Calculate the pOH, pH, and percent protonation of solute in the following aqueous solution.
0.059 M quinine, given that the pKa of its conjugate acid is 8.52.
Please show me how to do it and not just the answers. Thanks!
Quinine has a tertiary amine group so acts as base
QN + H2O -----> QNH+ + OH-
given pka is 8.52
-log ka=8.52
ka= 3*10^-09,
for conjugate acid base pair at 25degrees Celsius kw= ka*kb
therefore Kb= kw/ka
= 10^-14/ 3*10^-09 = 3.4 *10^-06
from equation kb=[QNH+][OH-]/[QN]
QN + H2O -----> QNH+ + OH-
initial 0.018
equlli 0.018-x x x
since quinine is a weak base 0.018-x can be written as 0.018
therefore kb= x^2/0.018
x= squre root of ( 3.4*10^-6*0.018)
=2.47 *10^-04
POH= -log[OH-]= -logx= -log 2.47*10^-4
=3.61
PH= 14-POH =10.39
percent protonation= [QNH+]/Qn
=x/0.018 *100
=1.4%
To calculate the pOH, pH, and percent protonation of the solute in the given aqueous solution, first, we need to understand the relationship between pOH, pH, and the concentration of the solute.
pOH is a measure of the hydroxide ion concentration, while pH is a measure of the hydrogen ion concentration. The two values are related through the equation:
pH + pOH = 14
The percent protonation of a solute refers to the extent to which the solute has gained a proton and become ionized. In the case of an acid and its conjugate base, the percent protonation refers to how much of the solute exists in its acidic form.
To calculate these values, we'll follow these steps:
Step 1: Calculate the hydronium ion concentration ([H3O+])
Since quinine is a base, we need to consider its conjugate acid, which is present in water. The concentration of the conjugate acid will determine the hydronium ion concentration.
Given that the pKa of the conjugate acid is 8.52, we can determine the concentration of hydronium ions ([H3O+]) using the equation:
pH = pKa + log ([conj. acid]/[acid])
pH = 8.52 + log ([conj. acid]/[acid])
Here, [conj. acid] represents the concentration of the conjugate acid, and [acid] represents the concentration of the acid (quinine) in the solution.
Step 2: Calculate the hydroxide ion concentration ([OH-])
Since quinine is a base, it will react with water to form hydroxide ions ([OH-]). The concentration of hydroxide ions can be determined by taking the inverse of the hydronium ion concentration:
[OH-] = 1 x 10^(-pH)
Step 3: Calculate the pOH
Using the hydroxide ion concentration calculated in Step 2, we can determine the pOH using the equation:
pOH = -log10 ([OH-])
Step 4: Calculate the percent protonation
To calculate the percent protonation, we need to determine the amount of the solute present in its acidic form. For this, we'll need the concentrations of the acidic and conjugate acid forms of quinine.
The percent protonation can be calculated using the equation:
% protonation = ([acid] / ([acid] + [conj. acid])) x 100
Now, let's apply these steps to the given information.
Step 1: Calculate the hydronium ion concentration ([H3O+])
Using the equation:
pH = pKa + log ([conj. acid]/[acid])
Let's assume the concentration of the conjugate acid is [conj. acid]. Since quinine is the base, its concentration will be [acid].
pH = 8.52 + log ([conj. acid]/[acid])
Step 2: Calculate the hydroxide ion concentration ([OH-])
Using the equation:
[OH-] = 1 x 10^(-pH)
Step 3: Calculate the pOH
Using the equation:
pOH = -log10 ([OH-])
Step 4: Calculate the percent protonation
Using the equation:
% protonation = ([acid] / ([acid] + [conj. acid])) x 100
By following these steps, you can calculate the pOH, pH, and percent protonation of the solute in the given aqueous solution.