Organic Chemistry · Structure Determination: Nuclear Magnetic Resonance Spectroscopy
Integration of 1H NMR Absorptions: Proton Counting
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In 30 seconds
Every signal in a 1H NMR spectrum carries three independent pieces of information: its position (chemical shift — the environment), its splitting (multiplicity — neighboring protons), and its area (Integration The measured area under an NMR signal Full entry → — how many protons). Integration works because each equivalent proton contributes equally to signal intensity: the area under an absorption is proportional to the number of protons producing it. Spectrometers display this area as an integrator trace — a stepped line whose step heights, or printed numbers on modern instruments, give the relative proton counts.
Crucially, integration gives relative counts, not absolute ones. A 3:2:1 pattern could be 3:2:1, 6:4:2, or 30:20:10 protons. To fix the scale, combine the ratio with the Molecular formula The total count of each element (e.g., C4H8O2) Full entry →: the smallest whole-number ratio that multiplies to the formula's total hydrogens is the correct proton count per signal. That single operation — matching an integration ratio to a formula — is what turns a list of signals into a structure.
Why this matters
- Integration is how you decide whether a signal represents 1, 2, 3, or 6 protons — information that eliminates most candidate structures instantly (a 6H singlet says "two equivalent methyl groups").
- Structure-determination problems on exams always pair shifts with integrations: "a compound C4H8O2 shows singlets integrating 3:3:2" is solvable only if you can convert ratios to absolute counts.
- In pharmaceutical QC, integration verifies stoichiometry and detects impurities: an unexpected integrated signal reveals a by-product even at low concentration.
- Understanding that integration is relative prevents the classic error of reading a 3:2:1 trace as "3, 2, and 1 protons" without checking the formula.
The college version
Core Concepts
What integration measures
Signal intensity in 1H NMR is proportional to the number of Equivalent protons Protons identical in environment that share one signal Full entry → absorbing at that frequency: every proton in an equivalent set contributes the same amount of absorption, and each set contributes in proportion to its size. The instrument integrates (measures the area under) each absorption and prints either a stepped Integral trace The stepped line (or printed numbers) showing relative signal areas Full entry → (older instruments) or a set of numbers (modern FT instruments). The step heights or printed areas are the raw integration data.
Reading an integration ratio
To use integration: (1) measure each step height (or read each integral value); (2) reduce the values to the smallest whole-number ratio; (3) multiply that ratio by the integer that makes the total equal the number of hydrogens in the molecular formula. The result is the number of protons in each signal.
Example pattern: a compound C3H7Cl (7 H) with step heights in ratio 3:2:2 — the ratio already sums to 7, so the signals represent 3, 2, and 2 protons. The same 3:2:2 pattern in a compound with 14 hydrogens would mean 6:4:4.
Why exchangeable protons complicate counting
O–H and N–H protons exchange with each other and with traces of water, and their signals are broad and variable. Because exchange rate and line shape depend on conditions, an OH integration often reads slightly low — the signal is so broad that baseline integration misses part of it. The practical rule: trust integrations of C–H signals for counting, and use the D₂O test to confirm an OH/NH signal rather than relying on its area.
Integration cannot stand alone
Integration tells you how many protons are in each environment, never which environment is which. That assignment comes from chemical shift (topic 4) and splitting (topic 6). A 6H singlet at δ 2.1, for example, means two equivalent methyls attached to a carbonyl (CH3)2C=O: the integration says "6," the shift says "methyl next to a C=O," and the singlet says "no neighboring protons."
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Integration ratio (relative) | Absolute proton count | 3:2:1 is relative; the molecular formula fixes whether it means 3:2:1, 6:4:2, etc. |
| Step height = number of protons directly | Step height ∝ protons | Heights must be reduced to a ratio, then scaled by the formula's total H count |
| Equivalent protons sharing one signal | Nonequivalent protons sharing a shift | Equivalent protons give ONE signal whose area sums them; nonequivalent protons give separate signals |
| Broad OH integration | Reliable C–H integration | Exchange broadens/spreads OH signals, so their areas read low; confirm OH with D₂O |
| A 6H singlet | Two different 3H singlets | A 6H singlet = one set of six equivalent protons; two 3H singlets = two different methyl environments |
| Integration ratio matching a formula by coincidence | Correct assignment | Always cross-check with shifts and multiplicity — different isomers can share an integration pattern |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Imagine a class photo where every student holds a sign. The chemical shift tells you which grade each student is in, and integration counts how many students are in each grade. If the photo shows three groups with signs in the ratio 3:2:1 and the whole class has 6 students, the groups have exactly 3, 2, and 1 students. The ratio alone doesn't give real numbers — you need the class size (the molecular formula) to convert "3:2:1" into "3, 2, and 1."
Worked example
Example 1: Ethanol — the classic 3:2:1
Ethanol, CH3-CH2-OH (C2H6O, 6 H), shows three signals whose integral trace steps measure 15, 10, and 5 mm. Determine the proton count of each signal.
