Calculate results from titrations and gravimetry, compare methods statistically, read chromatograms and spectra, validate methods to ICH Q2, plan sampling, and work in GMP, GLP, EPA and ISO 17025 labs.

Analytical Chemistry Methods

## Why it matters

Chromatography separates mixtures so each component can be measured on its own. **High-performance liquid chromatography (HPLC)** is the most used quantitative technique in pharmaceutical QC: assay, impurities, dissolution and stability testing all run on it. **Gas chromatography (GC)** does the same for volatile compounds: residual solvents, fuels, flavors, environmental pollutants. The basics of how a column separates were covered in `lab-techniques-instrumentation`. This lesson is about what an analyst does every day: **read a chromatogram, check that the system is suitable, and integrate peaks correctly.**

> **Scope.** Instrument operation, solvents and gases are hazardous and are learned on the job or in a teaching lab with supervision. The activity uses simulated data only.

## The instruments in one paragraph each

- **HPLC:** a pump pushes a liquid mobile phase at high pressure through a packed column. The sample is injected by an autosampler. Components interact differently with the stationary phase (most often C18, reversed phase) and leave the column at different **retention times**. A detector (UV-Vis diode array is the most common; also fluorescence, refractive index, or a mass spectrometer) records signal vs time.
- **GC:** the sample is vaporized in a hot inlet and carried by an inert gas (helium, hydrogen or nitrogen) through a long, thin capillary column inside an oven. Temperature programming speeds elution of high-boiling compounds. Common detectors: flame ionization (FID) for organics, electron capture for halogenated compounds, and mass spectrometry.

## Reading a chromatogram

- **Retention time (t_R):** identifies a peak by comparison with a reference standard run under the same conditions. Retention time alone does not prove identity; a diode-array spectrum or MS adds confidence.
- **Peak area:** proportional to the amount of compound, which is why it is the basis of quantitation. Peak height is used sometimes, but area is more robust.
- **Resolution (Rs):** how well two neighboring peaks are separated: Rs = 2 (t_R2 - t_R1) / (w1 + w2), where w is the baseline peak width (about 4 standard deviations for a Gaussian peak). **Rs of at least 1.5** means baseline separation and is a common requirement.
- **Tailing factor:** asymmetry. A peak with a long tail integrates less reliably; many methods require a tailing factor at most 2.
- **Plate count (N):** column efficiency. Higher N gives sharper peaks.

These go into **system suitability**: before samples are run, a standard is injected and Rs, tailing, plate count and the RSD of replicate injections must meet the method's criteria. If system suitability fails, no sample results are valid.

## Peak integration

The chromatography data system (CDS) finds where each peak starts and ends, draws a **baseline**, and calculates the area between the signal and the baseline. Numerically this is the **trapezoidal rule**: for adjacent points (t_i, y_i) and (t_i+1, y_i+1), the area slice is (y_i + y_i+1) / 2 x (t_i+1 - t_i), summed over the peak.

Baselines are where judgement comes in:

- **Drop-line (perpendicular) split:** two overlapping peaks are separated by a vertical line at the valley.
- **Valley-to-valley:** the baseline follows the valleys, which removes a small peak riding on a larger one.
- **Tangent skim:** a small peak on the tail of a large one is skimmed off with a tangent line.

The integration events (threshold, peak width, baseline type) are part of the **validated method**. Changing them per injection to get a desired result is **manual integration**, which regulators scrutinize closely as a data-integrity risk. Any manual integration must be justified, documented and reviewed.

