.240g Benzoic acid is dissolved in water at 100C and crystals of it formed when cooled to 20C that weighed .172g. What is the percent recovery (given solubility of benzoic acid at 20C is 2.9mg/mL)

I understand the %recovery equation, but am not sure how to set up the theoretical yield.

Isn't %recovery just (0.172/0.240)*100 = ?

So am just making this harder than it really is! That is what I wanted to do but thought it was too easy. HAHA

I guess you could say the theoretical yield is 0.240g.

To determine the percent recovery, you need to compare the actual yield (crystals formed) to the theoretical yield (maximum amount of benzoic acid that could have been recovered).

The theoretical yield is calculated by considering the solubility of benzoic acid at 20°C and the volume of the solution.

Let's calculate the theoretical yield step by step:

Step 1: Determine the volume of the solution
To find the volume of the solution, you need to convert the mass of benzoic acid dissolved in water into milliliters (ml) using the given solubility of benzoic acid at 20°C (2.9 mg/mL).

Given: Mass of benzoic acid = 0.240 g
Solubility of benzoic acid at 20°C = 2.9 mg/mL

The volume (V) can be calculated using the formula: V = Mass / Concentration

V = (0.240 g) / (2.9 mg/mL) * (1 mL / 1000 mg) = 0.0828 mL

Step 2: Calculate the theoretical yield
The theoretical yield is the maximum amount of benzoic acid that could have been recovered based on the volume of the solution.

The theoretical yield (TY) can be calculated using the formula: TY = Volume (V) * Concentration

TY = 0.0828 mL * 2.9 mg/mL = 0.239 g

Step 3: Calculate the percent recovery
Now that you have the actual yield (0.172 g) and the theoretical yield (0.239 g), you can calculate the percent recovery using the formula:

% Recovery = (Actual Yield / Theoretical Yield) * 100

% Recovery = (0.172 g / 0.239 g) * 100 ≈ 71.97%

Therefore, the percent recovery is approximately 71.97%.