Use peak integration to count protons

A C₄H₈O spectrum has integral areas 30, 20 and 30 units. Divide by 10 to obtain 3:2:3, totalling eight protons.

GCE A-Level H3 Chemistry 9813-2027

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Learning objectives

Use peak integration to count protons

Area gives a ratio

A C₄H₈O spectrum has integral areas 30, 20 and 30 units. Divide by 10 to obtain 3:2:3, totalling eight protons.

Integration is area under a signal/multiplet, not its tallest line.

Integration compares the area under signals, not their maximum heights. The raw values may be scaled, so reduce them to the simplest whole-number ratio before matching them to a molecular formula.

Integral and scaling

Integrated area is proportional to the number of equivalent protons contributing to a signal.

Convert areas to the simplest ratio, then scale to a known total or candidate molecular formula.

An integral is proportional to the number of equivalent protons producing that signal under suitable acquisition conditions. It gives relative counts unless the spectrum has been calibrated to an absolute total.

Use totals as a checksum

For areas 1.5:1.0:1.5, divide by 0.5 to get 3:2:3. Confirm the sum equals the eight hydrogens available.

Exchangeable OH/NH integrals can be unreliable; use supplied data and other evidence.

After reducing the ratio, test it against the total number of hydrogens in the proposed structure. If the smallest ratio sums to half the required total, multiply every term by two rather than altering one signal independently.

Scale 1:2 to six H

Let counts be k and 2k. Since 3k = 6, k = 2.

The two environments contain 2H and 4H.

For areas 6.0, 4.0 and 6.0, divide by 2.0 to obtain 3:2:3. Those counts fit the three ethyl-ethanoate environments COCH₃, OCH₂ and terminal CH₃.

Try this

Scale an area ratio 1:2 to a six-proton total.

Check your answer

A strong answer should include algebra or proportional reasoning to 2H:4H.

Read an ethyl ester

Supplied data for ethyl ethanoate, CH₃COOCH₂CH₃: δ2.0 singlet, δ4.1 quartet and δ1.3 triplet, integrals 3:2:3.

Use chemical shift and splitting to decide which 3H is which.

Keep a table linking δ, multiplicity, raw area, reduced area and proposed group. This makes it easy to see whether all independent clues support the same assignment.

Try this

Assign each signal to a group and give its proton count.

Check your answer

δ2.0 singlet, 3H: CH₃C=O, with no neighbouring H. δ4.1 quartet, 2H: OCH₂, deshielded by oxygen and split by the CH₃. δ1.3 triplet, 3H: terminal CH₃, split by the CH₂. The areas give counts only; neighbours come from splitting.

Normalise decimal areas

Supplied relative areas: 4.8, 3.2 and 1.6, for a compound C₃H₆O.

Divide every area by the smallest, then compare the total with the formula's hydrogen count.

If an O–H signal integrates poorly because of exchange, say so explicitly and use the reliable carbon-bound signals plus the formula. Do not silently force a broad labile peak into an exact ratio.

Try this

Normalise 4.8:3.2:1.6 and check a C₃H₆O candidate.

Check your answer

Dividing by 1.6 gives 3:2:1, which totals six protons and matches C₃H₆O. Propanal, CH₃CH₂CHO, fits this pattern; propanone would give a single 6H signal.

Height is not area

A narrow line can be taller than a broad line with the same or smaller area.

Use the integral trace/value supplied across the entire multiplet.

A narrow tall singlet can have less area than a broad low signal. Proton count follows the integrated area, not how visually prominent the line appears.

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Better reasoning: “The tallest signal contains the most protons.”

Check your answer

Replace height with integrated area and keep multiplicity separate.

Count, scale, then assign

After the check questions, analyse the aromatic-ketone integrals without notes. Return later for a different diol question.

Try this next: interpret spin–spin splitting.

Show the normalisation calculation and the final structural match. Examiners should be able to follow how each raw area became a proton count.

Try this

Show the scaling of 30:20:30 for C₄H₈O.

Check your answer

A strong answer should include simplest ratio 3:2:3, eight-proton checksum and bounded structural use.