Step 1 — Reduce to the smallest whole-number ratio:
15 : 10 : 5 = 3 : 2 : 1
Step 2 — Check against the total. 3 + 2 + 1 = 6, matching the 6 hydrogens in C2H6O — no scaling needed.
Step 3 — Assign with shift and multiplicity. The 3H signal is the CH3 (triplet, δ ≈ 1.2), the 2H signal is the CH2 (quartet, δ ≈ 3.7), and the 1H signal is the OH (broad singlet, δ ≈ 2.6, D₂O-exchangeable). The 3:2:1 fingerprint identifies ethanol among all C2H6O isomers.
Example 2: Scaling an integration ratio with the formula
A compound with formula C4H10O (10 H) shows four signals with integrals 15, 10, 10, and 5 units. How many protons does each signal represent?
Step 1 — Reduce the ratio:
15 : 10 : 10 : 5 = 3 : 2 : 2 : 1
Step 2 — Scale to the formula. The reduced ratio sums to 3 + 2 + 2 + 1 = 8, but the formula demands 10 H. Multiplying by 2 gives 6:4:4:2 (sum 16) — overshoot. The correct interpretation for a 10-H compound is 3:2:2:2:1 (sum 10): the fifth signal (the 1H OH) overlapped or the trace rounded. This is butan-1-ol, CH3-CH2-CH2-CH2-OH: 3H (CH3), 2H, 2H, 2H (three CH2), 1H (OH).
Lesson: the formula is the referee. When a ratio doesn't multiply cleanly to the formula's H count, re-examine the spectrum for overlapping signals or an exchangeable proton before trusting the numbers.
Example 3: Distinguishing isomers with integration
Two isomers of C3H6O (6 H each) are propanal, CH3-CH2-CHO, and acetone, (CH3)2C=O. How does integration alone separate them?
Propanal: three signals — CH3 (3H, triplet, δ ≈ 1.1), CH2 (2H, δ ≈ 2.4), CHO (1H, δ ≈ 9.8) → integration 3:2:1.
Acetone: one signal — six equivalent methyl protons, 6H singlet, δ ≈ 2.1 → a single 6-unit step.
Interpretation: the number of steps in the integral trace (3 vs. 1) and the 6H vs. 3:2:1 pattern separate the isomers immediately, before any shift or splitting analysis. Integration answers "how many different kinds of protons, and how many of each?"
Key takeaways
- Integration = area under each 1H NMR signal ∝ number of equivalent protons producing it.
- Step heights / integral numbers → reduce to smallest whole-number ratio → scale up to the formula's total H count.
- Integration is relative: 3:2:1 could be 6:4:2 in a molecule with 12 hydrogens.
- Combine integration with molecular formula; never assign absolute counts from the ratio alone.
- OH and NH integrations can be unreliable (broad, exchanging); confirm exchangeable protons with D₂O.
- Integration pairs with shift (environment) and multiplicity (neighbors) for complete assignments.
- A 6H singlet = two equivalent methyls with no neighboring protons (e.g., (CH3)2C=O); a 9H singlet = three equivalent methyls, as in a tert-butyl group C(CH3)3.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
What physical quantity does a 1H NMR integrator measure, and what is it proportional to?
Show answer
The area under each absorption, which is proportional to the number of equivalent protons producing that signal.
A compound C3H7Cl shows integrals in ratio 2:2:3. How many protons does each signal represent, and why is no scaling needed?
Show answer
The ratio 2:2:3 sums to 7, matching the formula's 7 hydrogens, so the signals represent 2, 2, and 3 protons directly.
A compound C8H10 shows two signals integrating 5:3. Assign proton counts, and identify a likely structure.
Show answer
The ratio 5:3 sums to 8, matching C8H10. Five aromatic + three methyl protons = toluene, C6H5-CH3.
Why can an OH proton's integration be unreliable, and how do you confirm the proton is present anyway?
Show answer
Exchange broadens and shifts the OH signal, so baseline integration can miss part of its area; confirm the proton with the D₂O shake (the signal disappears when O–H becomes O–D).
A spectrum shows one singlet integrating to 6H at δ 2.1. What does the molecule contain, and why?
Show answer
A 6H singlet means six equivalent protons with no neighboring protons — two equivalent methyl groups attached to a carbonyl: acetone, (CH3)2C=O.
Why can't integration alone distinguish two isomers with the same integration pattern?
Show answer
Integration gives only counts, not environments; two isomers can share a 3:2:1 pattern. Shifts and multiplicities (topics 4 and 6) assign each signal to its protons.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Integration
- The measured area under an NMR signal
- Integral trace
- The stepped line (or printed numbers) showing relative signal areas
- Relative proton count
- The ratio of protons among signals (e.g., 3:2:1)
- Absolute proton count
- The actual number of protons per signal
- Equivalent protons
- Protons identical in environment that share one signal
- Exchangeable proton
- O–H or N–H proton that exchanges with water/D₂O
- Molecular formula
- The total count of each element (e.g., C4H8O2)
Sources & references
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