Assume the solubility of benzoic acid in ice-cold water is 1.70 g/L and the solubility of benzoic acid in hot water is 68.0 g/L. Calculate the minimum volume of water (in mL) needed to recrystallize 0.950 g of benzoic acid.
You want to calculate the volume of water needed to dissolve 0.950 g benzoic acid in hot water. That will be
1000 mL x (0.950/68.0) = ?
I obtained 13.97 which I would round to 14.0 mL to 3 significant figures.
Do we not need to take the solubility into account in the calculation?
To calculate the minimum volume of water needed to recrystallize benzoic acid, we need to determine the solubility of benzoic acid at the desired temperature.
Given:
Solubility of benzoic acid in ice-cold water = 1.70 g/L
Solubility of benzoic acid in hot water = 68.0 g/L
Amount of benzoic acid = 0.950 g
First, we need to determine the temperature at which we want to recrystallize benzoic acid. Let's assume a temperature of 25°C (close to room temperature).
We know that benzoic acid is more soluble in hot water than in cold water, so we can assume that its solubility at room temperature (25°C) would be between the solubilities in ice-cold water and hot water.
To find the approximate solubility at 25°C, we can use a linear approximation, assuming that the solubility increases linearly with temperature.
The slope of the line can be calculated using the formula:
Slope = (solubility in hot water - solubility in ice-cold water) / (temperature of hot water - temperature of ice-cold water)
Slope = (68.0 g/L - 1.70 g/L) / (100°C - 0°C)
Slope = 66.3 g/L / 100°C
Slope = 0.663 g/L/°C
Now, let's calculate the solubility at 25°C using the linear approximation:
Solubility at 25°C = solubility in ice-cold water + slope * (temperature at 25°C - temperature of ice-cold water)
Solubility at 25°C = 1.70 g/L + 0.663 g/L/°C * (25°C - 0°C)
Solubility at 25°C = 1.70 g/L + 16.575 g/L
Solubility at 25°C ≈ 18.275 g/L
Now, we have the solubility of benzoic acid at 25°C (18.275 g/L). To calculate the minimum volume of water needed to recrystallize 0.950 g of benzoic acid, we can use the formula:
Minimum volume of water = amount of benzoic acid / solubility at 25°C
Minimum volume of water = 0.950 g / 18.275 g/L
Since the solubility is given in grams per liter (g/L), we need to convert it to milliliters (mL). We know that 1 mL of water is approximately equal to 1 g.
Minimum volume of water = 0.950 g / 18.275 g/L ≈ 0.052 mL
Therefore, the minimum volume of water needed to recrystallize 0.950 g of benzoic acid is approximately 0.052 mL.