Final answer:
To find the mass of sulfur that can be melted by 29 kJ, we calculate the number of moles of sulfur that corresponds to that amount of energy and then convert moles to mass using the molar mass of sulfur. However, the calculated mass does not match any of the given answer choices, suggesting a potential discrepancy in the presented data or choices.
Step-by-step explanation:
To calculate the mass of sulfur that can be melted by 29 kJ using the given enthalpy of melting, which is +17.7 kJ/mol, we use the formula:
Q = ΔH × n
where Q is the amount of heat energy (in kJ), ΔH is the enthalpy change per mole (in kJ/mol), and n is the number of moles. Rearranging the formula to solve for n gives us:
n = Q / ΔH
So, for 29 kJ:
n = 29 kJ / 17.7 kJ/mol = 1.64 mol
Next, we calculate the mass using the molar mass of sulfur (32.07 g/mol):
Mass = n × Molar Mass
Mass = 1.64 mol × 32.07 g/mol = 52.27 g
However, since none of the answer choices match this result, there might have been an error in the calculations or in the interpretation of the question. Assuming the information provided in the question is correct, none of the given answer choices (a) 16.23 g, (b) 20.54 g, (c) 13.01 g, (d) 32.07 g are correct.