Question

T20 is the “heavier' isotopologue of H20. Without explicit calculation of the translational partition function (qtrans), predict which molecule has a higher value of qtrans at a given temperature and pressure. You may assume the ideal gas approximation. Select one: O a. T20 would have a smaller (trans because it has more kinetic energy. b. H2O would have a larger qtrans because it is lighter. c. H2O would have a smaller Otrans because it is lighter. O d. T20 would have a larger (trans because it occupies a larger volume.

Please explain your answer

Answer 1

Answer. The translational energy of an alom or molecule in a volume V is given by a no E ht (mit net n) where n,, me and my are quantum numbers, each having values of 1, 2, 3 enero mo mass of atom or molecule. ha plank's constant The partition function written as a sum over quantum staves is 94. Ž Ě Ē ope) (shere Box) n=1 n - [21 )JE, elam)] * Šele ms) 7 Since the three exponential functions and a summation over n, , 12 and 3 are identical, we can write the above expression as 9-et emotion)

4 l )-273 Jeglecting one in comparison to the summabion Negle form, wege 73 9° le celebration on the translational energy levels are very close to each other, the summation in the above expression may be replaced by integration which on integrating ince we offerte e or this doma? 2 *[ + Tai lengvas jy gives This is the expression of translational partition function from this expression we get q, is directly proportional to the mass of alom or molecule

Now between Tzos H₂O the mooniles mass of T20 is higher than H₂O . Hence the promis labional partition function (20) of T20 is higher than H₂O And C. H2O would have a smaller troms because it is lighter.