Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
At room temperature and ordinary pressure, graphite is the more stable form of carbon by for graphite changing to diamond. The densities are for graphite and for diamond. Take the molar mass of carbon as . Find the volume of one mole of each form, and the pressure at which the two forms are in equilibrium, assuming that the volumes do not change with pressure. Use and give the pressure in gigapascals.
A fullerene with carbon atoms has edges, 12 pentagons and hexagons, and . The diamond cell holds 8 atoms, with . At equilibrium between two forms, .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Find the change in molar volume. Then find the pressure that cancels the Gibbs energy difference.
Step 1. Molar volumes. Graphite: . Diamond: .
Step 2. The change. .
Step 3. Equilibrium. , so .
Answer: , and (about 15 000 atmospheres).
Check. Real diamond synthesis uses about to , because the change is too slow at unless a metal catalyst and a high temperature are used. The estimate has the right size.
Source. The Gibbs energy of formation of diamond, , is a standard value from the NIST tables and the CRC Handbook.
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