A 0.1276 g sample of a monoprotic acid (molar mass = 1.10 x 10^2) was dissolved in 25.0 ml of water and titrated with 0.0633 M NaOH. After 10.0 ml of base has been added, the pH=5.47. What is the Ka for the acid?
A 0.1276-g sample of an unknown monoprotic acid was dissolved in 25.0 mL of water and titrated with a 0.0633 M NaOH solution. The volume of base required to bring the solution to the equivalence point was 18.4 mL. (a) Calculate the molar mass of the acid, (b) After 10.0 mL of base had been added during the titration, the pH was determined to be 5.87. What is the Ka of the unknown acid?
To find the Ka for the acid, we can use the Henderson-Hasselbalch equation, which relates the pH of a solution to the concentration of the acid and its conjugate base.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Where:
pH = the measured pH of the solution
pKa = the logarithmic value of the acid dissociation constant
[A-] = concentration of the conjugate base
[HA] = concentration of the acid
In this case, we are given the pH and the volume of base added when the pH reaches 5.47. To calculate the concentrations of the acid and the conjugate base, we need to know the initial concentration of the acid and the amount of base required to reach the pH of 5.47.
Step 1: Calculate the amount of acid used
We know that 10.0 ml of NaOH was added, which means that 25.0 - 10.0 = 15.0 ml of NaOH is remaining. We can convert this into moles of NaOH by multiplying the volume by its molarity:
moles of NaOH = 0.0633 M * (15.0 ml / 1000 ml) = 0.0009495 mol
Since NaOH is a 1:1 reaction with the monoprotic acid, the amount of acid used is also 0.0009495 mol.
Step 2: Calculate the concentration of the acid
The volume of water is given as 25.0 ml, which is equal to 0.0250 L. We can calculate the initial concentration of the acid using the amount of acid and the volume of water:
Concentration of acid = (0.0009495 mol) / (0.0250 L) = 0.03798 M
Step 3: Calculate the concentration of the conjugate base
We already found the amount of acid used, so we need to subtract this from the initial amount of acid:
Amount of the conjugate base = Initial amount of acid - Amount of acid used = 0.03798 mol - 0.0009495 mol = 0.03703 mol
Now, we can calculate the concentration of the conjugate base using the remaining volume of water:
Concentration of the conjugate base = (0.03703 mol) / (0.0250 L) = 1.4812 M
Step 4: Calculate the pKa
Now that we have the pH and the concentrations of the acid and the conjugate base, we can rearrange the Henderson-Hasselbalch equation to solve for the pKa:
pKa = pH - log([A-]/[HA])
pKa = 5.47 - log(1.4812/0.03798) = 5.47 - log(39.024)
Using a calculator, we find that the pKa is approximately 4.11.
Step 5: Calculate the Ka
Finally, we can calculate the Ka by taking the antilog of the pKa:
Ka = 10^(-pKa) = 10^(-4.11)
Using a calculator, we find that the Ka is approximately 7.07 x 10^(-5).