40.0 mL of 0.1880 M formic acid is titrated with 30.0 mL of 0.2010 M NaOH. Pka of formic acid is 3.8. What is the pH of the titration?

moles formic acid = M x L = ??

moles NaOH = M x L = ??
pH = pKa + log [(formate)/(formic acid)]

To find the pH of the titration, we need to determine the concentration of each species present at the equivalence point. The equivalence point is the point in the titration where the moles of the acid and base are stoichiometrically balanced.

First, let's determine the number of moles of formic acid and NaOH used in the titration:

Moles of formic acid = volume (L) x concentration (M)
= 0.040 L x 0.1880 M
= 0.00752 moles

Moles of NaOH = volume (L) x concentration (M)
= 0.030 L x 0.2010 M
= 0.00603 moles

Since the stoichiometric ratio between formic acid and NaOH is 1:1, the number of moles of formic acid neutralized by NaOH is the same as the moles of NaOH used.

The total volume of the solution at the equivalence point is the sum of the volumes of formic acid and NaOH used in the titration:

Total volume = volume of formic acid + volume of NaOH
= 0.040 L + 0.030 L
= 0.070 L

Now, let's calculate the concentration of formic acid at the equivalence point:

Concentration of formic acid = Moles of formic acid / Total volume
= 0.00752 moles / 0.070 L
= 0.1074 M

At the equivalence point, formic acid is completely neutralized by NaOH to form sodium formate (NaHCOO), which is the salt of a weak acid (formic acid) and a strong base (NaOH). The reaction can be represented as:

HCOOH + NaOH -> HCOONa + H2O

The resulting solution contains the sodium formate and the conjugate base of formic acid (HCOO-). Since sodium formate is the salt of a strong base and a weak acid, it dissociates completely in water. However, the conjugate base of a weak acid can hydrolyze in water, releasing hydroxide ions (OH-).

To calculate the concentration of hydroxide ions (OH-) from the hydrolysis of sodium formate, we can use the Kw expression:

Kw = [H+][OH-]

At equilibrium, the concentration of hydroxide ions (OH-) will be equal to the concentration of the conjugate base of formic acid (HCOO-), which is 0.1074 M.

Now, let's solve the equation for Kw:

Kw = [H+][OH-]
= x * 0.1074

Since the concentration of hydroxide ions (OH-) is equal to the concentration of the conjugate base of formic acid (HCOO-), we can substitute 0.1074 M for [OH-].

Using the fact that Kw = 1.0 x 10^-14 at 25°C, we can calculate the concentration of hydronium ions (H+), which will give us the pH of the solution.

Rearranging the equation for Kw, we get:

[H+][OH-] = 1.0 x 10^-14

[H+] * 0.1074 = 1.0 x 10^-14

[H+] = (1.0 x 10^-14) / 0.1074

[H+] = 9.31 x 10^-14 M

Taking the negative logarithm (base 10) of the concentration of hydronium ions, we get the pH:

pH = -log10[H+]
= -log10(9.31 x 10^-14)
≈ 13.03

Therefore, the pH of the titration is approximately 13.03.