Answer :
Final answer:
To find the change in entropy for the vaporization of 0.50 mol of ethanol, use the formula ΔS = ΔH/T, convert the temperature to Kelvin, and solve the equation using the given molar heat of vaporization.
Explanation:
To calculate the change in entropy (ΔS) for the vaporization of 0.50 mol ethanol, we can use the formula ΔS = ΔH / T, where ΔH is the molar heat of vaporization and T is the temperature in Kelvin. The molar heat of vaporization of ethanol is given as 39.3 kJ/mol, and the boiling point is specified as 78.3°C.
First, we must convert the boiling point to Kelvin by adding 273.15 to the Celsius temperature, yielding T = 78.3°C + 273.15 = 351.45 K. Then the ΔS for 0.50 mol ethanol can be calculated as (0.50 mol × 39.3 kJ/mol) / 351.45 K. To express ΔS in proper units, we must convert kJ to J by multiplying by 1000. Therefore, ΔS = (0.50 × 39.3 × 1000 J/mol)/ 351.45 K, which simplifies to ΔS = 55.95 J/K.