The correct answer is C. P-IV, Q-III, R-V, S-II.
The carbonyl stretching frequency is a characteristic absorption band in the infrared spectrum of carbonyl compounds. The frequency of the absorption band depends on the structure of the carbonyl compound. In general, the carbonyl stretching frequency decreases as the electron density in the carbonyl group increases.
In acetone, the carbonyl group is attached to two carbon atoms. The electron density in the carbonyl group is therefore relatively low, and the carbonyl stretching frequency is high. The carbonyl stretching frequency of acetone is typically around 1870 cm-1.
In ethyl acetate, the carbonyl group is attached to a carbon atom and an oxygen atom. The electron density in the carbonyl group is therefore higher than in acetone, and the carbonyl stretching frequency is lower. The carbonyl stretching frequency of ethyl acetate is typically around 1800 cm-1.
In acetamide, the carbonyl group is attached to a carbon atom and two nitrogen atoms. The electron density in the carbonyl group is therefore much higher than in acetone or ethyl acetate, and the carbonyl stretching frequency is even lower. The carbonyl stretching frequency of acetamide is typically around 1740 cm-1.
In acetyl chloride, the carbonyl group is attached to a carbon atom and a chlorine atom. The electron density in the carbonyl group is therefore very low, and the carbonyl stretching frequency is very high. The carbonyl stretching frequency of acetyl chloride is typically around 1700 cm-1.
Therefore, the correct match of compounds P-S with their carbonyl stretching frequencies I-VI in IR spectroscopy is C. P-IV, Q-III, R-V, S-II.