Calculate the change in enthalpy (amount of heat at constant pressure) when a mole of iodine goes from 300 K to 500 K under the pressure of one atmosphere. We give: the molar heat capacities of pure bodies: Cp (I2, solid) =22.6 J/mol K, Cp (I2, liquid) = 81.6 J/mol K Cp (I2, gas) = 37.7 J/mol K, ΔH°v(I2) at 457K = 25.52 kJ/mol, ΔH°F (I2) at 387K = 15.65 KJ/mol
Question
Calculate the change in enthalpy (amount of heat at constant pressure) when a mole of iodine goes from 300 K to 500 K under the pressure of one atmosphere. We give: the molar heat capacities of pure bodies: Cp (I2, solid) =22.6 J/mol K, Cp (I2, liquid) = 81.6 J/mol K Cp (I2, gas) = 37.7 J/mol K, ΔH°v(I2) at 457K = 25.52 kJ/mol, ΔH°F (I2) at 387K = 15.65 KJ/mol
Solution
To calculate the change in enthalpy, we need to consider the phase changes that iodine undergoes when heated from 300 K to 500 K.
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Heating solid I2 from 300 K to 387 K: ΔH1 = ∫Cp(solid) dT from 300 K to 387 K = Cp(solid) * (Tfinal - Tinitial) = 22.6 J/mol K * (387 K - 300 K) = 1963.8 J
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Melting solid I2 at 387 K to liquid I2: ΔH2 = ΔH°f(I2) at 387K = 15.65 kJ/mol = 15650 J/mol
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Heating liquid I2 from 387 K to 457 K: ΔH3 = ∫Cp(liquid) dT from 387 K to 457 K = Cp(liquid) * (Tfinal - Tinitial) = 81.6 J/mol K * (457 K - 387 K) = 5707.2 J
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Vaporizing liquid I2 at 457 K to gaseous I2: ΔH4 = ΔH°v(I2) at 457K = 25.52 kJ/mol = 25520 J/mol
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Heating gaseous I2 from 457 K to 500 K: ΔH5 = ∫Cp(gas) dT from 457 K to 500 K = Cp(gas) * (Tfinal - Tinitial) = 37.7 J/mol K * (500 K - 457 K) = 1619.1 J
The total enthalpy change is the sum of these five steps:
ΔHtotal = ΔH1 + ΔH2 + ΔH3 + ΔH4 + ΔH5 = 1963.8 J + 15650 J + 5707.2 J + 25520 J + 1619.1 J = 51460.1 J/mol = 51.46 kJ/mol
So, the change in enthalpy when a mole of iodine goes from 300 K to 500 K under the pressure of one atmosphere is 51.46 kJ/mol.
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