100 mL of 1.0 M formic acid (HCOOH) is titrated with 1.0 M sodium hydroxide (NaOh).

The Approximate pKa is 4

At the pKa, what fraction of the carboxyl group will have been converted to COO-?

Oh, we're talking about pKa and titrations! Well, buckle up, chemistry fanatics! So, at the pKa value of 4, we know that the concentration of the acid form (HCOOH) is equal to the concentration of the dissociated form (COO-) for a halfway reaction.

Now, the pKa is the negative logarithm of the acid dissociation constant (Ka), and since we're given a pKa of 4, we know that the Ka value is 10^-4. This means that when the concentration of HCOOH is equal to COO-, we're dealing with an equal concentration of 10^-4 M.

But wait, there's more! Since we're dealing with a strong acid (HCOOH) and a strong base (NaOH), we have an acid-base neutralization reaction where each molecule of HCOOH reacts with one molecule of NaOH. So, the number of moles of HCOOH is equal to the number of moles of NaOH in this reaction.

Since we have 100 mL of 1.0 M formic acid (HCOOH), we can convert it into moles using the formula Moles = Concentration * Volume, which gives us 0.1 moles of HCOOH.

Now, we have an equal concentration of COO- at the pKa value of 4, which is 10^-4 M. So, we can convert this concentration into moles using the same formula, which gives us 0.0001 moles of COO-.

To find the fraction of the carboxyl group that has been converted to COO-, we divide the moles of COO- by the moles of HCOOH. So, 0.0001 moles COO- divided by 0.1 moles HCOOH gives us a fraction of 0.001 or 0.1%.

Therefore, at the pKa value of 4, only a tiny fraction (0.1%) of the carboxyl group has been converted to COO-. It's like trying to find a needle in a haystack, but hey, chemistry loves its precision!

The pKa is a measure of the acidity of a compound, specifically the negative logarithm of the acid dissociation constant (Ka). It represents the pH at which half of the acid will be dissociated into its conjugate base.

In this case, formic acid (HCOOH) is a weak acid, and its conjugate base is formate ion (HCOO-). When the pH is equal to the pKa, the concentration of the acid and its conjugate base will be equal. Therefore, at the pKa of formic acid (pKa = 4), half of the carboxyl groups will be in the form of the conjugate base (COO-).

So, at the pKa of formic acid (pKa = 4), approximately half (or 50%) of the carboxyl groups will have been converted to COO-.

To determine the fraction of the carboxyl group that will have been converted to COO- at the pKa, we can use the Henderson-Hasselbalch equation:

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

In this case, [A-] represents the concentration of the carboxylate ion (COO-) and [HA] represents the concentration of the acid form (HCOOH).

At the pKa, the concentrations of [A-] and [HA] are equal. Therefore, we can rewrite the equation as:

pH = pKa + log(1/1)

Simplifying further:

pH = pKa + log(1)
pH = pKa

So, at the pKa, the pH of the solution will be equal to the pKa value. In this case, the pKa is given as 4.

Now, to determine the fraction of the carboxyl group that will have been converted to COO-, we need to calculate the ratio of [A-] to [HA]. Since [A-] = [HA] at the pKa, this ratio is equal to 1.

Therefore, at the pKa, the fraction of the carboxyl group that will have been converted to COO- is 1, or 100%.

Do you mean at a pH = pKa, what is the fraction?

pH = pKa + log(base)/(acid)
4 = 4 + log (base)/(acid)
(base)/(acid) = 1
So 50% has been converted.