
Rings
 The number of rings in a given structure is the minimum number of bonds
that must be broken so that there is no rings, not the perceived cycles.
 The number of rings is given by the names mono, bi, tri, tetra,
pentacyclic or cyclo, etc.
Exam question 10: How many rings are
in a given structure?
Number of Hydrogens
 By insertions starting with hydrogen, H_{2}, for saturated
acyclic hydrocarbons, H = 2 + 2 C.
 For acyclic hydrocarbons, H = 2 + 2 C  2 unsaturations.
 For hydrocarbons, H = 2 + 2 C  2 unsaturations  2 rings.
 From 3, hydrocarbons have an even number of hydrogens and molecular
weight.
 By extensions, H = 2 + 2 C + N  X  2 unsaturations 2 rings = 2 +
S (valency of element Y  2) Y 2 unsaturations 
2 rings.
 The normal valency of carbon is 4, nitrogen 3, oxygen 2, halogens 1.
 Take care with elements with multiple valences, for example sulfur, and
salts or more than one molecule.
Exam question 11: How
many hydrogens in a given structure?
Number of Rings Plus Unsaturations
 2 (unsaturations + rings) = 2 + 2 C + N  X  H = 2 +
S (valency of element Y  2) Y.
 2 (unsaturations + rings) is called the index of hydrogen deficiency
which equals the difference in hydrogens between having and not having
unsaturations and rings.
 unsaturations + rings = 1 + C + N/2  H/2  X/2 = 1 +
S (valency of element Y  2)/2 Y.
 If you know a compound is saturated then the equation gives you the
number of rings, otherwise you cannot assume rings or unsaturations from the
molecular formula, just an upper bound.
 If you know a compound has no rings then the equation gives you the
number of unsaturations, otherwise you cannot assume rings or unsaturations
from the molecular formula, just an upper bound.
Exam question 12: How
many rings plus unsaturations are implied from a given molecular formula?
Number of Rings after Hydrogenations
 Hydrogenation catalyzed by transition metals saturates compounds.
 The molecular formula after hydrogenation gives the number of rings.
 The unsaturations + rings before hydrogenations  the number of rings
determined from the molecular formula after hydrogenation gives the number
of unsaturations.
Exam question 13: Given
molecular formulas before and after hydrogenations, how many rings and how many
unsaturations are in a given compound?
Number of Sigma Bonds
 By insertions starting with hydrogen, H_{2}, for saturated
acyclic hydrogcarbons, sigma bonds = 1 + 3 C.
 For acyclic hydrocarbons, sigma bonds = 1 +3 C 2 usaturations.
 For hydrocarbons, sigma bonds = 1 + 3 C 2 unsaturations  rings.
 By extension, sigma bonds = 1 + 3 C + 2 N + O 2 unsaturations  rings.
 Since bonds to hydrogen are always sigma bonds, sigma bonds that do not
involve hydrogens = sigma bonds  H = 1 + 3 C + 2 N + O  2 unsaturations 
rings  (2 + 2C + N  X  2 unsaturations  2 rings) = 1 + C + N + O + X +
rings.
 Therefore sigma bonds = 1 + C + N + O + X + H + rings =
S atoms + rings 1.
Exam questions 14: How many sigma
bonds are implied from a given molecular formula?
Total Number of Bonds
 The total bonds = sigma bonds + pi bonds = S
atoms + rings + pi bonds 1 = S atoms + C + N/2 
H/2 X/2 = S atoms + S
(valency of element Y  2)/2 Y = S (Y
+ (valency of element Y  2)/2 Y) = S (valency
of element Y)/2 Y = the number of bonds that should be contained in a
molecular modeling kit.
Exam questions 15: How
many total bonds are implied from a given molecular formula?

