calculate the change in entropy that occurs in the system when 1.80 mol of isopropyl alcohol (C3H8O) melts at its melting point (-89.5°C). ΔH°fus = 5.37 kJ/mol.Express your answer in joules per kelvin to three significant figures.
Question
calculate the change in entropy that occurs in the system when 1.80 mol of isopropyl alcohol (C3H8O) melts at its melting point (-89.5°C). ΔH°fus = 5.37 kJ/mol.Express your answer in joules per kelvin to three significant figures.
Solution
The change in entropy (ΔS) can be calculated using the formula:
ΔS = ΔH/T
where ΔH is the heat of fusion and T is the absolute temperature.
First, convert the temperature from Celsius to Kelvin. The conversion formula is:
T(K) = T(°C) + 273.15
So, T(K) = -89.5°C + 273.15 = 183.65 K
Next, convert ΔH from kJ/mol to J/mol:
ΔH = 5.37 kJ/mol * 1000 J/kJ = 5370 J/mol
Now, substitute ΔH and T into the entropy formula:
ΔS = ΔH/T = 5370 J/mol / 183.65 K = 29.24 J/(mol*K)
However, the problem asks for the entropy change for 1.80 mol of isopropyl alcohol, so we need to multiply this result by the number of moles:
ΔS = 29.24 J/(mol*K) * 1.80 mol = 52.6 J/K
So, the change in entropy when 1.80 mol of isopropyl alcohol melts at its melting point is 52.6 J/K.
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