Percent Concentration. Chemistry Help!?

A 10.0% m/v solution means that there is 10.0 g of sucrose dissolved in every 100.0 mL of water multiplied by 100.

A 10.0% m/m solution means that there is 10.0 g of sucrose dissolved in every 100.0 g of solution multiplied by 100.

I will do both and you can see which one applies.

For 10.0% m/v, you would need 450 mL of water:

(45 g sucrose / 450 mL) water x 100 = 10.0 % m/v

For 10.0% m/m, the calculation is a little more complicated.

10.0% m/m = (mass of sucrose / (mass of sucrose + mass of water)) x 100

0.1 = 45 / (45 + mass of water) ..... [divided both sides by 100]

4.5 + 0.1 x mass of water = 45 ..... [multiplied brackets out]

mass of water = 45 - 4.5 / 0.1 = 405 g

volume of water = mass / density = 405 g / 0.9982 g/mL = 405.7 mL