SME
Organic Chemistry I
IR and NMR spectroscopy
Use this for “C₅H₁₀O shows three ¹H NMR signals with integrals 21, 7.1 and 41.8. How many H does each stand for?”
Diagram
Ethyl ethanoate, C₄H₈O₂.
a: δ 2.03, singlet (0 neighboring H), 2.99 H; b: δ 4.12, quartet (3 neighboring H), 2 H; c: δ 1.26, triplet (2 neighboring H), 3 H.
Each signal splits into n + 1 lines with heights from Pascal’s triangle.
H
per
signal
=
8
×
I
69.5
(the
integrals
add
to
69.5).
The lines of each multiplet are drawn wider apart than scale.
This is an example. Type your own values to start a new problem.
H
H in the formula
example
I₁
Integral of signal a
example
I₂
Integral of signal b
example
I₃
Integral of signal c
example
ΣI
Total integral
calculated
h₁
H in signal a
calculated
h₂
H in signal b
calculated
h₃
H in signal c
calculated
Formulas
ΣI
=
I₁
+
I₂
+
I₃
69.5 = 26 + 17.4 + 26.1
h₁
=
H
×
I₁
ΣI
2.99
=
8
×
26
69.5
h₂
=
H
×
I₂
ΣI
2
=
8
×
17.4
69.5
h₃
=
H
×
I₃
ΣI
3
=
8
×
26.1
69.5
Assumptions
•
The area under a signal (its integral) counts the H that give it, never the carbons.
•
Integrals come in any units; only their ratios matter, so a signal’s share of the total is its share of the H in the formula.
•
Round each count to a whole number: a CH₃ gives 3, a CH₂ 2, and a CH, OH or NH 1.
•
The picture draws ethyl ethanoate’s spectrum, each signal lettered on the structure, its integral step scaled to the values typed.
Step-by-step
WE KNOW
H = 8, I₁ = 26, I₂ = 17.4, I₃ = 26.1
FIND
total integral (ΣI), H in signal a (h₁), H in signal b (h₂), H in signal c (h₃)
Step 1 · Find total integral (ΣI)
Use ΣI = I₁ + I₂ + I₃
Add the three integrals.
ΣI = 26 + 17.4 + 26.1
ΣI = 69.5
Step 2 · Find H in signal a (h₁)
Use h₁ = H × I₁ ÷ ΣI
This
signal’s
share
of
the
total
integral
is
its
share
of
the
H
:
multiply
H
by
its
integral,
then
divide
by
the
total.
h₁
=
8
×
26
69.5
h₁
=
208
69.5
h₁
=
2.99
→
Round
to
3
H
(a
CH₃).
Step 3 · Find H in signal b (h₂)
Use h₂ = H × I₂ ÷ ΣI
This
signal’s
share
of
the
total
integral
is
its
share
of
the
H
:
multiply
H
by
its
integral,
then
divide
by
the
total.
h₂
=
8
×
17.4
69.5
h₂
=
139.2
69.5
h₂
=
2
→
Round
to
2
H
(a
CH₂).
Step 4 · Find H in signal c (h₃)
Use h₃ = H × I₃ ÷ ΣI
This
signal’s
share
of
the
total
integral
is
its
share
of
the
H
:
multiply
H
by
its
integral,
then
divide
by
the
total.
h₃
=
8
×
26.1
69.5
h₃
=
208.8
69.5
h₃
=
3
→
Round
to
3
H
(a
CH₃).
Check
Put the numbers back in. Both sides should match.
69.5 = 26 + 17.4 + 26.1 ✓
2.99
=
8
×
26
69.5
✓
2
=
8
×
17.4
69.5
✓
3
=
8
×
26.1
69.5
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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