Calculate the pH at 25 ° C when 120 mL of a HCl solution having a concentration of 50 mM is added 50.0 mL of a 120 mM ephedrine solution. Assume no change in temperature.
Amitriptyline is a drug used in treating depression. It is typically formulated as the hydrochloride salt (structure see below). pKa of the corresponding acid to amitriptyline is 9.76 at 25 ° C.
To calculate the pH of the solution, we need to consider the chemical reactions that occur between the hydrochloric acid (HCl) and ephedrine.
First, let's calculate the number of moles of HCl and ephedrine in each solution:
Moles of HCl = concentration x volume = 50 mM x 0.120 L = 0.006 moles
Moles of ephedrine = concentration x volume = 120 mM x 0.050 L = 0.006 moles
Since the moles of HCl and ephedrine are equal, they will react in a 1:1 ratio:
HCl + Ephedrine → Ephedrine-HCl
This reaction will produce 0.006 moles of Ephedrine-HCl.
Next, let's calculate the concentrations of the reactants and products:
For HCl:
Initial concentration = 50 mM
Final concentration = (0.006 moles) / (0.120 L + 0.050 L) = 0.0357 M
For Ephedrine-HCl:
Initial concentration = 0 M
Final concentration = (0.006 moles) / (0.120 L + 0.050 L) = 0.0357 M
Now, let's consider the dissociation of the Ephedrine-HCl salt. The pKa of the corresponding acid to amitriptyline is provided as 9.76.
The pKa is defined as the negative logarithm (base 10) of the acid dissociation constant (Ka). To calculate the Ka, we use the equation:
Ka = 10^(-pKa) = 10^(-9.76) = 1.664 x 10^(-10)
Since the Ephedrine-HCl salt is a 1:1 electrolyte, it will fully dissociate in water, resulting in the formation of Ephedrine and HCl ions.
Let's define the concentration of the dissociated Ephedrine as x:
[Ephedrine] = x M
[HCl] = x M
The equilibrium expression for the dissociation reaction is:
Ka = [Ephedrine] x [HCl] / [Ephedrine-HCl]
Substituting the given values:
1.664 x 10^(-10) = (x)(x) / (0.0357 M)
Rearranging and solving for x:
x^2 = 1.664 x 10^(-10) x 0.0357 M
x^2 = 5.94 x 10^(-12)
x ≈ 7.708 x 10^(-6) M
Therefore, the approximate concentration of Ephedrine and HCl ions after dissociation is 7.708 x 10^(-6) M.
Finally, let's calculate the pH:
pH = -log[H+]
[H+] = 2x (since HCl fully dissociates into H+ ions)
[H+] = 2(7.708 x 10^(-6)) = 1.542 x 10^(-5) M
pH = -log(1.542 x 10^(-5)) = 4.81
Therefore, the pH of the solution at 25 °C, after mixing 120 mL of a 50 mM HCl solution and 50.0 mL of a 120 mM ephedrine solution, is approximately 4.81.