The organic compound acetylene (C_2H_2) has the following reported data: triple point: T= 192 K, P= 128 kPa critical point = T= 309 K, P = 6100 kPa (a) Sketch the phase diagram for acetylene in the space below. Assume that the solid-liquid phase boundary has a positive slope. Label the regions corresponding to the solid, liquid, gaseous, and supercritical fluid phases, and also label the triple point and critical point. (b) The standard molar entropy of acetylene (at a pressure of 1 bar) is 200.9 J K^-1 mol^-1. Calculate the change in free energy for a sample of 0.75 mol acetylene upon heating from 293.15 to 303.15 K at 1 bar.
Phase diagram of Acetylene (C2H2) has shown below.
Point A is the triple point as shown in the figure.
Ttp = triple point = 192 K
Corresponding pressure Ptp = 128 kPa
Point B is the critical point
Tc = critical point temperature = 309 K
Corresponding Pc = critical point pressure = 6100 kPa
All phases have been shown in the phase diagram.
The balanced chemical reaction of acetylene upon heating
C2H2 (G ACETYLENE) + 3 O2 (G) → 2 CO2 (G) + H2O (G)
ENTHALPY OF REACTION
[2ΔHf(CO2 (g)) + 1ΔHf(H2O (g))] – [1ΔHf(C2H2 (g acetylene)) + 2.5ΔHf(O2 (g))]
[2(-393.51) + 1(-241.82)] – [1(226.73) + 2.5(0)] = -1255.57 kJ
-1,255.57 kJ (exothermic)
[2ΔSf(CO2 (g)) + 1ΔSf(H2O (g))] – [1ΔSf(C2H2 (g acetylene)) + 2.5ΔSf(O2 (g))]
[2(213.68) + 1(188.72)] – [1(200.9) + 2.5(205.03)] = -97.325 J/K
-97.33 J/K (decrease in entropy)
FREE ENERGY OF REACTION (AT 298.15 K)
From ΔGf° values:
[2ΔGf(CO2 (g)) + 1ΔGf(H2O (g))] – [1ΔGf(C2H2 (g acetylene)) + 2.5ΔGf(O2 (g))]
[2(-394.38) + 1(-228.59)] – [1(209.2) + 2.5(0)] = -1226.55 kJ
-1,226.55 kJ (spontaneous)
From ΔG = ΔH – TΔS:
-1226.55 kJ (spontaneous)