Molecular Statistics
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Rings

  1. 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.
  2. 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

  1. By insertions starting with hydrogen, H2, for saturated acyclic hydrocarbons, H = 2 + 2 C.
  2. For acyclic hydrocarbons, H = 2 + 2 C - 2 unsaturations.
  3. For hydrocarbons, H = 2 + 2 C - 2 unsaturations - 2 rings.
  4. From 3, hydrocarbons have an even number of hydrogens and molecular weight.
  5. By extensions, H = 2 + 2 C + N - X - 2 unsaturations -2 rings = 2 + S (valency of element Y - 2) Y -2 unsaturations - 2 rings.
  6. The normal valency of carbon is 4, nitrogen 3, oxygen 2, halogens 1.
  7. 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

  1. 2 (unsaturations + rings) = 2 + 2 C + N - X - H = 2 + S (valency of element Y - 2) Y.
  2. 2 (unsaturations + rings) is called the index of hydrogen deficiency which equals the difference in hydrogens between having and not having unsaturations and rings.
  3. unsaturations + rings = 1 + C + N/2 - H/2 - X/2 = 1 + S (valency of element Y - 2)/2 Y.
  4. 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.
  5. 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

  1. Hydrogenation catalyzed by transition metals saturates compounds.
  2. The molecular formula after hydrogenation gives the number of rings.
  3. 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

  1. By insertions starting with hydrogen, H2, for saturated acyclic hydrogcarbons, sigma bonds = 1 + 3 C.
  2. For acyclic hydrocarbons, sigma bonds = 1 +3 C -2 usaturations.
  3. For hydrocarbons, sigma bonds = 1 + 3 C -2 unsaturations - rings.
  4. By extension, sigma bonds = 1 + 3 C + 2 N + O -2 unsaturations - rings.
  5. 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.
  6. 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

  1. 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?

 

 

 

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