Final answer:
To find the change in heat when 50.0 g of isopropyl alcohol melts, convert the mass to moles using the molar mass, then multiply by the given heat of fusion. The calculated heat change is approximately 4.47 kJ, not matching any of the options.
Step-by-step explanation:
The question involves calculating the heat of fusion for isopropyl alcohol (C3H8O) when it melts. The heat of fusion is the amount of energy required to change a substance from its solid state to its liquid state at constant temperature and pressure. Given that the heat of fusion (ΔHfus) of isopropyl alcohol is 5.37 kJ/mol, and the mass of isopropyl alcohol being melted is 50.0 g, we must first convert the mass of isopropyl alcohol to moles using its molar mass.
The molar mass of isopropyl alcohol is (3 × 12.01 g/mol) + (8 × 1.008 g/mol) + (16.00 g/mol) = 60.10 g/mol. Now, calculate the number of moles of isopropyl alcohol:
50.0 g ÷ 60.10 g/mol = 0.832 moles
Next, we use the heat of fusion to find the total heat change:
0.832 moles × 5.37 kJ/mol = 4.468 kJ
Therefore, the answer is that the heat change when 50.0 g of isopropyl alcohol melts is approximately 4.468 kJ, which when rounded to two decimal places is 4.47 kJ, which is not included in the given options, indicating a potential error in the question or the options provided.