Question 69 in the attatched photo.i.e.Gibbs energy for the decomposition of ........is at least.

To determine the Gibbs energy for the decomposition of a substance, we need to understand the relationship between Gibbs free energy (G) and the spontaneity of a reaction. The Gibbs free energy change (ΔG) is a crucial factor in predicting whether a reaction will occur spontaneously at constant temperature and pressure. If ΔG is negative, the reaction is spontaneous; if it is positive, the reaction is non-spontaneous.

Understanding Gibbs Free Energy

The Gibbs free energy is defined by the equation:

ΔG = ΔH - TΔS

• ΔH is the change in enthalpy (heat content) of the system.
• T is the absolute temperature in Kelvin.
• ΔS is the change in entropy (disorder) of the system.

Factors Influencing Gibbs Energy

To assess the Gibbs energy for the decomposition reaction, consider the following:

• Enthalpy Change (ΔH): If the decomposition is endothermic (absorbs heat), ΔH will be positive. Conversely, if it is exothermic (releases heat), ΔH will be negative.
• Entropy Change (ΔS): Decomposition reactions often lead to an increase in the number of moles of gas, resulting in a positive ΔS, which favors spontaneity.
• Temperature (T): The temperature at which the reaction occurs can significantly influence the Gibbs energy. Higher temperatures can enhance the impact of the entropy term.

Example Calculation

Let’s consider a hypothetical decomposition reaction:

A(s) → B(g) + C(g)

Assume the following values:

• ΔH = +100 kJ/mol (endothermic)
• ΔS = +200 J/(mol·K)

To find ΔG at a specific temperature, say 298 K (25°C), we first convert ΔS to kJ:

ΔS = 200 J/(mol·K) = 0.2 kJ/(mol·K)

Now, we can substitute the values into the Gibbs free energy equation:

ΔG = ΔH - TΔS

ΔG = 100 kJ/mol - (298 K × 0.2 kJ/(mol·K))

ΔG = 100 kJ/mol - 59.6 kJ/mol = 40.4 kJ/mol

Since ΔG is positive, the decomposition reaction is non-spontaneous at 298 K.

Conclusion

In summary, to determine the Gibbs energy for the decomposition of a substance, you need to analyze the changes in enthalpy and entropy, along with the temperature. By applying the Gibbs free energy equation, you can predict the spontaneity of the reaction. If you have specific values for ΔH and ΔS for the decomposition in question, you can plug them into the equation to find the Gibbs energy change.