What is the molecular formula of a hydrocarbon with m+ = 166? (write the formula with no subscripts, e. g. c4h10.) what is the sum of rings and double bonds in this compound?

A molecular formula represents the exact number of atoms present for each element in the compound.  

For carbon atom: = ( as molar mass of carbon is 12 g/mol)

Now, 6 carbon atoms are present and rest are hydrogen atoms i.e. 6

Thus, formula becomes (

Now, check for unsaturation:

Degree of unsaturation  =

Substitute the value of x and y,

Degree of unsaturation  =

=

= implies one ring and three double bonds.

Thus, formula comes out to be i.e. benzene ring.

C8H18
   Since it hasn't been otherwise specified, I will be making a few assumptions for this problem.
 1. The mystery hydrocarbon is in the form of a chain of carbon atoms with each carbon atom not at the end of the chain linked via a single bond to 2 carbon atoms. Then there will be a hydrogen atom linked to every unused valiance bond for the carbon atoms.
 2. Hydrogen will be assumed to have an atomic weight of 1 and carbon an atomic weight of 12.
   If you contemplate assumption #1 above, you'll realize that there is 1 hydrogen atom at each end of the chain. Between those 2 hydrogen atoms will be multiple groups of a carbon atom linked to 2 hydrogen atoms. So if we use the variable C for the number of carbon atoms, the weight of the hydrocarbon is expressed by the equation:
 W = C*(12+2)+2
 W = C*14+2
   So let's substitute 114 for W and calculate C
 W = C*14+2
 114 = C*14+2
 112 = C*14
 112/14 = C
 8 = C
   So we have 8 carbon atoms.
And therefore we have 2 + 2*8 = 2+16 = 18 hydrogen atoms.
Which means that the desired formula is C8H18