Suppose a student obtained a 0.15g of cruse salicylic acid. How much water would be needed to just dissolve it at 75 degrees Celsius?

How much salicylic acid would remain dissolved in that amount of water at just 10 degrees Celsius?
What percent of the original mass of the crude salicylic acid remains in the water at 10 degrees Celsius and cannot be recovered?

You need more information that what you posted. You need to know the solubility of SA at 75 C and at 10 C. Technically you can't answer the first part of the question BECAUSE it is crude SA and not pure. So you CAN calculate how much will dissolve IF you have the solubility to begin with.

To determine how much water is needed to dissolve 0.15g of crude salicylic acid at 75 degrees Celsius, we need to refer to the solubility of salicylic acid in water at that temperature. The solubility of salicylic acid varies with temperature, so we need to find the solubility data at 75 degrees Celsius.

We can start by conducting a search for the solubility of salicylic acid in water at different temperatures using reliable sources such as scientific literature or chemical databases. Once we find the solubility data, we can determine the amount of water needed to dissolve the given mass of salicylic acid at 75 degrees Celsius.

To determine how much salicylic acid would remain dissolved in the water at 10 degrees Celsius, we need to know the solubility of salicylic acid in water at that temperature. Again, we can refer to the solubility data obtained from reliable sources at 10 degrees Celsius. This data would give us an indication of how much salicylic acid remains dissolved in the given amount of water at that temperature.

To calculate the percent of the original mass of the crude salicylic acid that remains in the water at 10 degrees Celsius and cannot be recovered, we can use the mass of salicylic acid initially dissolved in water and compare it to the mass of salicylic acid that remains dissolved at 10 degrees Celsius. The difference in mass would give us the amount of salicylic acid that precipitated out of the solution. Dividing this amount by the initial mass and multiplying by 100 would give us the percent.