I am assuming you are refering to a one molar solution. I am also assuming that you have simplified the problem, because sucrose takes up space in water, so a 1 molar solution of sucrose would have less than 1000mL of water. I do not know the what volume of solution is desired, so I will use one liter in my equation. For the sake of organization: 1L sucrose solution * (0.2 moles sucrose/ 1L) * (342.12 g/ 1 mole sucrose) = 68.42 g sucrose In one liter there will be 1000 mL of water (if you simplify the equation so that sucrose doesn't displace any water). In summary: in a 0.2 molar solution of sucrose, there are 68.2 grams of sucrose.
A solution with a 22 millimolarity will have 22 millimoles of solute per liter of solvent. This means in 100 mL, there will be 2.2 millimoles or .0022 moles. With a molar mass of 342 grams per mole, this is .7524 grams of sucrose.
You weight 342 g sucrose, which equals the weight of exactly one mole (hence it is the molar mass, = 342 g/mol) and dissolv it in 750 mL water and after stirring/dissolution add the volume up to 1.00 L
342 grams = 0.342 milligrams; just to keep things in milli.
0.22 mM sucrose = X millimole/100 milliters
= 22 millimoles, or 0.022 moles
22 millimoles X 0.342 milligrams = 7.542 milligrams. or....
= 0.007524 grams
A 0.20m [ 0.20 molality ] sucrose solution must contain 0.20 moles of sucrose per kilogram of water.
The molar mass of sucrose is 342 g per mol.
m sucrose needed with 1000 ml H2O = ( 0.2m ) (342 g / kg H2O ) = 68.4 g
m sucrose needed with 100 mL H2O = ( 100 /1000 ) ( 68.4 g ) = 6.86 g sucrose
Answer : 6.86 g sucrose <---------------------------
We need 75,306 g sucrose.
The needed mass is 6,846 g.
75.24g