Answer
Diazepam has 13 H atoms and a molecular formula of $C_{16}H_{13}ClN_{2}O$
Work Step by Step
The degree of unsaturation in a molecule is the number of multiple bonds and/or rings that the molecule possesses.
Here, Diazepam has a total of 11 degrees of unsaturation (3 rings and 8 double bonds). This corresponds to the absence of 11 pairs of H atoms from the formula of the corresponding saturated hydrocarbon.
Let there be $'x'$ number of H atoms in the formula, i.e. $C_{16}H_{x}ClN_{2}O$.
The formula of its corresponding hydrocarbon is achieved by
(i) Adding the number of halogen atoms to the number of H atoms.
(ii) Subtracting the nmber of N atoms from the number of H atoms
(iii) Ignoring the number of O atoms.
The final number of H atoms will be: $x+1-2$ = $x-1$
And the formula of the hydrocarbon will be: $C_{16}H_{x-1}$
The saturated hydrocarbon with 16 carbons has the formula: $C_{16}H_{34}$
Now, since the molecule has 11 degrees of unsaturation;
$H_{34} - H_{x-1} = H_{22} = 11 H_{2}$
i.e. (Number of H atoms in saturated hydrocarbon $-$ Number of H atoms in unsaturated hydrocarbon = Number of Pairs of H atoms missing from unsaturated hydrocarbon/Degree of unsaturation)
which when simplified, gives us:
$34-(x-1)=22$
$(x-1) = 34-22$
$(x-1) = 12$
$x = 13$
Therefore, the number of H atoms in Diazepam is 13.