## Worked example: area percent

A simulated chromatogram has a constant baseline of 2 mAU and two Gaussian peaks:

| Peak | t_R (min) | Height (mAU) | sigma (min) |
|---|---|---|---|
| A | 3.00 | 50 | 0.10 |
| B | 5.00 | 80 | 0.15 |

For a Gaussian, area = height x sigma x sqrt(2 pi):

- A: 50 x 0.10 x 2.507 = **12.53 mAU x min**
- B: 80 x 0.15 x 2.507 = **30.08 mAU x min**
- Area % of A = 12.53 / (12.53 + 30.08) x 100 = **29.4 %**
- Resolution: widths are 0.40 and 0.60 min, so Rs = 2 x 2.00 / 1.00 = **4.0** (well separated)

Area percent assumes every component gives the same detector response, which is rarely true. Real assays use **external standard** calibration (compare sample area with a reference standard's area) or an **internal standard** (ratio of analyte area to a compound added at a fixed amount), which corrects for injection-volume variation.

## Common mistakes

- Identifying a peak by retention time alone when a co-eluting impurity is possible.
- Running samples after system suitability fails.
- Integrating with a baseline drawn through noise or a drifting baseline.
- Changing integration parameters for one injection without documentation.
- Reporting area percent as if it were a weight percent.

## Quick recap

- HPLC for non-volatile compounds; GC for volatile ones. Both give peaks vs time.
- Retention time identifies (with a standard); area quantifies.
- System suitability (Rs, tailing, plates, replicate RSD) must pass before samples count.
- Integration is the trapezoidal sum above a baseline; integration rules are part of the validated method.

## Try it

Open the **Do** tab. A NumPy integrator is written except for the trapezoidal sum.


Read a chromatogram, check system suitability and integrate peaks with the trapezoidal rule.

HPLC and GC in practice

Quickly Understand High Performance Liquid Chromatography (HPLC)

Chromatography Theory Chapter 4, Part 1- Peak Integration and Detection

## Why it matters

Mass spectrometry (MS) measures the **mass-to-charge ratio (m/z)** of ions. It identifies unknown compounds, confirms the identity of peaks in a chromatogram, and, as LC-MS/MS, quantifies drugs, pesticides, metabolites and proteins at trace levels with high selectivity. It is now standard equipment in pharmaceutical, environmental, forensic, clinical and biochemistry labs, so analysts are expected to read a simple spectrum even if they do not run the instrument.

## The core idea: ionize, separate, detect

1. **Ion source:** turns molecules into gas-phase ions.
   - **Electron ionization (EI)**, used with GC: a 70 eV electron beam knocks out an electron, giving the **molecular ion M+.** and many reproducible **fragments**. EI spectra can be matched against libraries such as NIST's.
   - **Electrospray ionization (ESI)**, used with LC: a "soft" method that usually gives **[M+H]+** (positive mode) or **[M-H]-** (negative mode) with little fragmentation. Large molecules such as proteins pick up many charges.
2. **Mass analyser:** separates ions by m/z.
   - **Quadrupole:** a mass filter; robust and quantitative. Triple quadrupoles (QqQ) are the workhorse of LC-MS/MS quantitation.
   - **Time-of-flight (TOF):** measures flight time; high resolution and accurate mass.
   - **Orbitrap** and FT-ICR: very high resolution and mass accuracy.
3. **Detector:** counts ions. The **spectrum** plots relative abundance against m/z. The tallest peak is the **base peak** (set to 100 %).

## Reading a simple EI spectrum

- **Molecular ion:** usually the highest-m/z peak in the cluster (if it survives). Its m/z gives the molecular mass (for singly charged ions, m/z = mass).
- **Nitrogen rule:** an odd molecular mass suggests an odd number of nitrogen atoms.
- **Isotope patterns:**
  - Chlorine (35Cl and 37Cl about 3:1) gives an **M+2** peak about one third the height of M.
  - Bromine (79Br and 81Br about 1:1) gives M and M+2 peaks of nearly **equal** height.
  - Carbon-13 gives a small M+1 peak, about 1.1 % per carbon atom.
- **Fragments:** losses from M point to structure: M - 15 (loss of CH3), M - 18 (water, from alcohols), M - 29 (CHO or C2H5), M - 45 (COOH). Common fragment ions include m/z 43 (CH3CO+ or C3H7+), 77 (phenyl, C6H5+) and 91 (tropylium, C7H7+, typical of benzyl groups).

