Question

How much salt would one need to add to 1 kg water to change the boiling temperature by 5°C? Give your answer in moles. Show your work. (Kb = __________ for water and i = 2 for NaCl.)

A. 0.01
B. 0.1
C. 0.01
D. 0.1

Answer 1

Approximately 4.81 moles of salt (NaCl) would be required to increase the boiling point of 1 kg of water by 5°C, assuming the molal boiling point elevation constant (Kb) for water is 0.52°C/m and the van't Hoff factor (i) for NaCl is 2.

Step-by-step explanation:

To calculate how much salt (NaCl) is needed to raise the boiling point of 1 kg of water by 5°C, we use the colligative property known as boiling point elevation, which is expressed by the formula ΔTb = i * Kb * m, where ΔTb is the change in boiling point, i is the van't Hoff factor (which is 2 for NaCl as it dissociates into two ions: Na+ and Cl-), Kb is the molal boiling point elevation constant for water (0.52°C/m), and m is the molality of the solution in moles of solute per kilogram of solvent (water).

To find m, we rearrange the equation to m = ΔTb / (i * Kb). Inserting the values gives m = 5°C / (2 * 0.52°C/m) = 4.80769 mol/kg.

To find the number of moles of NaCl, we use the molality multiplied by the mass of the solvent. Thus, the number of moles of NaCl needed is 4.80769 mol/kg * 1 kg = 4.80769 moles which rounds to approximately 4.81 moles of salt needed to increase the boiling point by 5°C.