Buffer Problem 1

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What are the concentrations of acetic acid (CH3COOH) and the acetate anion (CH3COO-) in a 0.200 M acetate buffer whose pH is 5.5? The pka of acetic acid is 4.77

 
This question may seem wordy. To avoid confusion, write down what you’re given and what you need to find
 
Given: pH = 5.5, pka of acetic acid = 4.77, concentration of buffer = 0.200 M
Unknown: [CH3COOH] and [CH3COO-]
 
When dealing with buffers, use the Henderson-Hasselbalch equation: pH = pka + log ([A-]/[HA])
[A-] is the concentration of the anion, and [HA] is the concentration of the acid. In this problem, these variables are our unknowns
 
To get them, first recognize that the concentration of the buffer is equal to the concentration of the acid and the anion:
 
[Buffer] = [HA] + [A-]   rearranging this, we have [HA] = [Buffer] – [A-] so substitute this into the H-H equation:
 
pH = pka + log (A-/[Buffer - A-])
 
Then substitute in your known values
 
5.5 = 4.77 + log ( A-/(0.200-A-))      Solve for A-
 
0.73= log ( A-/(.200-A-))
 
100.73 = A-/(0.200-A-)                raise 10 to the 0.73 power to remove the log
 
A- = 0.16 M = [CH3COO-]
 
Using the equation from earlier [HA] = [Buffer] - [A-]
 
substitute [A-] into the equation
 
[HA] = 0.200 M -0.16 M = 0.04 M