For a process to be spontaneous, the total entropy of the system and its surroundings must increase; that is ΔStotal = ΔSsystem + ΔSsurr 7 0 for a spontaneous process Furthermore, the entropy change in the surroundings, ΔSsurr, is related to the enthalpy change for the process by the equa- tion ΔSsurr = - ΔH>T. (b) What is the value of ΔSsurr for the photosynthesis of glu- cose from CO2 at 298 K? 6 CO21g2 + 6 H2O1l2 S C6H12O61s2 + 6 O21g2 ΔG° = 2879 kJ ΔS° = - 262 J>K

Verified step by step guidance

1. Identify the given values: ΔG° (change in Gibbs free energy) is 2879 kJ, ΔS° (change in entropy of the system) is -262 J/K, and the temperature T is 298 K.
2. Convert ΔG° from kJ to J for consistency in units. Recall that 1 kJ = 1000 J.
3. Use the Gibbs free energy equation ΔG = ΔH - TΔS to rearrange and solve for ΔH (change in enthalpy). The equation becomes ΔH = ΔG + TΔS.
4. Substitute the values of ΔG, T, and ΔS into the rearranged equation to calculate ΔH.
5. Calculate ΔSsurr (change in entropy of the surroundings) using the equation ΔSsurr = -ΔH/T. Substitute the calculated ΔH and the given temperature T into this equation.

Key Concepts

Entropy and Spontaneity

Entropy is a measure of the disorder or randomness in a system. For a process to be spontaneous, the total entropy change (ΔStotal) of the system and its surroundings must be positive. This means that the increase in disorder in the universe is favored, which is a fundamental principle of thermodynamics.

Enthalpy and Entropy Relationship

The relationship between enthalpy change (ΔH) and entropy change in the surroundings (ΔSsurr) is given by the equation ΔSsurr = -ΔH/T, where T is the temperature in Kelvin. This equation indicates that the entropy change in the surroundings is inversely related to the temperature and directly related to the enthalpy change of the process, which is crucial for determining spontaneity.

Gibbs Free Energy

Gibbs Free Energy (ΔG) is a thermodynamic potential that helps predict the spontaneity of a process at constant temperature and pressure. A negative ΔG indicates that a process is spontaneous, while a positive ΔG suggests it is non-spontaneous. The relationship ΔG = ΔH - TΔS connects enthalpy, temperature, and entropy, providing a comprehensive view of the thermodynamic favorability of reactions.