The pH at the equivalence point is 8.72.
A mixture of a weak acid and its conjugate base is called a buffer solution. The acid-base reaction for the titration of a weak acid using a strong base is shown in the attached picture. The equivalence point is reached when there is enough base to neutralize the acid.
The number of moles of acetic acid can be calculated by multiplying molarity (0.10 M) and volume (50 mL or 0.05L), resulting in 5 x 10 -3 mol. This will also be equal to the moles of conjugate base produced.
For the next reaction, the concentration of the conjugate base must be determined by dividing its number of moles by the total volume. The calculation of the NaOH volume used is shown below.
molarity of NaOH = moles NaOH / volume NaOH
volume NaOH = 5 x 10-3 moles / 0.10 M
volume NaOH = 0.05 L
total volume = volume NaOH + volume acetic acid
total volume = 0.05 L + 0.05 L = 0.10 L
concentration of conjugate base CH3COO- = 5x 10-3 mol / 0.10 L = 0.05 M
Then, we will determine the value of x from the second reaction. The base dissociation constant or Kb is used to solve for x. The value of acid dissociation constant or Ka of acetic acid is 1.8x10-5.
Kw = 1 X 10 -14 = Ka * Kb
Kb = 1x10-14 / Ka = 1x10-14 / 1.8x10-5
Kb= 5.56 x 10-10
Kb = { [CH3COOH]*[OH-]} / [CH3COO-]
Use the equilibrium value from the second reaction to solve for x
[tex]5.56x10x^{-10}=\frac{[x][x]}{[0.05-x]}[/tex]
[tex](5.56x10^{-10})(0.05)- (5.56x10^{-10})(x)=x^{2}[/tex]
[tex]x^{2} +5.56x10^{-10}x-2.78x10^{-11}=0[/tex]
Solving for x through the quadratic equation, x is found to be equal to 5.27x10-6. This is also equal to the concentration of -OH.
pOH = -log (5.27x10-6) = 5.27
pH = 14 - pOH = 8.72
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