Calculations involving sucrose, molality, molarity, weight, mole fraction





A sucrose solution containing 30gram sucrose (C12H22O11) in 300ml of that solution, the density of the solution is 2.04g/mm. when these are provided: C=12, H=1, O=16, calculate:
(i)                 Molality of sucrose solution 
(ii)               Molarity of  sucrose solution
(iii)             Weight of sucrose solution
(iv)             Mole fraction of sucrose solution 


To answer question (i) and (ii) we should know what is molality and molarity to avoid confusion that may arise. Molality is a measure of the concentration of a solute in a solution in terms of amount of substance in specified amount of mass of the solvent. It is also known as molal concentration. Its common unit in chemistry is mol/kg while molarity which also known as molar concentration is a measure of the concentration of a solute in a solution or any chemical species in terms of amount of substance in a given volume. Its unit in chemistry is mol/L.
Calculations
(i)                 Basis: number of moles per 1000grams or 1 kilogram of the solvent, for us to get weight of the solution, it will be; volume multiply by density(W=V X D) i.e
V=300ml, D=2.04g/mm
W= (300 X 2.04) = 612 grams, now getting weight of the solvent; we subtract the weight of sucrose (30 grams) from the weight of solution (612 grams): (612-30) = 582 grams.
Weight of sucrose in 1000 grams solvent;
(30/582 X 1000) = 51.55 grams, molecular weight of sucrose will be; (12 X 12) + (22 X 1) + (11 X 16) = 342g/mole.
Molality of the sucrose solution is: (51.55/342) = 0.15073 molal.
(ii)               Basis: 1 Litre of the solution, hence this will be;
(30 X 1000)/ (300) = 100 grams,
Molecular weight of sucrose is (as calculated above) = 342 grams/mole,
Therefore molarity becomes; (100/342) = 0.2924 M
(iii)             The weight of sucrose in the solution will be; weight of (sucrose in grams)/(weight of solution in grams) X 100
(30/612) X 100 = 4.902%
(iv)              Mole fraction of sucrose solution will be;
In 300ml, how many moles of sucrose are there? i.e
(30/342) = 0.08772 moles, but in this solution (300ml) there is 582 grams of solvent (water). Therefore, the number of moles of water at (300ml solution) is;
(582/18) = 32.33 moles, a point to note molecular weight of water is 18 grams/ mole.
Hence mole fraction of sucrose is;
(0.09)/ (0.09 + 32.33) = 0.00278

NB: 0.08772 moles equivalent to 0.09 and it is the reason why 0.09 is used in the above calculation and mole fraction = (moles of the solute in the solution)/ {moles of the solvent + moles of solute in the solution}


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