Calculate the pH at the following points during the titration of 100.0 mL of 0.20 M acetic acid (Ka for acetic acid = 1.8 x 10-5) with 0.10M sodium hydroxide
1. before addition of any base
2. after addition of 30.0mL of base
3. after addition of 100.0mL of base
4. after addition of 200.0mL of base
5. after addition of 250.0 mL of base
Please help in detail because i am so lost
To calculate the pH at different points during the titration, we need to consider the reaction between acetic acid (CH3COOH) and sodium hydroxide (NaOH). In this case, NaOH is a strong base, and CH3COOH is a weak acid.
The reaction between CH3COOH and NaOH can be represented as follows:
CH3COOH + NaOH → CH3COONa + H2O
Step 1: Before the addition of any base
Before any base is added, the solution contains only acetic acid. To calculate the pH at this point, we need to consider the concentration of acetic acid and the dissociation constant (Ka) for acetic acid.
The formula for calculating the pH of a weak acid solution is pH = pKa + log ([A-] / [HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.
In this case, before the addition of any base, the concentration of acetic acid ([HA]) is 0.20 M (given), and the concentration of the conjugate base ([A-]) is 0 M.
Since no base has been added yet, the reaction has not occurred, and the acetic acid is not yet ionized. Therefore, the pH at this point is equal to the pKa of acetic acid.
The pKa of acetic acid can be determined by taking the negative logarithm of the dissociation constant (Ka). In this case, pKa = -log(Ka) = -log(1.8 x 10^-5) ≈ 4.74.
So, before the addition of any base, the pH is approximately 4.74.
Step 2: After the addition of 30.0 mL of base
After the addition of 30.0 mL of base, a reaction occurs between acetic acid and sodium hydroxide. However, the reaction is not complete yet, and we need to determine the limiting reagent to calculate the pH.
To find the limiting reagent, we compare the stoichiometric ratio between acetic acid and sodium hydroxide. From the balanced equation, we see that the ratio between acetic acid and sodium hydroxide is 1:1. Therefore, they will react in a 1:1 ratio.
Given that the initial concentration of acetic acid is 0.20 M and the volume of base added is 30.0 mL, we can calculate the amount of acetic acid that reacts (in moles) using the equation:
moles of acetic acid = initial concentration * initial volume (in liters)
= 0.20 M * 0.030 L
= 0.006 moles
Since the stoichiometry is 1:1, the amount of sodium hydroxide that reacts is also 0.006 moles.
To calculate the concentration of acetic acid and its conjugate base after the reaction, we need to consider the total volume of the solution. At this point, the total volume is the sum of the initial volume of acetic acid (100.0 mL) and the volume of base added (30.0 mL), which is 130.0 mL or 0.130 L.
The remaining amount of acetic acid ([HA] after reaction) can be calculated as follows:
[HA] = (initial moles – moles that reacted) / total volume
= (0.20 M * 0.100 L – 0.006 moles) / 0.130 L
≈ 0.129 M
The concentration of the conjugate base ([A-]) can be calculated by dividing the moles of sodium hydroxide that reacted by the total volume:
[A-] = (moles that reacted) / total volume
= 0.006 moles / 0.130 L
≈ 0.046 M
Now, we can calculate the pH using the Henderson-Hasselbalch equation:
pH = pKa + log ([A-] / [HA])
= 4.74 + log (0.046 M / 0.129 M)
≈ 4.74 - 0.670
≈ 4.07
So, after the addition of 30.0 mL of base, the pH is approximately 4.07.
Steps 3, 4, and 5 can be calculated in a similar manner by considering the volume of base added and recalculating the concentrations of the acid and its conjugate base.
I will calculate the remaining steps for you.