Question

describe the symmetries of each molecule shown
a. benzene b. water c. hydrogen peroxide
a. describe the symmetries of the benzene molecule select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice
a. the benzene molecule has line(s) of symmetry, point symmetry, and the following rotational symmetry(ies) °
(use a comma to separate answers as needed do not include the degree symbol in your answer.)
b. the benzene molecule does not have any symmetry
c. the benzene molecule has line(s) of symmetry and does not have rotational symmetry
d. the benzene molecule has the following rotational symmetry(ies) °, point symmetry, and does not have reflectional symmetry

Explanation:

Step1: Recall Benzene Symmetry

Benzene (\(C_6H_6\)) is a regular hexagon. A regular hexagon has 6 lines of symmetry (3 through opposite vertices, 3 through midpoints of opposite sides), point symmetry (inversion symmetry), and rotational symmetries. The rotational symmetries of a regular hexagon are angles where \(360^\circ/n\), \(n = 6\), so \(60^\circ, 120^\circ, 180^\circ, 240^\circ, 300^\circ\) (but also, the fundamental rotational symmetry is \(60^\circ\) increments, and it has \(6\)-fold rotational symmetry, but the key rotational symmetries here are \(60, 120, 180, 240, 300\), but also, the main ones for the question: lines of symmetry = 6, rotational symmetries include \(60, 120, 180, 240, 300\) (or simplified, the rotational symmetry angles are \(60, 120, 180, 240, 300\), but also, the order of rotation is 6, so angles are multiples of \(60^\circ\)). But the question's option A is the correct one. So lines of symmetry: 6. Rotational symmetries: 60, 120, 180, 240, 300 (or the fundamental angle is \(60^\circ\), but the question's box for rotational symmetry(ies) would take the angles. Wait, the benzene molecule has 6 lines of symmetry, point symmetry, and rotational symmetries of \(60, 120, 180, 240, 300\) (or \(60^\circ\) increments). So for option A: lines of symmetry = 6, rotational symmetries: 60, 120, 180, 240, 300 (but maybe the question expects the angles, so we fill 6 in the first box, and 60, 120, 180, 240, 300 in the second? Wait, no, maybe the rotational symmetry angles are \(60, 120, 180, 240, 300\) (since rotating by \(60^\circ\) maps it onto itself, \(120^\circ\), etc., up to \(300^\circ\)). But the key is option A is correct. So:

Step2: Fill in the Boxes

For option A: lines of symmetry = 6. Rotational symmetries: 60, 120, 180, 240, 300 (or the angles are multiples of \(60^\circ\)). So the first box (lines of symmetry) is 6. The second box (rotational symmetry(ies)) is 60, 120, 180, 240, 300 (or maybe the question expects the fundamental angle, but no, benzene has 6-fold rotational symmetry, so angles are \(60, 120, 180, 240, 300\)).

Answer:

A. The benzene molecule has \(\boldsymbol{6}\) line(s) of symmetry, point symmetry, and the following rotational symmetry(ies) \(\boldsymbol{60, 120, 180, 240, 300}\)° (Note: The degree symbol is not included in the answer as per instructions, so the rotational symmetry angles are 60, 120, 180, 240, 300)