Pressure above which graphite will spontaneously change into diamond

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SUMMARY

The pressure at which graphite spontaneously transforms into diamond can be calculated using the Gibbs free energy equation, G = H - TS. At 298.15 K, the change in Gibbs free energy (ΔGf) for graphite is 0, while for diamond it is 2.9 kJ/mol, indicating that graphite is the more stable form of carbon under these conditions. The volume change during the transformation is Vdiamond - Vgraphite = -2 x 10-6 m3/mol. This information is crucial for determining the equilibrium pressure at which both phases coexist.

PREREQUISITES
  • Understanding of Gibbs free energy and its relation to phase transitions
  • Familiarity with thermodynamic equations, particularly G = H - TS
  • Knowledge of phase equilibrium concepts
  • Basic principles of isothermal processes
NEXT STEPS
  • Research the calculation of equilibrium pressure using the Gibbs free energy equation
  • Study the thermodynamic properties of graphite and diamond at varying temperatures
  • Explore phase diagrams for carbon to understand stability regions
  • Learn about the implications of pressure and temperature on phase transitions in materials science
USEFUL FOR

Students in chemistry or materials science, particularly those studying thermodynamics and phase transitions, as well as researchers interested in carbon allotropes and their properties.

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Homework Statement



Calculate the pressure at which graphite spontaneously changes to diamond.

T = 298.15 K (isothermal)
Vdiamond - Vgraphite = -2 x 10-6m3/mol

At 273.15K and 1 bar (105 Pa):
ΔGf graphite = 0
ΔGf diamond = 2.9 kJ/mol
i.e. graphite is the more stable and preferred form of carbon in the above conditions.

Homework Equations



Not really sure here... Could be anything.

Perhaps useful is: G = H - TS

But I don't see where P fits in.

The Attempt at a Solution



Well, I know G will be 0 at the pressure I am trying to identify (i.e. graphite and diamond will be in equilibrium, with equal tendency for the carbon to form either).
 
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G = H - TS is definitely relevant if you expand H by using its definition.
 

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