Question

Each compound gives only one signal in its \({ }^{1} \mathrm{H}-\mathrm{NMR}\) spectrum. Propose a structural formula for each compound. (a) \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\) (b) \(\mathrm{C}_{5} \mathrm{H}_{10}\) (c) \(\mathrm{C}_{5} \mathrm{H}_{12}\) (d) \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{Cl}_{4}\)

Short answer

Question: Propose a structural formula for each compound based on their molecular formulas and the fact that each compound shows only one signal in their ¹H-NMR spectrum. a) C3H6O b) C5H10 c) C5H12 d) C4H6Cl4 Answer: a) Cyclopropanone b) Neopentane or Cyclopentane c) 2,2-dimethylpropane (neopentane) d) Tetrachlorocyclobutane

Step-by-step solution

Determine Degrees of Unsaturation

First, find the index of hydrogen deficiency (IHD) or degrees of unsaturation using the formula: IHD = (2C + 2 + N - X - H)/2, where C is the number of carbons, H is the number of hydrogens, N is the number of nitrogens, and X is the number of halogens. In this case, IHD = (2(3) + 2 + 0 - 0 - 6)/2 = 1. This means we either have a double bond or a ring in the structure.

Propose a Structure

With only one signal in the NMR spectrum, the hydrogens must be in equivalent environments. A molecule with IHD of 1 and chemically equivalent hydrogens is cyclopropanone. Structural Formula: O || -C--C-- / \ -C -C #b) C5H10#

Determine Degrees of Unsaturation

Use the formula for IHD again: IHD = (2(5) + 2 + 0 - 0 - 10)/2 = 0. This indicates no double bonds or rings present.

Propose a Structure

With a single signal in the NMR spectrum and an IHD of 0, the hydrogens should be in equivalent environments. The simplest symmetrical linear structure that satisfies this condition is neopentane. Structural Formula: -C- (CH3)3C-CH3

Another Possibility

An alternative to neopentane is cyclopentane, another molecule with a single signal in the NMR spectrum and an IHD of 0. Structural formula: -C-- / \ C C \ / --C-- #c) C5H12#

Determine Degrees of Unsaturation

Use the formula for IHD: IHD = (2(5) + 2 + 0 - 0 - 12)/2 = -1. But IHD can't be negative, so we need to reevaluate the formula and realize it's a straight alkane.

Propose a Structure

With a single signal in the NMR spectrum and no unsaturation, all hydrogens must be in equivalent environments. The only linear structure that satisfies this condition is 2,2-dimethylpropane (neopentane). Structural Formula: (CH3)3C-CH3 (As from b) #d) C4H6Cl4#

Determine Degrees of Unsaturation

Use the formula for IHD again: IHD = (2(4) + 2 + 0 - 4 - 6)/2 = 0. This means there are no double bonds or rings in the structure.

Propose a Structure

To satisfy the condition of all hydrogens being in equivalent environments, the molecule must be symmetric, with no double bonds or rings. The symmetrical structure that meets these conditions is tetrachlorocyclobutane. Structural Formula: -C-- / | \ C Cl C \ | / --C--