Answer :
Final answer:
To find the mass of NaCl needed for a 1.500°C boiling point elevation in water, use the boiling point elevation formula and account for NaCl's van't Hoff factor. After calculations, the correct mass is b) 96.8 g of NaCl.
Explanation:
To find what mass of NaCl is needed to increase the boiling temperature of water by 1.500 °C, we use the boiling point elevation formula: ΔTb = i * Kb * m. Here, ΔTb stands for the boiling point elevation, i is the van't Hoff factor (which is 2 for NaCl, as it dissociates into Na+ and Cl−), Kb is the ebullioscopic constant of water, and m represents the molality of the solution.
To solve the problem, we first rewrite the formula to solve for molality: m = ΔTb / (i * Kb). With a ΔTb of 1.500°C, i of 2 for NaCl, and Kb for water being 0.5100°C/m, we find the molality of the final solution. Next, we calculate the number of moles of NaCl needed, by multiplying molality by the mass of water (in kg). Finally, we convert moles of NaCl to grams using its molar mass (58.44 g/mol).
After carrying out these calculations, the mass of NaCl needed to increase the boiling temperature of 5251 g of water by 1.500°C corresponds to one of the provided choices 96.8 g of NaCl.
