Understanding NMR Splitting and Field Dependence

Proton NMR spectroscopy ($^1H$ NMR) splitting patterns can change with the magnetic field strength (spectrometer frequency). This phenomenon occurs when the chemical shift difference between coupled protons (in Hz) is comparable to their coupling constant ($J$). This is often referred to as second-order effects.

Analyzing Methyl Propyl Ether ($CH_3CH_2CH_2OCH_3$)

The molecule is methyl propyl ether: $CH_3^a CH_2^b CH_2^c OCH_3^d$. We need to identify the protons whose splitting patterns differ significantly between low field ($60$ MHz) and high field ($500$ MHz).

Key parameters influencing splitting patterns include:

• Chemical shifts ($\delta$ in ppm)
• Coupling constants ($J$ in Hz)
• Spectrometer frequency ($\nu_0$ in MHz)

The chemical shift difference in Hz is calculated as $ \Delta\nu = \nu_0 \times |\delta_1 - \delta_2| $. A common criterion for distinguishing first-order ($ \Delta\nu \gg J $) from second-order ($ \Delta\nu \lesssim J $) effects is the ratio $ \Delta\nu / J $. Ratios significantly greater than 10 suggest first-order behavior, while ratios near or below 1 indicate strong second-order effects.

Comparing Splitting Patterns at Different Field Strengths

Let's analyze the protons based on typical values:

• $ \delta_a \approx 0.9 $ ppm, $ \delta_b \approx 1.6 $ ppm, $ \delta_c \approx 3.4 $ ppm, $ \delta_d \approx 3.3 $ ppm
• Typical vicinal couplings: $ J_{ab} \approx J_{bc} \approx J_{cd} \approx 7 $ Hz

Reasoning for Different Splitting Patterns

The protons labeled 'c' ($CH_2$ adjacent to oxygen) exhibit the most significant change in splitting pattern.

• At 60 MHz, the chemical shift difference between protons 'c' and protons 'd' ($ \Delta\nu_{cd} = 6 $ Hz) is less than the coupling constant ($ J_{cd} = 7 $ Hz). The ratio $ \Delta\nu / J < 1 $, indicating strong second-order effects. The spectrum is complex and deviates significantly from a simple quartet.
• At 500 MHz, the chemical shift difference increases to $ \Delta\nu_{cd} = 50 $ Hz. The ratio $ \Delta\nu / J \approx 7.1 $. While not purely first-order, this ratio is much larger, leading to a simpler, less distorted spectrum compared to the 60 MHz spectrum.

The protons labeled 'b' also show some change, but the coupling interaction between 'c' and 'd' is the most sensitive to field strength due to the very small initial chemical shift difference.

Conclusion

Therefore, the set of protons $CH_3CH_2\underline{CH_2}OCH_3$ (protons 'c') would exhibit different splitting patterns in high and low field NMR due to the pronounced influence of second-order effects at lower field strength.