The solubility of benzoic acid in water is 2.56g in 100cm3 at 79 C and 0.29g in 100cm3 at 20 C. What is the minimum volume of water in which 1g of benzoic acid can be dissolved at 79 C?

I set up a dimensional analysis but since the question gives 2 sets of results, I do not know what to do.

The dimensional approach will work. The question asks for the minimun solubility AT 79 DEGREES C; therefore, just ignore the solubility of benzoic acid at 20 degrees C. As far as this problem goes, you don't really care what the solubility is at 20.

but what equation is used to find it? the delta H/RT equation won't solve for anything

I think you solve the first two given values and find delta H and then used the delta H to find solubility of water

what equation do you use??

The equation I would set up based on the information given is:

2.56g Benz. Acid /100cm^3 water = 1.00g Benz. Acid / x cm^3

Without the units,

2.56 /100 = 1.00 / x

Solve the above equation for "x" to get the minimum volume of water in cm^3 that would be needed to dissolve 1.00g of Benzoic acid.

To find the minimum volume of water in which 1g of benzoic acid can be dissolved at 79°C, we can use the provided solubility values as a guide.

First, let's analyze the given solubility values:

1. At 79°C: 2.56g benzoic acid in 100cm³ of water
2. At 20°C: 0.29g benzoic acid in 100cm³ of water

From these values, we notice that as the temperature increases, the solubility of benzoic acid in water also increases. Therefore, we can assume that at 79°C, the solubility will be higher than 2.56g in 100cm³.

To calculate the minimum volume of water in which 1g of benzoic acid can be dissolved at 79°C, we can set up a proportion using the solubility values:

x cm³ water = 1g benzoic acid * (100cm³ water / 2.56g benzoic acid)

Simplifying the proportion:

x cm³ water = (1g benzoic acid * 100cm³ water) / 2.56g benzoic acid

Now, substitute the given values into the equation:

x cm³ water = (1g * 100cm³) / 2.56g
x cm³ water = 100cm³ / 2.56
x cm³ water ≈ 39.06 cm³

Therefore, the minimum volume of water in which 1g of benzoic acid can be dissolved at 79°C is approximately 39.06 cm³.