Question

how many milliliters of a 5.0 m surcrose solution would be needed to prepare 45 mL of a 4.0 M solution?

Answer 1

This is a dilution problem... Use the dilution equation. (Molarity)(Volume)of concentrate = (Molarity)(Volume) of diluted soln. For these type problems you need to ask 'How many ml of the concentrate do I need to dilute to the needed concentration and volume?' ...

let x = Volume of Concentrate (ml)
Molarity of Concentrate = 5M
Molarity of Dilute Soln = 4M
Vol of Dilute Soln needed = 45ml

x(5M) = (4M)(45ml)
solve for x = (4M)(45ml)/(5M) = 36ml

Transfer 36ml of concentrate into mixing vessel and add solvent (water) up to but not to exceed 45ml total final volume.

Answer 2

I should point out that m and M are not the same. I assume that is a typo. It isn't easy to convert m to M with knowing the density.