What mass in grams of NaCl would need to be added to 2051 g of water to increase the boiling temperature of the solution by 1.500 °C? (Kb for water is 0.5100 °C/m)

• A. 175.0 g
• B. 43.8 g
• C. 87.5 g
• D. 131.3 g

Answer: (C)

Verified step by step guidance

1. First, understand that the boiling point elevation formula is ΔT_b = i * K_b * m, where ΔT_b is the change in boiling point, i is the van't Hoff factor (which is 2 for NaCl, as it dissociates into Na⁺ and Cl⁻), K_b is the ebullioscopic constant, and m is the molality of the solution.
2. Calculate the molality (m) using the formula m = ΔT_b / (i * K_b). Substitute ΔT_b = 1.500 °C, i = 2, and K_b = 0.5100 °C/m into the formula to find the molality.
3. Molality (m) is defined as moles of solute per kilogram of solvent. Rearrange the molality formula to find the moles of NaCl needed: moles of NaCl = m * mass of water (in kg). Convert the mass of water from grams to kilograms by dividing by 1000.
4. Calculate the moles of NaCl using the molality and the mass of water in kilograms. Use the molar mass of NaCl (approximately 58.44 g/mol) to convert moles of NaCl to grams.
5. Finally, multiply the moles of NaCl by the molar mass of NaCl to find the mass of NaCl in grams that needs to be added to the water to achieve the desired boiling point elevation.