How much would the boiling point of water increase if 4 mol of NaCl were added to 1 kg of water ([tex]K_{ b }=0.51^{\circ} C /( mol / kg )[/tex] for water and [tex]l=2[/tex] for NaCl )?
A. [tex]2.04^{\circ} C[/tex]
B. [tex]4.08^{\circ} C[/tex]
C. [tex]0.51^{\circ} C[/tex]
D. [tex]1.02^{\circ} C[/tex]
Answer (2)
Calculate the molality of the NaCl solution: m = 1 kg 4 mol = 4 mol/kg .
Use the boiling point elevation formula: Δ T b = i × K b × m .
Substitute the given values: Δ T b = 2 × 0.51 × 4 = 4.0 8 ∘ C .
The increase in the boiling point of water is 4.0 8 ∘ C .
Explanation
Problem Setup We are given that 4 moles of NaCl are added to 1 kg of water. We are also given the ebullioscopic constant for water, K b = 0.5 1 ∘ C / ( m o l / k g ) , and the van't Hoff factor for NaCl, i = 2 . We need to find the increase in the boiling point of water.
Calculating Molality The molality of the solution is calculated as the number of moles of solute (NaCl) divided by the mass of the solvent (water) in kg. In this case, the molality (m) is: m = m H 2 O n N a Cl = 1 kg 4 mol = 4 mol/kg
Calculating Boiling Point Elevation The boiling point elevation ( Δ T b ) is calculated using the formula: Δ T b = i K b m where:
i is the van't Hoff factor
K b is the ebullioscopic constant
m is the molality Substituting the given values, we get: Δ T b = 2 × 0.51 mol/kg ∘ C × 4 mol/kg = 4.0 8 ∘ C
Final Answer Therefore, the boiling point of water increases by 4.0 8 ∘ C .
Examples
Boiling point elevation has practical applications in cooking and food science. For example, adding salt to water when cooking pasta increases the water's boiling point, which can result in the pasta cooking faster. This principle is also used in antifreeze solutions for cars, where ethylene glycol is added to water to raise its boiling point and lower its freezing point, preventing the engine from overheating or freezing.
The boiling point of water increases by 4.08°C when 4 moles of NaCl are added to 1 kg of water, using the boiling point elevation formula. This has been calculated using the molality of the solution and factoring in the dissociation of NaCl into two ions. Thus, the correct answer is B. 4.08°C.
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