Calculate the molality of the solution: m = 1 k g 3 m o l = 3 m o l / k g .
Use the boiling point elevation formula: Δ T b = i × K b × m = 2 × 0.51 × 3 = 3.0 6 ∘ C .
Add the boiling point elevation to the normal boiling point of water: T b , n e w = 10 0 ∘ C + 3.0 6 ∘ C = 103.0 6 ∘ C .
The final boiling point of the solution is 103.0 6 ∘ C .
Explanation
Problem Analysis We are asked to find the final boiling point of water after adding 3 mol of NaCl to 1 kg of water. We are given the molal boiling point elevation constant for water, K b = 0.5 1 ∘ C / ( m o l / k g ) , and the van't Hoff factor for NaCl, i = 2 .
Boiling Point Elevation Formula The boiling point elevation is given by the formula Δ T b = i × K b × m , where m is the molality of the solution.
Calculating Molality First, we need to calculate the molality, m , which is defined as the number of moles of solute per kilogram of solvent. In this case, we have 3 mol of NaCl and 1 kg of water, so the molality is: m = 1 k g 3 m o l = 3 m o l / k g
Calculating Boiling Point Elevation Now, we can calculate the boiling point elevation, Δ T b , using the formula: Δ T b = i × K b × m = 2 × 0.5 1 ∘ C / ( m o l / k g ) × 3 m o l / k g Δ T b = 2 × 0.51 × 3 = 3.0 6 ∘ C
Calculating the New Boiling Point The normal boiling point of water is 10 0 ∘ C . The new boiling point, T b , n e w , is the sum of the normal boiling point and the boiling point elevation: T b , n e w = 10 0 ∘ C + Δ T b = 10 0 ∘ C + 3.0 6 ∘ C = 103.0 6 ∘ C
Final Answer Therefore, the final boiling point of the water after adding 3 mol of NaCl is 103.0 6 ∘ C .
Examples
Boiling point elevation is a colligative property, meaning it depends on the concentration of solute particles, not their identity. For example, when cooking pasta, adding salt to the water increases the boiling point slightly. This can lead to faster cooking times, as the water reaches a higher temperature before boiling. Understanding boiling point elevation helps in various applications, such as antifreeze in car radiators, where solutes are added to water to prevent freezing in winter and to raise the boiling point in summer, preventing overheating.