Use the data in Table 1 and your understanding of molecular motion to answer the

Question

Use the data in Table 1 and your understanding of molecular motion to answer the following questions. Why are there 4 vibrational constants given for ammonia and only 3 for water? Without doing any calculations, which molecule do you expect to have the highest molar entropy at 300 K? Briefly explain your answer. How much energy is required to raise each molecule from 300 K to 1000K? You may assume equipartition of energy holds. We can often simplify our model of system by only considering two possible energy states for the system. This is called the "two level system." For example proteins that contain both random coil and helical regions can be modeled this way by assuming that a residue is either in a helical state with energy E_H=0 or in a random coil state with energy E_c=.Since we expect the helical state to be the ground state, we set E_H to zero. Answer the following questions about this model. To simplify things, let b= and write an expression for the partition function of an amino acid residue in the protein in terms of b. Find an expression, in terms of b, for the probability that an amino acid in the peptide will be helical. What is the value of b for a peptide that is 75% helical? Find an expression for the average energy of an N-amino acid polypeptide in terms os b. What is the value of the average energy at 310 K for one mole of a peptide that has 50 residues and is 75% helical? What happen to the average energy as the percent helicity increases? Justify your answer from a physical and chemical point of view

Explanation / Answer

1.(a). Since there are 4 atoms in ammonia (1 N and 3 H) and 3 atoms in water (2 H and 1 O). So, ammonia have 4 vibrational constants and water have only 3.

(b). At 300 K, water is in liquid state while ammonia is in gaseous state. So, ammonia will have highest molar entropy at 300 K.

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