According to equation:

PhCOOH + MeOH ---> PhCOOMe + H₂O

What will be the percentage yield of product if 24.4g of PhCOOH reacts with 70 ml of MeOH OF density 0.8 g\ml to give 21.6g of PhCOOHMe

To determine the percentage yield of the product in the given reaction, we first need to calculate the theoretical yield based on the amounts of the reactants used. Then, we can compare this theoretical yield to the actual yield obtained to find the percentage yield.

Step 1: Calculate the moles of PhCOOH

The molecular weight of benzoic acid (PhCOOH) is approximately 122.12 g/mol. To find the number of moles of PhCOOH, we use the formula:

Moles = Mass (g) / Molar Mass (g/mol)

For 24.4 g of PhCOOH:

Moles of PhCOOH = 24.4 g / 122.12 g/mol ≈ 0.200 moles

Step 2: Calculate the moles of MeOH

Next, we need to find the number of moles of methanol (MeOH). First, we calculate the mass of MeOH using its volume and density:

Mass = Volume (mL) × Density (g/mL)

For 70 mL of MeOH with a density of 0.8 g/mL:

Mass of MeOH = 70 mL × 0.8 g/mL = 56 g

The molecular weight of methanol is approximately 32.04 g/mol. Now we can calculate the moles of MeOH:

Moles of MeOH = 56 g / 32.04 g/mol ≈ 1.75 moles

Step 3: Determine the limiting reagent

In the reaction, one mole of PhCOOH reacts with one mole of MeOH to produce one mole of PhCOOMe and one mole of water. Since we have 0.200 moles of PhCOOH and 1.75 moles of MeOH, PhCOOH is the limiting reagent because it is present in a smaller amount.

Step 4: Calculate the theoretical yield of PhCOOMe

Since PhCOOH is the limiting reagent, the theoretical yield of PhCOOMe will be equal to the moles of PhCOOH reacted, which is 0.200 moles. To find the mass of the theoretical yield, we multiply the moles by the molar mass of PhCOOMe (which is the same as PhCOOH plus the molar mass of methanol, approximately 122.12 g/mol + 32.04 g/mol = 154.16 g/mol):

Theoretical Yield (g) = Moles × Molar Mass

Theoretical Yield = 0.200 moles × 154.16 g/mol ≈ 30.83 g

Step 5: Calculate the percentage yield

The percentage yield can be calculated using the formula:

Percentage Yield = (Actual Yield / Theoretical Yield) × 100

Given that the actual yield of PhCOOMe is 21.6 g:

Percentage Yield = (21.6 g / 30.83 g) × 100 ≈ 69.98%

Final Thoughts

The percentage yield of the product, PhCOOMe, in this reaction is approximately 70%. This indicates that while the reaction was successful, there were some losses or inefficiencies in the process, which is common in chemical reactions.