¹H NMR — chemical shift, multiplicity (n + 1 rule), integration; common ranges: Question bank

This is a rapid-fire self-test built from the traps of the ¹H NMR topic. Cover the right side of each ::: line and force yourself to justify, not just guess. Every answer here is reasoning, not a bare label.

Symbols you need before the traps

Before we test you, every symbol below is nailed down in plain words. If a question uses one, it means exactly this.

Definition The four symbols in play

$ν$ (nu) — the radio frequency (in Hz) of the electromagnetic wave a proton absorbs when it flips. Think of it as the exact "radio station" that particular proton is tuned to.
$B_{0}$ — the big external magnetic field (in tesla) supplied by the spectrometer's magnet. It is fixed for a given machine and sets the scale of every energy gap. A "300 MHz" machine and a "600 MHz" machine differ precisely in their $B_{0}$ .
$δ$ (delta), the chemical shift — the position of a peak, defined by subtracting a reference frequency and dividing by the machine's own operating frequency $ν_{0}$ : $δ = \frac{ν _{sample} - ν _{ref}}{ν _{0}} \times 1 0^{6} ppm$ where $ν_{sample}$ is the proton's absorption frequency, $ν_{ref}$ is TMS's, and $ν_{0}$ is the operating (spectrometer) frequency. Dividing by $ν_{0}$ cancels the $B_{0}$ hidden inside every $ν$ , so $δ$ (in ppm) is the same number on any machine.
$J$ , the coupling constant — the spacing between the split lines of a multiplet, measured in Hz. It measures how strongly two protons feel each other's spin and, unlike $δ$ , does not change with $B_{0}$ .

Figure — ¹H NMR — chemical shift, multiplicity (n + 1 rule), integration; common ranges

True or false — justify

True or false: two protons with the same chemical shift always come from the same functional group.

False — equivalence of shift means equivalence of magnetic environment, which can coincidentally match across different groups; identical

δ

is necessary but not sufficient to prove same group.

True or false: chemically equivalent protons split each other into a multiplet.

False — equivalent protons have identical energy levels, so their mutual coupling produces no observable line splitting; a lone isolated CH₃ is a singlet.

True or false: a higher chemical shift (

δ

) always means a taller peak.

False —

δ

(position) reports environment while peak area (see integration) reports proton count; a 1H aldehyde at 9.7 ppm can be tiny.

True or false: the

δ

value in ppm changes if you switch from a 300 MHz to a 600 MHz spectrometer.

False — dividing by the operating frequency

ν_{0}

cancels

B_{0}

, so

δ

in ppm is field-independent (that is the whole point of ppm).

True or false: the coupling constant

J

(in Hz) gets bigger when you move to a higher-field magnet.

False —

J

is a fixed through-bond interaction independent of

B_{0}

; only the

δ

separation (in Hz) grows with field, which is why high-field spectra look more first-order.

True or false: a more shielded proton resonates at higher ppm.

False — shielding means the proton feels less than

B_{0}

, so it resonates upfield at lower

δ

; deshielding pushes it downfield to higher

δ

True or false: the sum of Pascal-triangle intensities for a proton with

n

neighbours is

2^{n}

True — each neighbour contributes an independent spin-up/spin-down choice, giving

2^{n}

total spin combinations, which is the row sum

\sum_{k} (k n)

(summing the index

k

from 0 to

n

True or false: OH and NH protons follow the

n + 1

rule as reliably as C–H protons.

False — OH/NH typically undergo fast proton exchange, appearing as a broad singlet at variable

δ

and often neither splitting nor being split.

True or false: Tetramethylsilane (TMS) is set to

δ = 0

because it has no protons.

False — TMS has 12 equivalent protons giving one sharp reference peak; it sits at 0 because Si is electropositive, making those protons unusually shielded.

True or false: aromatic protons are deshielded mainly by the electronegativity of the carbon atoms.

False — the dominant effect is the ring current, a circulating

π

-electron field that reinforces

B_{0}

at the ring's edge, deshielding those H's to ~7 ppm.

Spot the error

Error: "CH₃ in ethanol is a quartet because there are 3 protons on it."

The multiplicity comes from neighbours, not from the proton's own count; CH₃ has 2 vicinal CH₂ neighbours, so

n = 2

→ triplet.

Error: "For

n + 1

, I count every hydrogen in the molecule."

Count only vicinal (adjacent-carbon) protons that are inequivalent to the observed proton; distant and equivalent H's do not split it.

Error: "

δ = \frac{ν _{sample} - ν _{ref}}{ν _{sample}} \times 1 0^{6}

The denominator must be the operating frequency

ν_{0}

, not the sample frequency; only that choice cleanly cancels the

B_{0}

hidden inside each

ν

Error: "A quartet has intensity pattern 1:2:2:1."

