Step-by-step explanation:
To determine whether a reaction is spontaneous or not at a given temperature, we can use the Gibbs free energy change (ΔG) equation:
ΔG = ΔH - TΔS
Where:
ΔG is the Gibbs free energy change
ΔH is the enthalpy change
T is the temperature in Kelvin
ΔS is the entropy change
If ΔG is negative, the reaction is spontaneous, while if ΔG is positive, the reaction is non-spontaneous.
Given that ΔH = +210 kJ mol^(-1) and ΔS = +216 J K^(-1) mol^(-1), we can calculate the Gibbs free energy change at 298 K (25°C) as follows:
ΔG = ΔH - TΔS
ΔG = (+210 kJ mol^(-1)) - (298 K)(+216 J K^(-1) mol^(-1))
(Note: Conversion from J to kJ is necessary)
Let's convert the units and perform the calculation:
ΔG = (+210 kJ mol^(-1)) - (0.298 kJ)(+216 kJ mol^(-1))
ΔG = +210 kJ mol^(-1) - 64.368 kJ mol^(-1)
ΔG = -45.368 kJ mol^(-1)
The calculated value for ΔG at 298 K is -45.368 kJ mol^(-1), indicating that the reaction is not spontaneous at this temperature since ΔG is negative.
To find the temperature at which the reaction becomes spontaneous, we can rearrange the equation:
ΔG = ΔH - TΔS
T = (ΔH / ΔS)
Let's calculate the temperature:
T = (+210 kJ mol^(-1)) / (+216 J K^(-1) mol^(-1))
(Note: Conversion from kJ to J is necessary)
T = (210 kJ mol^(-1)) / (216 × 10^3 J K^(-1) mol^(-1))
(Note: Conversion from kJ to J)
T ≈ 972 K
Therefore, the reaction becomes spontaneous at approximately 972 K (or 699°C) and above, where the temperature allows ΔG to become negative.