Calculate the pH of a solution prepared by dissolving 0.250 mol of benzoic acid ( H)and of sodium benzoate (Na )in water sufficient to yield 1.00 L of solution.The of benzoic acid is
A)4.409
B)3.965
C)10.035
D)9.591
E)5.190

Question

Calculate the pH of a solution prepared by dissolving 0.250 mol of benzoic acid (    H)and  of sodium benzoate (Na    )in water sufficient to yield 1.00 L of solution.The  of benzoic acid is 
A)4.409 
B)3.965 
C)10.035 
D)9.591 
E)5.190

Quizplus · Accepted Answer

The solution contains a weak acid (benzoic acid) and its conjugate base (sodium benzoate). We can use the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log([A-]/[HA])
where pKa is the acid dissociation constant of benzoic acid (4.202), [A-] is the concentration of the conjugate base (sodium benzoate), and [HA] is the concentration of the weak acid (benzoic acid).
First, we need to calculate the concentration of sodium benzoate:
moles of NaC7H5O2 = 0.250 mol
moles of NaC7H5O2 = [NaC7H5O2] x 1.00 L
[NaC7H5O2] = moles of NaC7H5O2 / 1.00 L
[NaC7H5O2] = 0.250 mol / 1.00 L
[NaC7H5O2] = 0.250 M
Since the solution was prepared by dissolving benzoic acid and sodium benzoate in water, the initial concentration of benzoic acid is also 0.250 M.
Now we can substitute the values into the Henderson-Hasselbalch equation:
pH = 4.202 + log(0.250/0.250)
pH = 4.202 + log(1)
pH = 4.202
Therefore, the pH of the solution is 4.202, which is closest to choice B (3.965).

Calculate the PH of a Solution Prepared by Dissolving 0