Respuesta :
Answer : The percentage of protonated pentobarbitone is 20%
Explanation :
Let's say B represents pentobarbitone and BH⁺ represents protonated pentobarbitone.
The protonation reaction can be written as
[tex] B + H_{2}O \leftrightarrow BH^{+} + OH^{-} [/tex]
When the above reaction reaches equilibrium, we get a mixture of B and BH⁺.
This mixture contains a weak base pentobarbitone and its protonated form which is a conjugate acid. Therefore the mixture acts as a buffer.
The pH of a buffer is calculated using Henderson formula which is written below.
[tex] pH = pka + log [\frac{Base}{acid}] [/tex]
We have acid = BH⁺
base = B
pH = 8.7
pka = 8.0
Let us plug in the above values in Henderson equation.
[tex] 8.7 = 8.0 + log [\frac{B}{BH^{+}}] [/tex]
[tex] 8.7 - 8.0 = log [\frac{B}{BH^{+}} ] [/tex]
[tex] 0.7 = log [\frac{B}{BH^{+}}] [/tex]
[tex] 10^{0.7} =\frac{B}{BH^{+}} [/tex]
[tex] 5.01 =\frac{B}{BH^{+}} [/tex]
We want to find fraction of BH⁺ , which is written as BH⁺/B.
Therefore we will inverse the above equation.
[tex] \frac{1}{5.01} =\frac{BH^{+}}{B} [/tex]
[tex] 0.200 =\frac{BH^{+}}{B} [/tex]
The percentage of protonated pentobarbitone is 0.200 x 100 = 20%
