Question

Desalinization of water attracts growing interest as potable water becomes more scarce, but the process itself is not simple. Even assuming that ions do not interact strongly with the solvent, desalinization fights an uphill battle against entropy. Calculate the (minimum; since we only consider the effect of de-mixing) entropy for obtaining pure water from 10 L of some 1.0 M NaCl solution. Assume ideal mixing, that NaCl dissociates completely, and that each ion species contributes independently to the entropy.

Answer 1

Entropy of desalination= - entropy of mixing the salt with water.

entropy of mixing = -nRxi Ln xi

where Xi is the mole fraction of the ion.

Number of moles of NaCl in 10L of solution = 10 moles.

If NaCl dissociates completely, them 10 mole of na+ ion and 10 moles of Cl- ion are generated in the solution.

Moles of water = 10l/22.4L = 0.45

Total moles = 10 +10+0.45 = 20.45

mole fraction of na+ = 10/10+10 = 10/20.45 = 0.49

mole fraction of Cl- = 0.49

mole fraction of water = 0.45/20.45 =0.02

entropy of mixing =-20.45 *8.314J/K/mol [0.49ln(0.49) + 0.49ln(0.49) + 0.02ln(0.02)] = + 132.11 J/K

entropy of desalination = -132.11J/K