Link I. answered • 02/08/20
Experienced tutor: pre- and post-college levels
Hello!
I think you may have some errors in your question. Based on my experience, I can tell that the question is most likely intending to ask, "If the molarity of the Sulfuric Acid solution is .750M and the density is 1.046g/ml, what is the molality of the solution?" I know this because the standard unit for the concentration of a solution is moles/liter, in other words, M. Similarly, the standard unit for density is grams/ml.
You have.750 moles of Sulfuric Acid and .9724 kg of water. So the molality is .750moles/.9724kg = .771 molal.
Detailed Solution:
If you have a 0.750 molar solution of Sulfuric Acid, that means that you have .750 moles dissolved in 1 Liter of solution. Since they don't specify how much Sulfuric Acid you actually have, you can decide what amount we have, because as long as the ratios of solute to solvent or solution are consistent the math works out. So let's say we have .750 moles in 1L of solution. If you have 1L of solution, it means you have 1000ml of solution.
If we have 1000ml of solution, and the solution has a density of 1.046g/ml, we can solve for the number of grams of solution by multiplying the two numbers. So 1.046g/ml times 1000ml is 1046 grams. We have 1046 grams of Sulfuric Acid solution.
Since you have the number of moles of Sulfuric Acid in your solution, you can calculate the mass of Sulfuric Acid in your solution. 0.750 moles multiplied by its molar mass of 98.079 equals 73.6 grams of Sulfuric Acid. You have 73.6 grams of Sulfuric Acid in your solution.
Now here's the part most people get stuck on. The formula for molality is moles of solute divided by kilograms of solvent. Our solvent is water, so you need to figure out how much of the 1046 grams of Sulfuric Acid solution is water. You can do this by subtracting the mass of Sulfuric Acid from the mass of Sulfuric Acid solution. 1046 grams minus 73.6 grams equals 972.4 grams. You have 972.4 grams, or .9724 kg of water.
Now you've got everything you need. .750 moles of Sulfuric Acid divided by .9724 kg of water gives you a molality of .771.