Final answer:
To change the boiling temperature of 1 kg of water by 5°C, you would need to add 4.9 moles of salt. The equation ΔT = xKbxm can be used to calculate the change in temperature, where ΔT is the change in temperature, Kb is the molal boiling point elevation constant, m is the molality of the solution, and i is the number of particles formed when the compound dissolves. For NaCl, i is 2.
Step-by-step explanation:
The equation that describes the change in temperature of a solvent due to a solute is ΔT = xKbxm. To determine how much salt would need to be added to 1 kg of water to change the boiling temperature by 5°C, we can use the equation ΔT = Kb × m × i. Here, ΔT is the change in temperature, Kb is the molal boiling point elevation constant, m is the molality of the solution, and i is the number of particles formed when the compound dissolves. For NaCl, i is 2. Given that the boiling point elevation constant for water, Kb, is 0.51°C/m, we can calculate the molality, m, using the equation ΔT = Kb × m × i:
5 = 0.51 × m × 2
m = 5 / (0.51 × 2) = 4.9 mol/kg
Since 1 kg of water is equivalent to 1 L, we can convert the molality to moles by multiplying by the mass of water:
moles of salt = 4.9 mol/kg × 1 kg = 4.9 moles
Therefore, you would need to add 4.9 moles of salt to 1 kg of water to change the boiling temperature by 5°C.