Answer : The fraction of the molecules in the neutral (imidazole) form are, 0.799
Explanation : Given,
pH = 6.6

Using Henderson Hesselbach equation :
![pH=pK_a+\log \frac{[Salt]}{[Acid]}](https://tex.z-dn.net/?f=pH%3DpK_a%2B%5Clog%20%5Cfrac%7B%5BSalt%5D%7D%7B%5BAcid%5D%7D)
![pH=pK_a+\log \frac{[\text{Imidazole}]}{[\text{Imidazolium ion}]}](https://tex.z-dn.net/?f=pH%3DpK_a%2B%5Clog%20%5Cfrac%7B%5B%5Ctext%7BImidazole%7D%5D%7D%7B%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D)
Now put all the given values in this expression, we get:
![6.6=6.0+\log \frac{[\text{Imidazole}]}{[\text{Imidazolium ion}]}](https://tex.z-dn.net/?f=6.6%3D6.0%2B%5Clog%20%5Cfrac%7B%5B%5Ctext%7BImidazole%7D%5D%7D%7B%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D)
![\frac{[\text{Imidazole}]}{[\text{Imidazolium ion}]}=10^{6.6-6.0}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B%5Ctext%7BImidazole%7D%5D%7D%7B%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D%3D10%5E%7B6.6-6.0%7D)
![\frac{[\text{Imidazole}]}{[\text{Imidazolium ion}]}=10^{0.6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B%5Ctext%7BImidazole%7D%5D%7D%7B%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D%3D10%5E%7B0.6%7D)
![\frac{[\text{Imidazole}]}{[\text{Imidazolium ion}]}=3.98](https://tex.z-dn.net/?f=%5Cfrac%7B%5B%5Ctext%7BImidazole%7D%5D%7D%7B%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D%3D3.98)
...........(1)
Now we have to determine the fraction of the molecules are in the neutral (imidazole) form.
Fraction of neutral imidazole = ![\frac{[\text{Imidazole}]}{[\text{Imidazole}]+[\text{Imidazolium ion}]}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B%5Ctext%7BImidazole%7D%5D%7D%7B%5B%5Ctext%7BImidazole%7D%5D%2B%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D)
Now put the expression 1 in this expression, we get:
Fraction of neutral imidazole = ![\frac{3.98[\text{Imidazolium ion}]}{3.98[\text{Imidazolium ion}]+[\text{Imidazolium ion}]}](https://tex.z-dn.net/?f=%5Cfrac%7B3.98%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D%7B3.98%5B%5Ctext%7BImidazolium%20ion%7D%5D%2B%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D)
Fraction of neutral imidazole = ![\frac{3.98[\text{Imidazolium ion}]}{4.98[\text{Imidazolium ion}]}](https://tex.z-dn.net/?f=%5Cfrac%7B3.98%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D%7B4.98%5B%5Ctext%7BImidazolium%20ion%7D%5D%7D)
Fraction of neutral imidazole = 
Fraction of neutral imidazole = 0.799
Thus, the fraction of the molecules in the neutral (imidazole) form are, 0.799