Mass of sugar=34.2 gram.
Number of moles of sugar = 34.2/(mol.mass) = 34.2/342 = 0.1
Mass of water = (214.2-34.2)=180g or 180/1000 kg
Number of moles of water = 180/18 = 10 moles
Molarity = Number of moles of sugar/Mass of water per Kg
= 0.1/180 x 1000 = 0.555M
Hence, the molarity of sugar is 0.555 M.
Total number of moles =10.0+0.1=10.1
Mole fraction of sugar = Number of moles of sugar/Total moles
= 0.1/10.1 = 0.0099
Hence, the mole fraction of sugar syrup is 0.0099