Calculate the pH at the halfway point and at the equivalence point for each of the following titrations.100.0 mL of 0.56 M HCl titrated by 0.28 M NaOH

halfway point



equivalence point

This is a triplicate post.

To calculate the pH at the halfway point and the equivalence point for the given titration, we need to understand the concept of a titration and the stoichiometry of the reaction involved.

In a titration, a known volume of a solution with a known concentration (the titrant) is added to a solution of unknown concentration (the analyte) until the reaction between the two is complete. The halfway point refers to the point in the titration where exactly half of the analyte has reacted with the titrant. The equivalence point, on the other hand, refers to the point at which the reaction between the analyte and titrant is complete.

For this specific titration between HCl and NaOH, the reaction is as follows:

HCl + NaOH -> NaCl + H2O

At the halfway point, half of the HCl has reacted with NaOH. Since the reaction is a 1:1 ratio, this means that 0.5 moles of HCl has reacted. To determine the concentration of HCl remaining, we can use the following equation:

C1V1 = C2V2

Where:
C1 = Initial concentration of HCl
V1 = Initial volume of HCl
C2 = Final concentration of HCl (which is the concentration at the halfway point)
V2 = Final volume of the solution at the halfway point (which is half the initial volume)

Calculating the concentration at the halfway point:

C1 = 0.56 M (given)
V1 = 100.0 mL (given)
V2 = 100.0 mL / 2 = 50.0 mL = 0.050 L

Using the equation C1V1 = C2V2:

0.56 M * 0.100 L = C2 * 0.050 L

C2 = (0.56 M * 0.100 L) / 0.050 L
C2 = 1.12 M

Therefore, at the halfway point, the concentration of HCl is 1.12 M.

To calculate the pH at the halfway point, we need to consider that HCl is a strong acid, meaning it completely dissociates in water. Therefore, at the halfway point, the concentration of H+ ions (acidic) will be equal to the concentration of NaOH that has reacted with HCl. Since the reaction is 1:1, the concentration of OH- ions (basic) will also be equal.

At the halfway point, the concentration of OH- ions can be calculated using the following equation:

[OH-] = (n2 - n1) / V2

Where:
n2 = moles of NaOH added (which is half the moles of HCl that reacted)
n1 = moles of NaOH reacted (which is half the moles of HCl that reacted)
V2 = volume at the halfway point (which is half the initial volume)

Since the reaction is 1:1, n2 and n1 will be equal. So,

n2 = n1 = 0.5 moles (half of 1 mole of HCl)

V2 = 0.050 L (as calculated above)

Therefore,

[OH-] = (0.5 moles - 0.5 moles) / 0.050 L
[OH-] = 0 M

Since the concentration of OH- ions is 0 M, we can conclude that the concentration of H+ ions (acidic) is also 0 M. A pH of 0 indicates a highly acidic solution.

At the equivalence point, all of the HCl has reacted with the NaOH. This means that the moles of HCl that reacted is equal to the moles of NaOH added. The concentration of HCl and NaOH at the equivalence point will depend on the final volume of the solution.

Using the equation C1V1 = C2V2, we can determine the concentration of HCl at the equivalence point.

C1 = 0.56 M (given)
V1 = 100.0 mL (given)
V2 = final volume of the solution (at the equivalence point)

Assuming V2 is 100.0 mL (the sum of the NaOH and HCl volumes), the equation becomes:

0.56 M * 0.100 L = C2 * 0.100 L

C2 = (0.56 M * 0.100 L) / 0.100 L
C2 = 0.56 M

Therefore, at the equivalence point, the concentration of HCl is 0.56 M.

To calculate the pH at the equivalence point, we need to consider that HCl is completely neutralized by NaOH in a 1:1 ratio. This means that the concentration of H+ ions (acidic) will be completely neutralized by the concentration of OH- ions (basic). At the equivalence point, the concentration of H+ and OH- ions will be equal.

Since NaOH is a strong base and fully dissociates in water, at the equivalence point, the concentration of OH- ions can be calculated by dividing the moles of NaOH added by the total volume at the equivalence point.

nNaOH = CNaOH * VNaOH

Where,
CNaOH = concentration of NaOH
VNaOH = volume of NaOH added in liters

nNaOH = 0.28 M * 0.100 L = 0.028 moles

Total volume at equivalence point (Vequivalence) = VNaOH + Vinitial = 0.100 L + 0.100 L = 0.200 L

[OH-] = nNaOH / Vequivalence = 0.028 moles / 0.200 L = 0.14 M

Since the concentration of OH- ions is 0.14 M, we can conclude that the concentration of H+ ions (acidic) is also 0.14 M. A pH of 0.14 indicates a highly acidic solution.

In summary:
- At the halfway point, the pH is 0.
- At the equivalence point, the pH is 0.14.