Help on DAT question of the day

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May 31, 2013
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So I have been trying to figure out this degree of unsaturation problem, and I keep ending up with 12 degrees of unsaturation. Can someone explain to me why it is 11? I included a picture but the question is:
How many degrees of unsaturation are present in the anxiolytic drug Valium (diazepam), molecular formula C16H13ClN2O?

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This is how I approach this problem. The problem is asking you on the bond connectivity and if there are double or triple bond (unsaturation) present.

First use the saturated formula CnH(2n+2) which will get you to C16H34

Now lets deal with the Cl. How does it play a role in this molecule? It connects with a carbon and TAKES the place of a H. So the saturated molecule should have 1 less Hydrogen from what we predicted.

Now we have C16H33

Now the two nitrogens. Lets assume they are amines for the saturated solution. They connect with the carbon and TAKE the place of a hydrogen BUT add on TWO hydrogens (NH2). Net gain of 1 hydrogen per N. So the saturated molecules would have 2 more H of the current formula we predicted.

Now we have C16H35.

All you have to do now is subtract the H difference divided by two.

35-13=22/2= 11 degrees of unsaturation!!
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A faster alternative: C-1/2(X-N) + 1
X= H and Halos
N= nitrogens
O have no effect

16-1/2(14-2) +1
16-6+1 =11
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So in what cases can we use the formula (2c + N - H - X) / 2 ? Because the formula you find anywhere online does not apply in this case. I cannot even find any mention of the formula used in this question anywhere online. If you look up the aformentioned formula, it is going to produce a different result for any molecule which includes nitrogen atoms, so when do you use this formula over the one that is used to answer this question?