Question

You are a forensic scientist. You are investigating a murder involving poison. The victim was poisoned with a compound called di-chloro benzene whose formula is C6H4Cl2. Autopsy results show that the victim’s body contained about 31 g of the poison, but the actual amount could have been slightly higher due to tissue absorption. The main suspect is his wife, Suzanne, who works as a chemistry professor at the local university. Records show that she purchased 15 g of benzene (C6H6) two days before the murder. Benzene is one of the compounds used to make the poison, but she claims she was using it to make ethyl benzene (C6H5CH3), an innocuous compound, for use in her lab. She shows you the bottle of ethyl benzene she claims to have made. It contains 25 grams of ethyl benzene.

Is she telling the truth or did she have more nefarious motives? If you can show that it is possible to produce 25 g of ethyl benzene from 15 grams of benzene, then she was telling the truth. Otherwise, you will have caught her in a lie, which makes it likely she killed her husband with the poison. After extensive research in the literature, you find the two reactions related to this case.

To produce ethyl benzene, the reaction is:
CH4 + C6H6 → C6H5CH3 + H2

After balancing reactions, use stoichiometry to
solve this case. Be sure to show all your work and
explain whether the results show the wife to be
innocent or a murderer.

Answer 1

based on the evidence below, Suzanne is innocent

Step-by-step explanation:

calculate the theoretical yield of ethyl benzene from the given amount of benzene, and compare it to the actual yield of 25 g.

balance the chemical equation:

1 CH4 + 1 C6H6 → 1 C6H5CH3 + 1 H2

calculate the theoretical yield of ethyl benzene:

Molar mass of C6H6 = 78.11 g/mol

Molar mass of C6H5CH3 = 106.17 g/mol

15 g C6H6 x (1 mol C6H6 / 78.11 g) x (1 mol C6H5CH3 / 1 mol C6H6) x (106.17 g / 1 mol C6H5CH3) = 20.45 g C6H5CH3

the theoretical yield of ethyl benzene is 20.45 g.

Since the actual yield was 25 g, suzanne's claim is true. She could have used the 15 g of benzene to produce 25 g of ethyl benzene, with some remaining unused.