the pH of the solution obtained by mixing 400ml 0.1M acetic acid, 50ml 0.1M sulphuric acid and 50ml 0.3m sodium acetate is (Ka of acetic acid is 1x10-5)
First, use the Henderson-Hasselbalch equation to determine the pH of the buffer portion of the system (acetic acid/sodium acetate). Then add in the H2SO4 which increases the concn of the acid and decreases the concn of the base (acetate). Re-solve for pH.
To find the pH of the solution obtained by mixing these solutions, we need to determine the concentrations of the relevant ions and molecules and then apply the relevant equilibrium equations.
First, let's calculate the moles of acetic acid and sodium acetate in the solution:
moles of acetic acid = volume of acetic acid solution (L) * molarity of acetic acid solution (M)
= 0.400 L * 0.1 M
= 0.040 moles
moles of sodium acetate = volume of sodium acetate solution (L) * molarity of sodium acetate solution (M)
= 0.050 L * 0.3 M
= 0.015 moles
Next, we need to consider the dissociation of acetic acid in water:
CH3COOH ⇌ CH3COO- + H+
The equilibrium constant for this reaction is the acid dissociation constant (Ka) for acetic acid, which is given as 1x10^-5.
To find the concentration of acetate ions (CH3COO-) in the solution, we need to consider the reaction between acetic acid and sodium acetate:
CH3COOH + CH3COONa ⇌ CH3COO- + CH3COONaH
Since sodium acetate is a strong electrolyte and completely dissociates, we can assume that the concentration of acetate ions (CH3COO-) is equal to the initial concentration of sodium acetate. Thus, [CH3COO-] = 0.3 M.
Now, applying the principle of equilibrium, the concentration of H+ ions can be calculated using the equation for the dissociation of acetic acid:
[CH3COO-][H+] / [CH3COOH] = Ka
Substituting the values:
(0.3)([H+]) / 0.040 = 1x10^-5
Simplifying the equation:
[H+] = (1x10^-5)(0.040) / 0.3
[H+] = 1.33x10^-6 M
Finally, we can calculate the pH of the solution using the equation:
pH = -log[H+]
Substituting the value of [H+]:
pH = -log(1.33x10^-6)
≈ 5.88
Therefore, the pH of the solution obtained by mixing 400 mL of 0.1 M acetic acid, 50 mL of 0.1 M sulfuric acid, and 50 mL of 0.3 M sodium acetate is approximately 5.88.