1 g of acid was mixed with 120 ml of distilled water and the solution was filtered into a clean dry beaker. A 25 ml aliquot of this solution was titrated with 0.1120 M NaOH. The pH of the acid was recorded to be 4.42. Calculate the initial concentration of the weak acid and determine the Ka and pKa of the weak acid.
Step 1: Calculate the number of moles of NaOH used in the titration.
To find the moles of NaOH used, use the following formula:
moles of NaOH = Molarity of NaOH * Volume of NaOH used (in liters)
Given:
Molarity of NaOH = 0.1120 M
Volume of NaOH used = 25 ml = 0.025 L
moles of NaOH = 0.1120 M * 0.025 L
moles of NaOH = 0.0028 moles
Step 2: Calculate the number of moles of H+ ions in the solution.
Since NaOH is a strong base, it reacts completely with the weak acid to neutralize the H+ ions. Therefore, the moles of NaOH used in the titration represent the moles of H+ ions in the original solution.
moles of H+ ions = 0.0028 moles
Step 3: Calculate the volume of the original solution.
At the beginning of the titration, a 25 ml aliquot of the diluted solution was taken for titration. So, the volume of the original solution can be calculated using the following formula:
Volume of original solution = Volume of aliquot / Dilution factor
Given:
Volume of aliquot = 25 ml = 0.025 L
Dilution factor = Volume of original solution / Volume of aliquot
We know that 1 g of acid was mixed with 120 ml of water. The total volume of the solution is 120 ml.
Volume of original solution = 120 ml / 0.025 L
Volume of original solution = 4.8 L
Step 4: Calculate the initial concentration of the weak acid.
The initial concentration of the weak acid can be calculated using the formula:
Initial concentration of weak acid = moles of H+ ions / Volume of original solution
Initial concentration of weak acid = 0.0028 moles / 4.8 L
Step 5: Calculate the Ka of the weak acid.
The Ka of the weak acid can be calculated using the formula:
Ka = (concentration of A- ions * concentration of H+ ions) / (concentration of HA)
In this case, the concentration of A- ions is negligible as the acid is weak. Therefore, the formula simplifies to:
Ka = (concentration of H+ ions)^2 / (concentration of HA)
Given:
concentration of H+ ions = initial concentration of weak acid
concentration of HA = initial concentration of weak acid
Ka = (initial concentration of weak acid)^2 / (initial concentration of weak acid)
Step 6: Calculate pKa of the weak acid.
pKa = -log10(Ka)
Now, you can substitute the values into the formulas to calculate the initial concentration of the weak acid, Ka, and pKa.
To calculate the initial concentration of the weak acid, we need to use the equation for a titration, which is:
Molarity of Acid * Volume of Acid = Molarity of Base * Volume of Base
In this case, the volume of acid is 25 ml (or 0.025 L) and the molarity of the base (NaOH) is 0.1120 M.
First, we need to find the moles of NaOH used in the titration. This can be calculated by multiplying the molarity of NaOH by the volume of NaOH used (in liters):
Moles of NaOH = Molarity * Volume = 0.1120 M * 0.025 L
Next, we need to determine the moles of acid that reacted with the NaOH. According to the balanced equation of the reaction between a weak acid and a strong base, one mole of acid reacts with one mole of base. Therefore, the moles of acid will be the same as the moles of NaOH used:
Moles of Acid = Moles of NaOH
Now, we can calculate the initial concentration of the weak acid by dividing the moles of acid by the volume of acid used (in liters):
Initial concentration of weak acid = Moles of Acid / Volume of Acid
In this case, the initial concentration should be in moles per liter (M), but since the volumes used are given in milliliters, we need to convert the initial concentration to moles per milliliter (mol/mL). To do this, divide the initial concentration by 1000:
Initial concentration of weak acid (in mol/mL) = Initial concentration of weak acid (in M) / 1000
Now that we have the initial concentration of the weak acid, we can calculate the Ka of the weak acid. The Ka is the acid dissociation constant and represents the strength of the acid. It is given by the equation:
Ka = [H3O+][A-] / [HA]
To calculate the Ka, we need to determine the concentrations of the acid and its conjugate base after dissociation. Since the initial concentration of the weak acid is equal to the concentration of [HA] and the pH of the acid solution is given, we can use the following equation to calculate [H3O+]:
[H3O+] = 10^(-pH)
Once we have the concentration of [H3O+], we can calculate the concentration of [A-] by applying the conservation of moles. Since one mole of weak acid dissociates and produces one mole of acid and one mole of the conjugate base, the concentrations of [HA] and [A-] will be the same.
Finally, we can substitute the values of [H3O+], [A-], and [HA] into the Ka equation to find the Ka of the weak acid.
To calculate the pKa of the weak acid, use the formula:
pKa = -log(Ka)
Substitute the Ka value into this equation to get the pKa of the weak acid.
By following these steps, you should be able to calculate the initial concentration of the weak acid and determine the Ka and pKa of the weak acid.