Determine the pH at the equivalence point in the titration of 41.0 mL 0.096 M formic acid with 0.108 M NaOH at 25oC.

Calculate the pH of a solution that is 0.22 M pyridinium ion (C5H5NH+) at 25oC.

What is it that you don't understand about the problem? The pH at the equivalence point of formic acid and NaOH is determined by the hydrolysis of the salt, i.e., sodium formate.

To determine the pH at the equivalence point in the titration of formic acid with NaOH, we need to understand the chemical reaction that occurs.

The balanced equation for the reaction between formic acid (HCOOH) and sodium hydroxide (NaOH) is as follows:

HCOOH + NaOH -> HCOONa + H2O

At the equivalence point, the moles of acid will be equal to the moles of base. In this case, since the concentration and volume of both reactants are given, we can calculate the number of moles involved in the reaction as follows:

moles of formic acid = concentration × volume = 0.096 mol/L × 0.041 L = 0.003936 mol

Since the reaction is 1:1 between formic acid and sodium hydroxide, the number of moles of NaOH involved in the reaction will also be 0.003936 mol.

To determine the amount of NaOH remaining unreacted, we need to subtract the moles of NaOH involved in the reaction from the initial moles of NaOH:

Initial moles of NaOH = concentration × volume = 0.108 mol/L × 0.041 L = 0.004428 mol

moles of unreacted NaOH = initial moles of NaOH - moles of NaOH involved in the reaction
= 0.004428 mol - 0.003936 mol
= 0.000492 mol

At the equivalence point, the moles of unreacted NaOH will react with water to form hydroxide ions. Since NaOH is a strong base, it will completely dissociate in water, producing one hydroxide ion (OH-) for every NaOH molecule.

The volume of the NaOH solution is 41.0 mL, which is the same as 0.041 L. Therefore, the concentration of hydroxide ions at the equivalence point can be calculated as follows:

concentration of hydroxide ions = moles of unreacted NaOH / volume of NaOH solution
= 0.000492 mol / 0.041 L
= 0.012 mol/L

To determine the pH at the equivalence point, we can use the fact that water undergoes autoionization to produce equal concentrations of hydrogen ions (H+) and hydroxide ions (OH-).

The autoionization of water is represented by the following equation:

H2O ⇌ H+ + OH-

At 25°C, the concentration of hydrogen ions (H+) and hydroxide ions (OH-) in pure water are both equal to 1.0 × 10^-7 M.

In the presence of additional hydroxide ions from the NaOH, the concentration of hydroxide ions at the equivalence point will increase to 0.012 M.

Since the solution is now basic, we can calculate the pOH using the equation:

pOH = -log10[OH-]

pOH = -log10(0.012)
= 1.92

To determine the pH, we can use the fact that pH + pOH = 14.

pH = 14 - pOH
= 14 - 1.92
= 12.08

Therefore, the pH at the equivalence point in the titration of formic acid with NaOH is 12.08.

Now let's move on to calculating the pH of a solution that is 0.22 M pyridinium ion (C5H5NH+).

Pyridinium ion (C5H5NH+) is a weak acid. To determine the pH of its solution, we need to consider its acid dissociation constant (Ka) and apply the Henderson-Hasselbalch equation.

The acid dissociation constant (Ka) for pyridinium ion (C5H5NH+) is 5.6 × 10^-6 at 25°C.

The Henderson-Hasselbalch equation is given by:

pH = pKa + log10([A-] / [HA])

In this equation, [A-] represents the concentration of the conjugate base (C5H5N) and [HA] represents the concentration of the acid (C5H5NH+).

At equilibrium, the concentration of C5H5N is equal to the concentration of C5H5NH+. Thus, we can assume that [A-] = [HA].

Using the given concentration of pyridinium ion (C5H5NH+), we can substitute the values into the equation:

pH = pKa + log10([A-] / [HA])
= pKa + log10([C5H5N] / [C5H5NH+])
= pKa + log10(0.22 / 0.22)
= pKa + log10(1)
= pKa

Since the logarithm of 1 is equal to 0, the final equation simplifies to:

pH = pKa

Therefore, the pH of a 0.22 M pyridinium ion (C5H5NH+) solution is equal to the pKa of pyridinium ion, which is 5.6 × 10^-6.