Question

Diamond
a. At 298 K, what is the Gibbs free energy change G for the following reaction? Cgraphite ->  Cdiamond

b. Is the diamond thermodynamically stable relative to graphite at 298 K?

c. What is the change of Gibbs free energy of diamond when it is compressed isothermally from 1 atm to 1000 atm at 298 K?

d. Assuming that graphite and diamond are incompressible, calculate the pressure at which the two exist in equilibrium at 298 K.

e. What is the Gibbs free energy of diamond relative to graphite at 900 K? Assume the heat capacities of the two materials are equal.

f. Diamond is synthesized from graphite at high pressures and high temperatures. The need for high pressure should be obvious from your calculations, but why is the process carried out at high temperature?

DATA
Density of graphite is 2.25 g/cm3 Density of diamond is 3.51 g/cm3

	Delta Hf(298K)	So(298K)
Diamond	1.897 kJ/mol	2.38 J/(K mol)
Graphite	0	5.73 J/(K mol)

Hf(298 K)S0

298 K

Diamond 1.897 kJ/mol 2.38 J/(K mol)

Graphite 0 5.73 J/(K mol)

Answer 1

a] delta G = Delta H - T delta S

delta H = 1.897 KJ

delta S = 2.38 - 5.73 = -3.25 J/K

delta G = 1897 - 298*[-3.25] = 2898.28 Joules = 2.898 KJ

b] delta G is postive

so it is non spontaneous reaction which implies graphite is thermodynamically more stable than diamond

c] delta G = V* dP

delta G = [12*10^-6 / 3.51 ]*999*10130 = 34.29 J/mol

d] At 14939 atm

e] Cp values are zero

so

delta H and delta S are same at 900 K [same as of 298 K]

delta G = 4912 J

f] endothermic reactions are favoured at high temperatures only