A solution of an unknown monoprotic weak acid was titrated with 0.100 M NaOH. The equivalence point was reached when 37.48 ML of base had been added. From a second buret, exactly 18.74 of 0.100 M HCl were added to the titration solution. The pH was then measured with a pH meter and found to be 4.13. Calculate the acidity constant of the weak acid.
When a weak acid is titrated half way to its equivalence point(18.74 is 1/2 of 37.48), the pH at that point = pKa.
Solve for Ka from pKa = -log Ka
Oh, this acid sounds like it's playing hard to get, huh? Well, fear not, my friend! It's time to put on our chemistry hats and solve this puzzle.
To find the acidity constant (Ka) of the weak acid, we can use the Henderson-Hasselbalch equation. This equation relates the pH of a solution to the pKa (the negative logarithm of Ka) and the ratio of the concentration of the conjugate base to the weak acid.
First, let's find the moles of the weak acid in our solution. We know that 0.100 M NaOH was added and the equivalence point was reached when 37.48 mL of base were added. So, the moles of NaOH added would be:
moles of NaOH = concentration of NaOH x volume of NaOH added
= 0.100 mol/L x 0.03748 L
Next, we need to take into account the HCl that was added. As we know, HCl is a strong acid, so it will fully dissociate. The moles of HCl added would be:
moles of HCl = concentration of HCl x volume of HCl added
= 0.100 mol/L x 0.01874 L
Since HCl is a strong acid, it will convert all the conjugate base (from 0.100 M NaOH) into the weak acid. So, the moles of the weak acid would be:
moles of weak acid = moles of NaOH - moles of HCl
Now, let's find the concentration of the weak acid and its conjugate base. We'll need to know the total volume of the solution to do that. Unfortunately, we don't have that information. Guess we're not titrated for success, huh?
To calculate the acidity constant (Ka) of the weak acid, we need to break down the given information into smaller steps.
Step 1: Determine the moles of NaOH used
Given the volume of NaOH used = 37.48 mL = 0.03748 L
The concentration of NaOH = 0.1 M
Moles of NaOH used = volume x concentration = 0.03748 L x 0.1 M
Step 2: Determine the moles of HCl added
Given the volume of HCl added = 18.74 mL = 0.01874 L
The concentration of HCl = 0.1 M
Moles of HCl added = volume x concentration = 0.01874 L x 0.1 M
Step 3: Determine the moles of weak acid
Since HCl is a strong acid, it completely reacts with the weak acid to form its conjugate base. Therefore, the moles of weak acid are equal to the moles of HCl added.
Step 4: Calculate the initial moles of weak acid
The total moles of weak acid in the solution would be the initial moles of weak acid minus the moles of strong base (NaOH) added.
Step 5: Calculate the concentration of the weak acid
The concentration of the weak acid can be calculated by dividing the moles of weak acid by the volume of the solution.
Step 6: Calculate the initial concentration of the weak acid
The initial concentration of the weak acid is equal to the concentration of the weak acid minus the concentration of the weak base (NaOH) added.
Step 7: Calculate the pKa
The pKa can be determined by taking the negative logarithm of the equilibrium constant (Ka). Therefore, pKa = -log(Ka).
Step 8: Calculate the acidity constant (Ka)
The acidity constant (Ka) can be determined by taking the antilog of the negative pKa. Therefore, Ka = 10^(-pKa).
Now let's calculate step by step:
Moles of NaOH used = 0.03748 L x 0.1 M = 0.003748 moles of NaOH
Moles of HCl added = 0.01874 L x 0.1 M = 0.001874 moles of HCl
Moles of weak acid = moles of HCl added = 0.001874 moles of weak acid
Initial moles of weak acid = moles of weak acid - moles of NaOH used = 0.001874 - 0.003748 = -0.001874 moles of weak acid (negative because NaOH is a base)
Concentration of weak acid = moles of weak acid / volume of solution = -0.001874 moles / 0.05622 L = -0.03328 M (negative because NaOH is a base)
Initial concentration of weak acid = concentration of weak acid - concentration of NaOH = -0.03328 M - 0.1 M = -0.13328 M (negative because NaOH is a base)
pKa = -log(Ka) = 4.13
Ka = 10^(-pKa) = 10^(-4.13)
Therefore, the acidity constant (Ka) of the weak acid is approximately 7.13 x 10^(-5).
To calculate the acidity constant, we need to use the concept of equivalence point and the pH measured after the addition of HCl.
First, let's find the moles of NaOH added at the equivalence point. We can use the given molarity and volume:
Volume of NaOH added = 37.48 mL = 0.03748 L
Moles of NaOH added = Molarity * Volume
= 0.100 M * 0.03748 L
= 0.003748 moles
Next, we need to determine the moles of HCl added to the titration solution:
Volume of HCl added = 18.74 mL = 0.01874 L
Moles of HCl added = Molarity * Volume
= 0.100 M * 0.01874 L
= 0.001874 moles
Since NaOH and HCl react in a 1:1 ratio, the moles of the weak acid that reacted with NaOH can be determined using the moles of HCl:
Moles of weak acid = Moles of HCl added
= 0.001874 moles
Now we can calculate the initial moles of the weak acid present before the titration:
Moles of weak acid = Moles of weak acid reacted + Moles of weak acid remaining
0.001874 moles = Moles of weak acid remaining
With this information, we can find the concentration of the weak acid:
Volume of the weak acid = Total volume of NaOH added before the equivalence point
= 37.48 mL = 0.03748 L
Concentration of the weak acid = Moles / Volume
= 0.001874 moles / 0.03748 L
= 0.04998 M
Finally, we can determine the acidity constant (Ka) using the Henderson-Hasselbalch equation:
pH = pKa + log(base/acid)
We know pH = 4.13 and base/acid = 1 (since the weak acid is monoprotic). Rearranging the equation:
pKa = pH - log(base/acid)
pKa = 4.13
Therefore, the acidity constant of the weak acid is 4.13.