"A diamond is forever" is one of the most successful advertising slogans of all time. But is it true? For the reaction shown below, calculate the standard free energy change at 298K and determine whether or not a diamond is "forever". C(diamond) → C(graphite) Data: ΔH_f°(diamond) = 1.895 kJ/mol; S°(diamond) = 2.337 J mol^-1K^-1; S°(graphite) = 5.740 J mol^-1K^-1.

Question

Quizplus · Accepted Answer

The standard free energy change can be calculated using the equation: 
ΔG° = ΔH° - TΔS°

ΔH° for the reaction can be found by subtracting the standard enthalpy of formation of graphite from that of diamond: 
ΔH° = [0 kJ/mol (graphite)] - [-1.895 kJ/mol (diamond)] = 1.895 kJ/mol

ΔS° for the reaction can be found by subtracting the standard entropy of graphite from that of diamond: 
ΔS° = [5.740 J/K mol (graphite)] - [2.337 J/K mol (diamond)] = 3.403 J/K mol

Plugging these values into the equation for ΔG°: 
ΔG° = 1.895 kJ/mol - (298 K)(3.403 J/K mol) 
ΔG° = -2.890 kJ/mol

Since ΔG° is negative, the reaction is spontaneous at 298K and the diamond will eventually convert to graphite, meaning that it is not "forever". Therefore, the correct answer is C.

"A Diamond Is Forever" Is One of the Most Successful