SME
Organic Chemistry I · Problem type
Splitting, J and δ
Use this for “A CH₂ next to a CH₃ shows J = 6.8 Hz at 300 MHz. How many lines, how wide is it in Hz and ppm, and what is δ for 1110 Hz from TMS?”
Diagram
Row 2: 1, 2, 1; they add to 2² = 4.
This is an example. Type your own values to start a new problem.
n
Neighboring H
example
lines
Lines in the multiplet
calculated
J
Coupling constant
example · Hz
ν₀
Spectrometer frequency
example · MHz
W
Multiplet width
calculated · Hz
Wₚₚₘ
Width in ppm
calculated · ppm
Δν
Shift from TMS
example · Hz
δ
Chemical shift
calculated · ppm
Formulas
lines
=
n
+
1
3 = 2 + 1
W
=
n
×
J
14.2 = 2 × 7.1
Wₚₚₘ
=
W
ν₀
0.0355
=
14.2
400
δ
=
Δν
ν₀
3
=
1,200
400
Assumptions
•
The n equivalent H on the next carbons split a signal into n + 1 lines, all J apart, with heights from row n of Pascal’s triangle.
•
H on the same carbon, and H on O or N that trade places fast, do not split each other.
•
J and widths in Hz are the same on any magnet; δ in ppm is too, since it is the shift in Hz ÷ the frequency in MHz.
Step-by-step
WE KNOW
n = 2, J = 7.1 Hz, ν₀ = 400 MHz, Δν = 1,200 Hz
FIND
lines in the multiplet (lines), multiplet width (W), width in ppm (Wₚₚₘ), chemical shift (δ)
Step 1 · Find lines in the multiplet (lines)
Use lines = n + 1
n
equivalent
neighbors
split
the
signal
into
n
+
1
lines.
lines = 2 + 1
lines = 3 → A triplet: line heights 1, 2 and 1, row 2 of Pascal’s triangle.
Step 2 · Find multiplet width (W)
Use W = n × J
n
+
1
lines
leave
n
gaps
of
J
from
the
first
line
to
the
last.
W
=
2
×
7.1
W
=
14.2
Hz
Step 3 · Find width in ppm (Wₚₚₘ)
Use Wₚₚₘ = W ÷ ν₀
Hz divided by MHz gives parts per million.
Wₚₚₘ
=
14.2
400
Wₚₚₘ = 0.0355 ppm
Step 4 · Find chemical shift (δ)
Use δ = Δν ÷ ν₀
Divide the shift in Hz by the frequency in MHz to get ppm.
δ
=
1,200
400
δ
=
3
ppm
Check
Put the numbers back in. Both sides should match.
3 = 2 + 1 ✓
14.2 = 2 × 7.1 ✓
0.0355
=
14.2
400
✓
3
=
1,200
400
✓
Topic check
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