Calculate the molality of a solution containing 257 g glucose (c6h12o6) dissolved in 1.62 l of water. assume a density of 1.00 g/ml for water.

Molality is defined as the number of moles of solute in 1 kg of solvent.
since density and volume has been given we can calculate the mass of water
mass = density x volume
mass = 1.00 g/mL x 1620 mL = 1620 g
number of moles of glucose - 257 g / 180 g/mol = 1.43 mol
number of moles of glucose in 1620 g - 1.43 mol
therefore number of moles in 1000 g - 1.43 mol / 1.620 kg = 0.883 mol/kg
therefore molality is 0.883 mol/kg

Spontaneity tell us the direction of the reaction, but not how fast it goes. gibbs free energy brings together enthalpy, entropy and temperature in one easy formula. g = h - ts. and, finally the sign of delta g is always negative for a spontaneous reaction.