Question

1. Determine the ratio of populations in the lowest and first excited energy levels, P_o/P₁, for the indicated systems at two temperatures, 50 K and 298 K:

a) The 1700 cm⁻¹ stretching mode for the carbonyl group in the peptide bond of a polypeptide

b) the 150 cm−1 torsional mode for the C=C bond in trans-2-butadiene

2. The heat capacities of liquid water and of steam (water vapor) are 18.0 and 7.9 cal/mol K, respectively. Use a microscopic (structural, modes of energy storage) argument to account for the higher heat capacity of liquid water compared to water vapor.

Answer 1

Ans 1) a) Here wavenumber = 1700cm^-1

speed of light = 2.9x10¹⁰ cm/s

Now harmonic frequency = (2.9x10¹⁰ cm/s)(1700 cm^-1)

                                          =4.93x10¹³ /sec

At 50 K , the population ratio

      

Population ratio at 298K

b) Here wavenumber = 150cm^-1

speed of light = 2.9x10¹⁰ cm/s

Now, harmonic frequency =(2.9x10¹⁰ cm/s)(150 /cm)

                                          =4.35x10¹² /sec

At 50K , the population ratio

At 298K , the population ratio

Ans 2) Heat capacity is defined as the amount of heat required to raise the temperature by 1⁰C. In water ,the intermolecular force of attraction between hydrogen molecules is less ,so as a result the kinetic energy of the molecule increases and as a result the heat contained in the system also increases. Therefore water has very high heat capacity than vapour.