Determine the pH of the following aqueous solution.Initial concentrations are given.
[HC₂H₃O₂] = 0.250 M,[NaC₂H₃O₂] = 0.120 M ,K_a ( acetic acid) = 1.8 × 10^-5

Question

Quizplus · Accepted Answer

First, write the equation for the dissociation of acetic acid:
CH3COOH + H2O ⇌ CH3COO- + H3O+
The equilibrium constant expression is: 
Ka = [CH3COO-][H3O+]/[CH3COOH]
We need to find the concentration of CH3COOH, CH3COO-, and H3O+. 
CH3COOH is given as 0.250 M, and CH3COO- is initially 0 M. 
To find the concentration of H3O+, we need to use the initial concentrations and the equilibrium concentrations of CH3COO- and H3O+. Let x be the concentration of H3O+ and CH3COO-. Then at equilibrium: 
[H3O+] = x 
[CH3COO-] = x 
[CH3COOH] = 0.250 - x 
Now we can plug these concentrations into the equilibrium constant expression: 
1.8 x 10^-5 = (x)(x)/(0.250 - x) 
Solving for x, we get x = 1.17 x 10^-3 M. 
The pH is then calculated as pH = -log[H3O+] = -log(1.17 x 10^-3) = 3.93. 
However, we need to take into account the presence of a buffer, which will affect the pH of the solution. The buffer is composed of acetic acid (CH3COOH) and its conjugate base (CH3COO-). The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation: 
pH = pKa + log([CH3COO-]/[CH3COOH])
The pKa of acetic acid is 4.76. Plugging in the values: 
pH = 4.76 + log(0.120/0.250) = 4.40.

Determine the PH of the Following Aqueous Solution