All we have to do is calculate the value of the free energy change for diamond going to graphite.
#color(white)(mmmmmmmmm)"C(diamond) → C(graphite)"#
#Δ_fH^@"/kJ·mol"^"-1": color(white)(mm)1.895color(white)(mmmmmm)0#
#S^@"/J·K"^"-1""mol"^"-1":color(white)(mmll)2.337color(white)(mmmmmm)5.740#
#Δ_rH^@ = Δ_fH^@"(graphite)" - Δ_fH^@"(diamond)"= 0 - "1.895 kJ·mol"^"-1" = "-1.895 kJ·mol"^"-1"#
#Δ_rS^@ = S^@"(graphite)" - S^@"(diamond)" = "(5.740 - 2.337) J·K"^"-1"·"mol"^"-1" = "3.403 J·K"^"-1"·"mol"^"-1"#
#Δ_rG^@ = Δ_rH^@ -TΔ_rS^@ = "-1895 J·mol"^"-1" -298 color(red)(cancel(color(black)("K"))) × 3.403 "J"·color(red)(cancel(color(black)("K"^"-1")))·"mol"^"-1" = "-1895 J·mol"^"-1" - "1014 J·mol"^"-1" = "-2909 J·mol"^"-1" = "-2.909 kJ·mol"^"-1"#
Since #ΔG^@ < 0#, the reaction is spontaneous.
However, the activation energy for the conversion of diamond to graphite is so high (540 kJ/mol) that our bones will have crumbled to dust long before the diamond disappears.