A quartet (

n = 3

) follows Pascal row 1:3:3:1; three equivalent neighbours give binomial coefficients

(k 3)

for

k = 0..3

Error: "The CH₂ in

C H C l_{2} - C H_{2} C l

is a triplet because it has 2 protons."

Its multiplicity depends on the single CHCl₂ neighbour (

n = 1

) → doublet; its own 2 protons determine integration, not splitting.

Error: "Deshielded protons appear on the right (upfield) side of the spectrum."

Deshielded protons appear downfield, on the left (high

δ

); upfield/right is the shielded, low-

δ

region.

Error: "Because carboxylic acid H exchanges, it can never be seen at 11 ppm."

Exchange broadens and makes it variable, but it is routinely observed far downfield (10–12 ppm) due to strong deshielding and H-bonding; a D₂O shake is what removes it.

Error: "Two peaks whose

δ

separation is comparable to their

J

still give clean 1:3:3:1 quartets."

When the

δ

gap (in Hz) is not much larger than

J

, the system is second-order (strongly coupled) and intensities distort (leaning "roofing"), breaking the tidy Pascal pattern.

Why questions

Why do we reference against TMS instead of just reporting the raw absorption frequency

ν

Raw

ν

depends on

B_{0}

and drifts between machines; referencing to a fixed peak and dividing by the operating frequency

ν_{0}

yields a portable, field-independent

δ

Why does one neighbouring proton produce two lines rather than a broadened single line?

That neighbour is a magnet pointing either with or against

B_{0}

, splitting the local field into two discrete values, so the observed proton absorbs at two distinct frequencies (a doublet) separated by

J

Why is the CH₂ of ethanol further downfield than its CH₃?

The CH₂ is bonded to the electronegative oxygen (see Electronegativity), which pulls electron density away, deshielding it toward ~3.7 ppm versus ~1.2 ppm for CH₃.

Why does the splitting intensity pattern follow Pascal's triangle and not equal weights?

Each line corresponds to a net neighbour-spin arrangement, and the number of ways to reach the

k

-th arrangement is the binomial coefficient

(k n)

— more ways means a taller line.

Why doesn't integration give absolute proton counts directly?

Peak areas are only proportional to proton number; without an internal standard you read reliable ratios, then scale to the smallest whole-number set.

Why does an aldehyde –CHO proton sit near 9–10 ppm despite being just one H?

It is deshielded twice over — by the adjacent electron-withdrawing C=O and the sp² carbon — so its environment, not its abundance, sets the position.

Why can ¹³C NMR show a signal for a carbon that bears no attached hydrogen, while ¹H NMR cannot?

¹H NMR only detects protons, so a quaternary carbon is invisible; ¹³C NMR detects the carbon nucleus itself regardless of attached H's.

Edge cases

Edge case: what multiplicity does a proton with zero neighbours show?

A singlet —

n + 1 = 0 + 1 = 1

line; with no coupling partners the resonance is undivided.

Edge case: a proton coupled to two inequivalent sets of neighbours (say 2 of type A and 1 of type B, different

J

) — does the simple

n + 1

rule apply?

No; the simple rule assumes one equivalent set, so you get a multiplet-of-multiplets (e.g. a doublet of triplets), governed by separate J values.

Edge case: two diastereotopic protons on the same CH₂ (a carbon next to a stereocentre) — do they couple to each other?

Yes — being inequivalent, they have different

δ

and show a real geminal (

^{2} J

) splitting of each other, unlike equivalent CH₂ protons which do not.

Edge case: two enantiotopic/equivalent protons on the same carbon — do they split each other?

No — being magnetically equivalent, their mutual coupling causes no observable splitting even though they are chemically real protons.

Edge case: can protons four bonds apart (e.g. allylic or aromatic meta pairs) ever couple?

Yes — long-range

^{4} J

coupling exists (small, ~0–3 Hz) through

π

systems or W-shaped saturated paths, adding fine splitting the naive vicinal-only rule misses.

Edge case: what happens to a spectrum when two coupled protons have very similar

δ

It becomes strongly coupled / second-order: line spacings and intensities skew (peaks "lean" toward each other) and the clean

n + 1

Pascal picture no longer holds.

Edge case: what happens to an OH signal when you shake the sample with D₂O?

The exchangeable OH proton is swapped for deuterium and its peak disappears, confirming an exchangeable OH/NH group — a standard diagnostic.

Edge case: if a molecule is fully symmetric with all protons equivalent (e.g. benzene, TMS), how many ¹H signals appear?

Exactly one, since every proton shares the same environment; a single peak whose area accounts for all the equivalent H's.

Edge case: what would you observe for a proton whose only neighbour is a rapidly exchanging OH?

Often a simple singlet, because fast exchange averages out the coupling and the OH cannot maintain a fixed spin partner to split it.