Final answer:
The boiling point of a solution of 400 g ethylene glycol in 400 g water is calculated to be 108°C, after determining molality and applying the boiling point elevation formula using the given constants.
Step-by-step explanation:
The boiling point elevation of a solution can be calculated using the formula ΔTb = i * Kb * m, where ΔTb is the boiling point elevation, i is the van't Hoff factor (which is 1 for non-electrolytes like ethylene glycol), Kb is the ebullioscopic constant of the solvent (water in this case), and m is the molality of the solution.
First, calculate the moles of ethylene glycol (EG) by using its molar mass. The molar mass of ethylene glycol (C₂H₆O₂) is 62.07 g/mol. Therefore, the moles of ethylene glycol are 400.0 g / 62.07 g/mol = 6.44 mol.
Next, calculate the molality (m) of the solution: molality = moles of solute / kg of solvent = 6.44 mol / 0.400 kg = 16.1 m.
Now use the ebullioscopic constant of water (Kb) to find the boiling point elevation: ΔTb = 1 * 0.512°C/m * 16.1 m = 8.24°C. So, the boiling point of the solution is the boiling point of pure water plus the elevation: 100°C + 8.24°C = 108.24°C.
Rounded to the nearest whole number, the boiling point is 108°C.