NMR Integration

The area under each NMR peak (integration) is proportional to the number of equivalent hydrogens contributing to that signal. Comparing peak areas gives you the ratios of different hydrogen types in the molecule, which combined with chemical shift and splitting gives a complete structural picture.

How Integration Works

Modern NMR spectrometers automatically integrate peaks, producing a “staircase” integration trace above the spectrum or printed numerical values below each peak. Each integral is expressed as a relative number. To interpret:

1. Find the smallest integration value.
2. Divide all integrals by that value to get simple ratios.
3. Apply those ratios to the total expected H count.

Example: a spectrum of an unknown molecule shows peaks with integrations 3, 2, 1. If the molecular formula has 6 H total (common for a C4-5 compound), then 3:2:1 = 3H: 2H: 1H matches 6 total.

Classic Ethanol Integration

Ethanol (CH₃CH₂OH) has 3 + 2 + 1 = 6 hydrogens in three environments:

• 3H triplet at 1.2 ppm (the CH₃).
• 2H quartet at 3.7 ppm (the CH₂).
• 1H broad singlet at 2.6 ppm (the OH).

Integration ratio 3:2:1 confirms the assignment. If the molecular formula matches (C₂H₆O, MW 46), we have identified the compound.

Combining Integration with Other Data

Integration tells you the RATIO of H’s. To get the ABSOLUTE number, you need the molecular formula (from mass spec, for example):

• Integrations 3:2 can mean 3H:2H (if molecule has 5H total) or 6H:4H (10H total) or other multiples.
• Pair integration with MW and chemical formula to determine the multiplier.

The Exchangeable H Problem

Broad peaks from exchangeable protons (O-H, N-H) can be harder to integrate accurately. The peak width and baseline uncertainty introduce errors. Chemists often add D₂O to shake out the exchangeable H’s (replace with D), which:

1. Cleans up the spectrum.
2. Confirms which peaks were exchangeable (they disappear).
3. Leaves only the C-H signals for clean integration.

Equivalent H’s Give One Integrated Peak

Groups of equivalent H’s (related by molecular symmetry) appear as ONE peak with integration equal to the total number of equivalent H’s:

• In benzene (C₆H₆), all 6 aromatic H’s are equivalent → ONE peak with 6H integration.
• In p-xylene (1,4-dimethylbenzene), the 4 aromatic H’s are equivalent → one peak with 4H integration; the 6 methyl H’s are equivalent → one peak with 6H integration.

Integration Lies for Certain Peaks

Integration is reliable for most organic samples but can be distorted by:

• Exchangeable protons (O-H, N-H) that trade with solvent D₂O.
• Paramagnetic impurities (iron in glassware) that broaden peaks.
• Very fast or very slow relaxation that leads to saturation effects. Usually controlled by the pulse sequence.

For MCAT purposes, assume integration is accurate.

A Complete Interpretation Example

Molecule: ethyl acetate (CH₃COOCH₂CH₃), MW 88.

Expected NMR:

• CH₃ of acetate (3H): singlet (no neighbors on adjacent C), ~2.0 ppm.
• OCH₂ (2H): quartet (neighbors = 3 H of adjacent CH₃), ~4.1 ppm (shifted downfield by adjacent O).
• CH₃ of ethyl (3H): triplet (neighbors = 2 H of adjacent OCH₂), ~1.2 ppm.

Integrations: 3:2:3. Matches 8 total H’s expected for C₄H₈O₂.