Final answer:
To calculate the mass of acetamide that was dissolved to achieve a boiling point of 100.208°C, we need to calculate the molality based on the boiling point elevation, then use this molality to find the number of moles, and subsequently the mass in grams.
Step-by-step explanation:
To determine how much acetamide was dissolved to yield a solution with a boiling point of 100.208°C, we utilize the concept of boiling point elevation, which relates to the colligative properties of solutions. The boiling point elevation is given by ΔTb = i · Kb · m, where ΔTb is the change in boiling point, i is the van't Hoff factor (which is 1 for non-electrolytes like acetamide), Kb is the ebullioscopic constant (also known as the boiling point elevation constant) of the solvent (water), and m is the molality of the solution.
First, we need to find the change in boiling point (ΔTb), which is the observed boiling point minus the normal boiling point of water (100.208°C - 100.00°C = 0.208°C). Then, we calculate the molality (m) using the equation m = ΔTb / (Kb · i), and from there, we can find the number of moles of acetamide. Finally, we convert moles to grams using the molar mass of acetamide. The molar mass of acetamide is 59 g/mol.
By following these steps, you can calculate the mass of acetamide added to the water:
- Calculate the change in boiling point (ΔTb): 0.208°C.
- Calculate the molality (m) using the formula m = ΔTb / Kb, where Kb for water is 0.52 °C kg mol-1.
- With m calculated, determine the moles of acetamide by the formula moles = molality · mass of water in kg.
- Convert moles of acetamide to grams using its molar mass.
The mass of acetamide used is found by multiplying the number of moles by its molar mass.