Answer: Therefore, the change in entropy when 536 g of gold are melted is 0.132 J/K.
Explanation: To calculate the change in entropy when 536 g of gold are melted, we need to know the entropy of fusion of gold and the temperature at which it melts.
The entropy of fusion of gold is 2.35 J/g·K, and the melting point of gold is 1064 °C or 1337 K.
The change in entropy when gold is melted can be calculated using the formula:
ΔS = Q/T
where ΔS is the change in entropy, Q is the heat absorbed during the process, and T is the temperature at which the process occurs.
The heat absorbed when gold is melted can be calculated using the formula:
Q = m × ΔH_fus
where m is the mass of the gold and ΔH_fus is the enthalpy of fusion of gold, which is 64.9 kJ/mol.
Converting the mass of gold to moles:
536 g / 196.97 g/mol = 2.72 mol
The heat absorbed by the gold when it is melted is:
Q = 2.72 mol × 64.9 kJ/mol = 176.2 kJ
Finally, we can calculate the change in entropy:
ΔS = Q/T = 176.2 kJ / 1337 K = 0.132 J/K