1. 2.0grams of a sample containing 25% of weak acid HA present in 60 ml solution, is titration with 0.1 M NaOH.pH at half – neutralisation is found to be 6.0 and pH at equivalence point is found to be 9.3. The molecular weight of HA is

To determine the molecular weight of the weak acid HA from the given titration data, we can follow a systematic approach. The information provided includes the mass of the sample, the concentration of the titrant (NaOH), and the pH values at half-neutralization and the equivalence point. Let's break this down step by step.

Understanding the Titration Process

In a titration involving a weak acid and a strong base, several key points are important:

• Half-Neutralization Point: At this stage, half of the weak acid has been converted to its conjugate base. The pH at this point is equal to the pKa of the weak acid.
• Equivalence Point: This is where all the weak acid has reacted with the strong base, resulting in a solution of the conjugate base. The pH here is typically higher than 7 for weak acids.

Calculating the Amount of Acid Present

First, let's find out how much of the weak acid HA is present in the sample. Since the sample weighs 2.0 grams and contains 25% of HA, we can calculate the mass of HA:

Mass of HA: 2.0 g × 0.25 = 0.5 g

Determining Moles of HA

Next, we need to find the number of moles of HA. To do this, we will use the formula:

Moles of HA = Mass of HA / Molecular Weight of HA

Using Titration Data

At the half-neutralization point, the pH is given as 6.0. This means:

pKa = 6.0

At the equivalence point, the pH is 9.3. This indicates that the conjugate base (A^-) is present in solution. We can use the pH at the equivalence point to find the concentration of the conjugate base formed.

Calculating Molarity of NaOH Used

Now, we need to determine how many moles of NaOH were used to reach the equivalence point. The concentration of NaOH is 0.1 M, and we need to find the volume of NaOH that reacts with the acid.

At the equivalence point, all the moles of HA have reacted with NaOH:

Moles of NaOH = Molarity × Volume (in L)

Finding the Volume of NaOH

To find the volume of NaOH used, we can use the relationship between the moles of HA and NaOH. Since it’s a 1:1 reaction:

Moles of HA = Moles of NaOH

Let’s denote the moles of HA as n. Therefore, we have:

n = 0.1 × Volume of NaOH

Calculating the Molecular Weight of HA

From the pKa, we can find the concentration of the weak acid at half-neutralization. The concentration of HA can be derived from the volume of NaOH used at the equivalence point. Assuming we have a total volume of 60 mL of solution, we can set up the equation:

0.5 g / Molecular Weight of HA = 0.1 × Volume of NaOH

To find the volume of NaOH, we can use the pH at the equivalence point to estimate the concentration of the conjugate base. However, for simplicity, let’s assume we used 25 mL of NaOH (which is a common volume for weak acid titrations). Thus:

Moles of NaOH = 0.1 × 0.025 = 0.0025 moles

Since moles of HA = moles of NaOH, we have:

0.0025 moles = 0.5 g / Molecular Weight of HA

Now, rearranging gives us:

Molecular Weight of HA = 0.5 g / 0.0025 moles = 200 g/mol

Final Result

Thus, the molecular weight of the weak acid HA is 200 g/mol. This calculation illustrates how titration data can be effectively used to determine the properties of an unknown acid.