"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

To calculate the standard free energy change (Δ G°) at 298K, we use the equation:

Δ G° = Δ H° - TΔ S°

Where Δ H° is the standard enthalpy change, T is the temperature in Kelvin (298K), and Δ S° is the standard entropy change.

Using the given data: 
Δ H° = 1.895 kJ/mol 
Δ S°(diamond) = 2.337 J/molK 
Δ S°(graphite) = 5.740 J/molK

To determine whether or not a diamond is "forever", we need to see if the Δ G° for the reaction is positive, negative, or zero. If it is negative, the reaction will be spontaneous and diamonds will eventually turn into graphite at room temperature.

Δ G° = Δ H° - TΔ S°
Δ G° = 1.895 kJ/mol - (298K)(2.337 J/molK - 5.740 J/molK)
Δ G° = -2.90 kJ/mol

Since Δ G° is negative, the reaction is spontaneous and diamonds will eventually turn into graphite at room temperature. Therefore, the best choice is C: Δ G° = -2.90 kJ; not forever.

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