[namesis]

Compound X has a molecular formula $$C_7 H_9 O_2 F_3$$ and relative molecular mass (RMM) of 182.  The IR spectrum of X has two characteristic bands at 1650 and 1815 $$cm^{–1}$$.  In polar solvents such as DMSO (dimethyl sulfoxide, Me2SO) the compound readily ionises to give a stabilised, symmetrical carbocation, A+, and the anion B–: 
 
  Cation A+:  13C NMR:  δ 206, 85, 18 ppm.  RMM = 69. 
  Anion B–:  13C NMR:  δ 161 (1:3:3:1 quartet, J = 44 Hz), 118 (1:3:3:1 quartet, J = 282 Hz) ppm.  RMM = 113.     

Suggest, with explanation, a possible structure for compound X that fits these data.

From the IR, I can deduce that there will be a ketone on a 3 membered ring (1815) and probably a carbon double bond.

For cation A+ the presence of a ketone seems reasonable and possibly a carbon with a single bond with an Oxygen.

For anion B- the most reasonable thing seems to be a carbon with all 3 Fluorines on it connected to another Carbon that has a double bond with an oxygen.

Any help with that?

[Dan]

For anion B- the most reasonable thing seems to be a carbon with all 3 Fluorines on it connected to another Carbon that has a double bond with an oxygen.

Any help with that?

Start with B^- (easy), then go back to A⁺ (hard until you figure out B^-).

I think you're very close here: CF₃ and C=O groups - what else do you need to make an anion at MW = 113?

Now that you have B^-, subtract its formula from X to give the formula of A⁺.

I know from the NMR and IR it looks like A⁺ is a carbonyl, but I suspect this is a red herring - allylic/benzylic carbocations also typically come around 200 ppm.