how can we find out the ph at ¾ equivalence point of a reaction?

To determine the pH at the ¾ equivalence point of a titration reaction, we first need to understand what the equivalence point represents and how it relates to the acid-base reaction taking place. The equivalence point is where the amount of titrant added is stoichiometrically equivalent to the amount of substance in the solution being titrated. The ¾ equivalence point is simply a quarter of the way to that full equivalence point.

Understanding the Concept

In a typical acid-base titration, you are often dealing with a weak acid and a strong base (or vice versa). The pH at the equivalence point can be different from 7, especially when weak acids or bases are involved, due to the formation of conjugate bases or acids that can affect the pH.

Steps to Calculate pH at ¾ Equivalence Point

• Identify the Reaction: Determine the weak acid and strong base involved in the titration. For example, acetic acid (CH₃COOH) being titrated with sodium hydroxide (NaOH).
• Calculate the Equivalence Point: Find the volume of titrant needed to reach the equivalence point. This is where the moles of acid equal the moles of base.
• Determine the ¾ Equivalence Point: Calculate the volume of titrant needed to reach the ¾ equivalence point. This would be ¾ of the total volume calculated in the previous step.
• Calculate the Concentration of the Conjugate Base: At the ¾ equivalence point, you will have a mixture of unreacted weak acid and its conjugate base. Use the dilution formula to find the concentrations of both species.
• Use the Henderson-Hasselbalch Equation: This equation relates the pH of a solution to the pKa of the weak acid and the ratio of the concentrations of the conjugate base and the weak acid. The formula is: pH = pKa + log([A⁻]/[HA])

Example Calculation

Let’s say we are titrating 0.1 M acetic acid (pKa ≈ 4.76) with 0.1 M NaOH. If the equivalence point is reached at 50 mL of NaOH, then the ¾ equivalence point would be at 37.5 mL of NaOH.

At this point, you would have:

• 37.5 mL of NaOH added, which reacts with 37.5 mL of acetic acid.
• 12.5 mL of unreacted acetic acid remaining.

Now, calculate the concentrations:

• Concentration of acetate ion (A⁻) = 0.1 M (from NaOH)
• Concentration of acetic acid (HA) = (0.1 M * 50 mL) / (50 mL + 12.5 mL) = 0.1 M * (50/62.5) = 0.08 M

Now plug these values into the Henderson-Hasselbalch equation:

pH = 4.76 + log(0.1/0.08) = 4.76 + log(1.25) ≈ 4.76 + 0.096 = 4.86

Final Thoughts

Thus, the pH at the ¾ equivalence point in this example would be approximately 4.86. This method can be applied to any weak acid-strong base titration, allowing you to find the pH at various points throughout the titration process.