2) What is the point group of diborane (B2H6)? (1 point) a. Find the reducible representation for four H atoms labeled as "a" b. Find the reducible representation for two H atoms labeled as "b" (Show all work. Select the correct character table to answer this question) (6 points) a H b H 8. B. X H. a HD b H a

1. (7 points) Symmetry is an important topic in chemistry because the symmetry of a molecule may affect its physical and chemical properties. One important task is to identify the point group of a given molecule. Please complete the following tasks for each molecule. Molecule Any LC₂ ? Any oh? Any ov? Point Highest symmetry rotation Group CI H H P H H H H H + CI cl H H 2- H H Br Br H H CI OC MICO OC CO CO

What is the order, h, of the D3h point group? (6m2) 3C, 203 E 2S, 30, A 1 1 1 1 1 1 1 1 -1 1 1 -1 E' -1 -1 A 1 -1 -1 A, 1 1 -1 1 E" -1 -2 1 10 12 8.

5. The most stable structure for N₂O4 is planar and belongs to the D2h point group, which has the character table shown below. D2h E C₂(X) C₂(V) C₂ (2) i o(xy) o(yz) o(x2) Ag 1 1 1 1 1 1 1 1 B1g 1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 B2g B3g Au B1u 1 B2u 1 B3u 1 1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 5.1 How many translational degrees of freedom does N₂04 have? 5.2 How many rotational degrees of freedom does N₂04 have? 5.3 How many normal modes of vibration does N204 have? x², y², z² xy 5.5 How many of the vibrational modes of N₂04 are IR-active? XZ yz 5.6 How many of the vibrational modes of N₂O4 are Raman-active? Z y X Rz Ry Rx 3. 5.4 The displacement vectors for the atoms of N₂O4 span 3Ag + 3B1g + 2B2g + B3g + Au + 2B1u + 3B2u + 3B3u. What are the symmetry species of the normal modes of vibration? ☐☐☐