## Worked example: two unknowns

**Unknown 1** shows peaks at m/z 156 and 158 of almost equal height, and a base peak at 77.

- Equal M and M+2: one **bromine**.
- 77: a phenyl group.
- 156 - 79 = 77, so the molecule is **bromobenzene**, C6H5Br.

**Unknown 2** (ESI positive mode) shows a strong peak at m/z 152.07.

- In ESI the main ion is usually [M+H]+, so the neutral mass is about 151.06.
- Paracetamol (acetaminophen), C8H9NO2, has a monoisotopic mass of 151.063: a plausible match, to be confirmed with a reference standard's retention time and MS/MS fragments. The odd mass is consistent with one nitrogen.

## Quantitation with LC-MS/MS

A triple quadrupole selects a **precursor ion** in the first quadrupole, fragments it in the collision cell, and selects a **product ion** in the third. Monitoring a specific precursor-to-product pair is called **multiple reaction monitoring (MRM)**. It filters out almost all background, which is why LC-MS/MS can measure nanograms per liter. Quantitation uses calibration curves and, ideally, a **stable-isotope-labelled internal standard** (the same molecule with 13C or deuterium), which corrects for **matrix effects**: other compounds in the sample that suppress or enhance ionization.

## Common mistakes

- Assuming the highest peak is the molecular ion (it is the base peak, which is often a fragment).
- Forgetting that ESI gives [M+H]+, so the neutral mass is 1.007 lower.
- Ignoring isotope patterns that reveal Cl or Br immediately.
- Quantifying in complex matrices without an appropriate internal standard.

## Quick recap

- MS measures m/z: ion source (EI hard, ESI soft), mass analyser (quadrupole, TOF, Orbitrap), detector.
- Molecular ion gives the mass; isotope patterns reveal Cl (3:1) and Br (1:1); fragments reveal structure.
- ESI usually gives [M+H]+ or [M-H]-.
- LC-MS/MS with MRM and isotope-labelled internal standards is the standard for trace quantitation.

## Try it

Open the **Do** tab for the quiz: interpret four small spectra.


Interpret a simple mass spectrum from its molecular ion, isotope pattern and fragments, and see how LC-MS/MS quantifies.

Mass spectrometry

Mass Spectrometry

Mass spectrometry | Atomic structure and properties | AP Chemistry | Khan Academy

## Why it matters

Spectroscopy uses the interaction of light (electromagnetic radiation) with matter to identify compounds and measure how much is present. Three techniques do most of the everyday work: **infrared (IR)** for functional groups and identity tests, **UV-Visible** for quantitation, and **nuclear magnetic resonance (NMR)** for full structure. A pharmacopoeia identity test, for example, often requires the sample's IR spectrum to match a reference standard's. Analysts need to read all three at a basic level and know which one answers which question.

## IR: which bonds are present?

IR light makes bonds vibrate. Each type of bond absorbs at a characteristic **wavenumber** (cm^-1). Key regions:

| Bond | Wavenumber (cm^-1) | Look |
|---|---|---|
| O-H (alcohol) | 3200 to 3550 | Broad, strong |
| O-H (carboxylic acid) | 2500 to 3300 | Very broad, overlapping C-H |
| N-H | 3300 to 3500 | Sharper; primary amines show two peaks |
| C-H (sp3) | 2850 to 3000 | Just below 3000 |
| C-H (sp2, alkene or aromatic) | 3000 to 3100 | Just above 3000 |
| C≡N | about 2250 | Sharp, medium |
| C=O | 1650 to 1750 | Strong, sharp (ketones about 1715, esters about 1735) |
| C=C | 1600 to 1680 | Medium |

Below about 1500 cm^-1 is the **fingerprint region**: too complex to assign peak by peak, but unique to each compound, which is why it is used for identity matching. Most labs now use **ATR-FTIR**, which needs only a drop or a few milligrams pressed on a crystal.

