Final answer:
To find ΔG°rxn at 55°C, convert the temperature to Kelvin and use the formula ΔG°rxn = ΔH°rxn - TΔS°rxn, resulting in a value of −255.06921 kJ. At 55°C, ΔG°rxn is -255.06921 kJ, indicating a spontaneous reaction.
Step-by-step explanation:
To calculate the standard free energy change (ΔG°rxn) for a reaction at a given temperature, we use the equation:
ΔG°rxn = ΔH°rxn - TΔS°rxn
Where ΔH°rxn is the standard enthalpy change, T is the temperature in Kelvin, and ΔS°rxn is the standard entropy change. To calculate ΔG°rxn at 55°C, we first convert the temperature to Kelvin:
T = 55°C + 273.15 = 328.15 K
Then we substitute the given values into the equation:
ΔG°rxn = (−255 kJ) - (328.15 K)(211 J/K)(1 kJ/1000 J) = −255 kJ - 0.06921 kJ = −255.06921 kJ
The sign of ΔG°rxn tells us whether the reaction is spontaneous or not.
In the determination of ΔG°rxn at 55°C, the conversion of temperature to Kelvin is a crucial initial step, with T = 55°C + 273.15 = 328.15 K. The application of the formula ΔG°rxn = ΔH°rxn - TΔS°rxn follows, incorporating the standard enthalpy change ΔH°rxn, temperature (T), and the standard entropy change ΔS°rxn.
For example, if ΔH°rxn = -255kJ and ΔS°rxn = 211 J/K, the calculation yields a value of ΔG°rxn = -255 kJ - 0.06921 kJ = -255.06921 kJ. This negative result signifies that the reaction is spontaneous at 55°C.