Question

2.82g of glucose (MOLAR MASS=180)are dissolved in 30g of water . calculate(a) the molarity(b)mole fraction of glucose and water.

Answer 1

you should ask molality , not molarity because for finding molarity we have require volume of solution , this is possible when you will give either volume of solution or density of solution .

(a) 2.82g of glucose are dissolved in 30g of water
∴ mass of solute = 2.82 g , mass of solvent = 30g
Now, molality = mass of solute × 1000/{mass of solvent (in g) × molar mass of solute }
= 2.82 × 1000/(30 × 180)
= 2820/5400
= 0.5222 m
Hence, molality = 0.5222m

(b) mole of glucose = 2.82/180 = 0.0156
mole of water = 30/18 = 5/3 = 1.66
total number of mole = 0.0156 + 1.66 = 1.6756
∴ mole fraction of glucose = mole of glucose/total number of mole
= 0.0156/1.6756
= 0.00931

Also mole fraction of water = mole of water/total number of mole
= 1.66/1.6756
= 0.990

Answer 2

Hello Dear.

We have to calculate the Molality instead of Molarity. For calculating the Molarity, Density or Volume must be given. Since these are not given we cannot calculate it. 
Rest of the Question is Correct.

Mass of the Glucose = 2.82 grams.
Molar Mass of the Glucose = 180 g/mol.

No. of moles of Glucose = Mass/Molar Mass
 = 2.82/180
 = 0.0156 mol.

(a) Mass of the Water = 30 g.
     = 0.030 kg.

∵ Molality = No. of moles of Solute (or Glucose)/Mass of the Solvent (or Water)
∴ Molality = 0.0156/0.030
   = 0.52 m.

Hence, the Molality of the Solution will be 0.52 m.

(b) No. of moles of Water = Mass/Molar Mass
      = 30/18
      = 5/3 moles.
      = 1.67 moles.

No. of moles of Glucose = 0.0156 moles.

Total Number of moles in the Solutions = 1.67 + 0.0156
 = 1.6856 moles.

∵ Mole Fraction of Glucose = Moles of Glucose/Total number of moles in the solutions
∴ Mole fraction = 0.0156/1.6856
    = 0.0093

∵ Mole Fraction of water= Moles of Water/Total No. of moles in a solution.
   = 1.67/1.6856
   = 0.991


Hope it helps.