1. The form of C-H out-of-plane vibrations -----The first two modes give rise to excellent group frequencies, while the third fundamental does not lend itself to these correlations.
a. Explain the factors that lead to the third mode being such a poor group frequency.
b. Predict the location in the spectrum of the third fundamental.

2. Acetylene has two C-H groups. It will have two C-H stretching frequencies, the in-phase and out-of-phase stretching modes. The in-phase (symmetric) stretch occurs at 3374 /cm and the out -of-phase stretch at 3333/cm. Explain why the in-phase vibration is located at a higher frequency than the out-of-phase stretch in the case of acetylene.

3. Explain how mass effects act to lower the carbonyl frequency, as well as how inductive and hyperconjugation effects act to raise the carbonyl frequency of aldehydes relative to ketones.

4. The carbonyl stretching frequency of aliphatic carboxylic acids in dilute solution is located near 1770/cm. This frequency is much higher than the carbonyl frequency of these substances when measured neat (1720/cm). Also, it is considerably higher than the corresponding simple aliphatic ester (1745/cm) value. Explain.