## UV-Vis: how much is present?

UV-Vis light promotes electrons to higher energy levels. Molecules with **conjugated** double bonds or aromatic rings absorb in the UV or visible range; more conjugation shifts absorption to longer wavelengths (that is why highly conjugated dyes are colored). UV-Vis spectra are broad and not very specific, but quantitation is excellent through the **Beer-Lambert law**:

```text
A = epsilon x b x c
```

with absorbance A, molar absorptivity epsilon (L mol^-1 cm^-1), path length b (cm) and concentration c (mol/L). The law holds best at absorbances of roughly 0.1 to 1. Calibration curves were covered in `lab-techniques-instrumentation` and `lab-data-quality`; HPLC UV detectors apply the same law.

## NMR: how are the atoms connected?

In a strong magnetic field, nuclei such as 1H and 13C absorb radio waves at frequencies that depend on their chemical surroundings. A **1H NMR** spectrum tells you three things:

1. **Chemical shift** (ppm): the environment. Alkyl C-H about 0.9 to 1.5; H next to C=O about 2.0 to 2.5; H on a carbon bearing oxygen about 3.3 to 4.5; alkene H about 4.5 to 6.5; aromatic H about 6.5 to 8; aldehyde H about 9 to 10; carboxylic acid H about 10 to 12.
2. **Integration:** the area of each signal is proportional to the number of H atoms.
3. **Splitting (n + 1 rule):** a signal is split into n + 1 lines by n equivalent neighboring H atoms. A CH3 next to a CH2 is a **triplet**; the CH2 next to a CH3 is a **quartet**.

## Worked example: matching spectra to structures

Two isomers of C2H6O: ethanol (CH3CH2OH) and dimethyl ether (CH3OCH3).

- **IR:** ethanol shows a broad O-H band near 3300 cm^-1; dimethyl ether has none.
- **1H NMR:** dimethyl ether has all six H in one environment, giving **one singlet** (about 3.2 ppm). Ethanol gives three signals: a **triplet** (3H, about 1.2 ppm), a **quartet** (2H, about 3.7 ppm) and an OH signal (1H, position varies).

A second case: a compound shows a strong IR band at 1715 cm^-1, no O-H, and a 1H NMR singlet of 6H near 2.1 ppm. A ketone with two equivalent CH3 groups next to C=O: **acetone**.

## Which technique for which question?

- "Is this the right material?" IR against a reference spectrum.
- "How much is in the solution?" UV-Vis (or HPLC-UV).
- "What is the structure of this unknown or impurity?" NMR, with MS for mass and IR for functional groups.

## Common mistakes

- Trying to assign every peak in the IR fingerprint region.
- Reading an absorbance above about 1.5 and trusting Beer-Lambert linearity.
- Forgetting that NMR integration gives *relative* numbers of H.
- Counting neighbors across an oxygen in the n + 1 rule (coupling through O-H is often not seen because the OH proton exchanges).

## Quick recap

- IR: functional groups and identity; C=O near 1700, O-H broad near 3300.
- UV-Vis: quantitation with A = epsilon b c; conjugation shifts absorbance to longer wavelengths.
- 1H NMR: shift (environment), integration (how many H), splitting (n + 1 neighbors).
- Combine IR, NMR and MS to determine a structure.

## Try it

Open the **Do** tab for the quiz: match spectra to structures.


Match IR, UV-Vis and 1H NMR spectra to structures and choose the right technique for each question.

IR, UV-Vis, and NMR

IR Spectroscopy and Mass Spectrometry: Crash Course Organic Chemistry #5

How to Identify Molecules - Proton NMR: Crash Course Organic Chemistry #26

Read and integrate chromatograms, interpret mass spectra, and match IR, UV-Vis and NMR spectra to structures.