Question 6f577

Apr 19, 2017

A diamond is NOT forever. The correct answer is C) ΔG^@ "= -2.90 kJ: not forever".

Explanation:

All we have to do is calculate the value of the free energy change for diamond going to graphite.

$\textcolor{w h i t e}{m m m m m m m m m} \text{C(diamond) → C(graphite)}$
Δ_fH^@"/kJ·mol"^"-1": color(white)(mm)1.895color(white)(mmmmmm)0
${S}^{\circ} \text{/J·K"^"-1""mol"^"-1} : \textcolor{w h i t e}{m m l l} 2.337 \textcolor{w h i t e}{m m m m m m} 5.740$

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.