \epsilon b c$).

Fluorescence Detector

A highly sensitive and selective non-destructive HPLC detector that measures emitted photons following excitation, often enhanced using fluorescence tagging.