Calculate the pH of the solute in an aqueous solution of 0.0047 M codeine, if the pKa of itsconjugate acid is 8.21.
What is the percentage protonation of the solute?
If we all codeine, C, then the hydrolysis is
C + HOH ==> HC^+ + OH^-
Kb = (Kw/Ka) = (OH^-)^2/(C)
Substitute into the Kb expression and solve for OH^-, convert to pOH, then to pH.
To calculate the pH of the solute in an aqueous solution of codeine, you need to consider its acidity and the dissociation equilibrium constant. The pKa of the conjugate acid is given as 8.21, which means it is a weak acid.
1. Determine the concentration of the codeine in Molarity (M). The given concentration is 0.0047 M.
2. Use the dissociation equilibrium of the acid to determine the concentration of the hydronium ion (H3O+) in the solution. The equilibrium equation is:
Codeine (base) + H2O ↔ Codeine-H+ (conjugate acid) + OH-
The dissociation constant (Ka) for the conjugate acid can be determined from the pKa value: Ka = 10^(-pKa).
3. Set up the equilibrium expression. Since it is a weak base, we assume that the concentration of the codeine-H+ is equal to [H3O+]. Therefore, the equilibrium expression becomes:
Ka = [H3O+][OH-] / [base]
As the concentration of water (H2O) is much greater than [OH-] and [base], we can safely assume that the concentration of OH- remains constant and negligible compared to the concentration of the codeine-H+. This simplifies the expression to:
Ka = [H3O+][OH-] / [base] ≈ [H3O+]/[base]
4. Solve the equation for [H3O+]. Rearrange the equation to solve for [H3O+]:
[H3O+] = Ka * [base]
Substitute the Ka value and the concentration of codeine into the equation:
[H3O+] = (10^(-pKa)) * [codeine]
[H3O+] = (10^(-8.21)) * (0.0047)
5. Calculate the pH. The pH is the negative logarithm (base 10) of [H3O+]:
pH = -log10([H3O+])
pH = -log10[(10^(-8.21)) * (0.0047)]
6. Calculate the percentage protonation. This is the ratio of protonated codeine to the total codeine concentration, multiplied by 100:
Percentage Protonation = [H3O+] / [codeine] * 100
Percentage Protonation = [(10^(-8.21)) * (0.0047)] / (0.0047) * 100
Plug in the values and calculate the answer using a calculator or computer software.
Note: The pKa value provided assumes that the codeine is considered to be in its acidic form. If it is in its basic form, you'll need to use the pKb (dissociation constant of the base) instead and make adjustments to the equations accordingly.