how many milliliters of a 5.0 m surcrose solution would be needed to prepare 45 mL of a 4.0 M solution?
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.
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.
To calculate the volume of a solution needed to prepare another solution with a different concentration, you can use the formula:
C1V1 = C2V2
Where:
C1 = initial concentration of the solution (in this case, 5.0 M)
V1 = initial volume of the solution (unknown)
C2 = final concentration of the solution (in this case, 4.0 M)
V2 = final volume of the solution (45 mL)
Rearranging the formula to solve for V1:
V1 = (C2V2) / C1
Now, let's substitute the values into the equation:
V1 = (4.0 M * 45 mL) / 5.0 M
V1 = (4.0 M * 45 mL) / 5.0
V1 = 36 mL
Therefore, you would need 36 mL of the 5.0 M sucrose solution to prepare 45 mL of a 4.0 M sucrose solution.