To determine the quantities in the titration of HC2H3O2 (acetic acid) with NaOH, we need to consider the reaction between them. The balanced equation for the reaction is:
HC2H3O2 + NaOH → NaC2H3O2 + H2O
From the balanced equation, we can see that the stoichiometric ratio between HC2H3O2 and NaOH is 1:1. This means that when the reaction reaches the equivalence point, the moles of HC2H3O2 will be equal to the moles of NaOH added.
a) To find the initial pH, we need to determine the concentration of H+ ions in the acetic acid solution. Acetic acid is a weak acid, so we can use the expression for the ionization of acetic acid to calculate its initial concentration of H+ ions:
HC2H3O2 → H+ + C2H3O2-
The initial concentration of H+ ions can be calculated using the initial concentration of HC2H3O2, assuming it fully ionizes. Thus, [H+] = [HC2H3O2] = 0.110 M.
To calculate the initial pH, we can use the formula for pH: pH = -log[H+]. Plugging in the value for [H+], we have:
pH = -log(0.110) ≈ 0.96
Therefore, the initial pH is approximately 0.96.
b) At the equivalence point, the moles of HC2H3O2 will be equal to the moles of NaOH added. To find the volume of NaOH required to reach the equivalence point, we can use the equation:
n(HC2H3O2) = n(NaOH)
Since the initial concentration of HC2H3O2 is 0.110 M and the volume is 25.0 mL (0.0250 L), the initial moles of HC2H3O2 can be calculated as:
moles(HC2H3O2) = concentration(HC2H3O2) × volume(HC2H3O2)
= 0.110 M × 0.0250 L
= 0.00275 moles
Since the stoichiometric ratio between HC2H3O2 and NaOH is 1:1, the moles of NaOH required to reach the equivalence point are also 0.00275 moles.
To find the volume of NaOH required, we divide the moles of NaOH by its concentration:
volume(NaOH) = moles(NaOH) / concentration(NaOH)
= 0.00275 moles / 0.125 M
= 0.022 L or 22.0 mL
Therefore, the volume of added base required to reach the equivalence point is 22.0 mL.
c) To find the pH at 6.00 mL of the added base, we need to determine how much HC2H3O2 and NaOH are left in the solution. Since the stoichiometric ratio between HC2H3O2 and NaOH is 1:1, the moles of NaOH added at 6.00 mL will also be 0.00275 moles.
To calculate the moles of HC2H3O2 remaining, we subtract the moles of NaOH added from the initial moles of HC2H3O2:
moles(HC2H3O2 remaining) = moles(HC2H3O2 initial) - moles(NaOH added)
= 0
d) At one-half of the equivalence point:
One-half of the equivalence point corresponds to the point where half of the acetic acid has reacted with sodium hydroxide. This means that the moles of HC2H3O2 will be equal to half of its initial moles.
First, calculate the initial moles of HC2H3O2:
Moles = concentration x volume
Moles of HC2H3O2 = 0.110 M x 0.025 L = 0.00275 mol
At one-half of the equivalence point, half of the moles of HC2H3O2 will have reacted, leaving half of the moles remaining:
Moles of HC2H3O2 remaining = 0.00275 mol / 2 = 0.001375 mol
To determine the concentration of HC2H3O2 remaining, divide the moles by the volume of the solution at one-half of the equivalence point. Since the volume doubles at the equivalence point, the volume at one-half of the equivalence point is half of the total volume (25.0 mL / 2 = 12.5 mL = 0.0125 L):
Concentration of HC2H3O2 remaining = 0.001375 mol / 0.0125 L = 0.11 M
Since acetic acid is a weak acid, we can use the Henderson-Hasselbalch equation to calculate the pH at one-half of the equivalence point:
pH = pKa + log([A-]/[HA])
The pKa of acetic acid is approximately 4.76, and [A-]/[HA] is the ratio of the concentrations of the acetate ion (C2H3O2-) and acetic acid (HC2H3O2). At one-half of the equivalence point, the concentration of HC2H3O2 remaining is the same as the concentration of C2H3O2- formed. Therefore:
pH = 4.76 + log(0.11/0.11) = 4.76
e) At the equivalence point:
The equivalence point corresponds to the point where all the moles of HC2H3O2 have reacted with an equal number of moles of NaOH. This means that the moles of NaOH added will be equal to the initial moles of HC2H3O2.
Moles of NaOH = concentration x volume
Moles of NaOH = 0.125 M x 0.025 L = 0.003125 mol
Since the stoichiometry of the reaction is 1:1 between NaOH and HC2H3O2, the moles of HC2H3O2 reacted are also 0.003125 mol.
At the equivalence point, all the acetic acid has been converted to sodium acetate (NaC2H3O2). Therefore, the concentration of HC2H3O2 is zero, and the pH will be determined by the hydrolysis of sodium acetate.
Sodium acetate undergoes hydrolysis, resulting in the formation of hydroxide ions (OH-) and acetic acid. This reaction affects the pH of the solution. The hydrolysis of the sodium acetate is given by:
NaC2H3O2 + H2O -> HC2H3
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