Question

Sketch the NMR spectrum you would expect from a partial molecule with the following parameters. \(\begin{aligned} &\mathrm{H}_{\mathrm{a}}=1.0 \mathrm{ppm} \\ &\mathrm{H}_{\mathrm{b}}=3.0 \mathrm{ppm} \\ &\mathrm{H}_{\mathrm{c}}=6.0 \mathrm{ppm} \\ &J_{\mathrm{ab}}=5.0 \mathrm{~Hz} \\ &J_{\mathrm{bc}}=8.0 \mathrm{~Hz} \\ &J_{\mathrm{ac}}=1.0 \mathrm{~Hz} \end{aligned}\)

Short answer

Question: Sketch the NMR spectrum for the following hydrogen atoms and their respective chemical shifts (in ppm) and coupling constants (in Hz): H_a at 1.0 ppm with J_ab = 5.0 Hz, H_b at 3.0 ppm with J_ab = 5.0 Hz and J_bc = 8.0 Hz, and H_c at 6.0 ppm with J_bc = 8.0 Hz. Answer: The sketched NMR spectrum should show H_a with a doublet at 1.0 ppm, H_b with a triplet at 3.0 ppm, and H_c with a doublet at 6.0 ppm. The splitting patterns for each hydrogen atom should be based on their coupling constants: H_a has a separation of 5.0 Hz, H_b has separations of 5.0 Hz and 8.0 Hz, and H_c has a separation of 8.0 Hz.

Step-by-step solution

Draw the baseline of the spectrum

Begin by drawing a horizontal line representing the baseline of the NMR spectrum. On the x-axis, label a range from 0 to at least 8 ppm, considering the given chemical shifts for H_a, H_b, and H_c lie between 1.0 and 6.0 ppm.

Identify the chemical shift peaks

For every given chemical shift, place a vertical mark on the baseline. For H_a at 1.0 ppm, place a mark at 1.0 ppm, for H_b at 3.0 ppm, place a mark at 3.0 ppm, and for H_c at 6.0 ppm, place a mark at 6.0 ppm. These marks will act as the center points of our peaks.

Determine splitting patterns based on coupling constants

Apply the coupling constants (J) between the hydrogen atoms to create splitting patterns for each peak. - For H_a (with J_ab = 5.0 Hz), create a doublet as there is only one neighboring hydrogen (H_b). The space between the doublet peaks should be 5.0 Hz. - For H_b (with J_ab = 5.0 Hz and J_bc = 8.0 Hz), create a triplet due to two different neighboring hydrogens (H_a and H_c). The space between the two doublets should be 5.0 Hz, and the space between the doublet and central peak should be 8.0 Hz. - For H_c (with J_bc = 8.0 Hz), create a doublet as there is only one neighboring hydrogen (H_b). The space between the doublet peaks should be 8.0 Hz.

Draw the fine structure of the peaks

Using the center points and the splitting patterns from Step 3, draw the peaks on the spectrum as follows: - H_a: a doublet centered at 1.0 ppm with a separation of 5.0 Hz. - H_b: a triplet centered at 3.0 ppm with a separation of 5.0 Hz and 8.0 Hz. - H_c: a doublet centered at 6.0 ppm with a separation of 8.0 Hz.

Label the peaks

Label each peak on the spectrum with the corresponding hydrogen atom (H_a, H_b, or H_c) and their respective coupling constants. This will allow for easy interpretation of the resulting NMR spectrum. Your sketched NMR spectrum should display H_a's doublet at 1.0 ppm, H_b's triplet at 3.0 ppm, and H_c's doublet at 6.0 ppm, with their corresponding splitting patterns based on the given coupling constants.