Edexcel International A Level (IAL) Chemistry (YCH11) - Unit 4 - 12.9–12.10 Feasibility, temperature and ΔS_total-Study Notes - New Syllabus
Edexcel International A Level (IAL) Chemistry (YCH11) -Unit 4 – 12.9–12.10 Feasibility, temperature and ΔS_total- Study Notes- New syllabus
Edexcel International A Level (IAL) Chemistry (YCH11) -Unit 4 – 12.9–12.10 Feasibility, temperature and ΔS_total- Study Notes -International A Level (IAL) Chemistry (YCH11) – per latest Syllabus.
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Edexcel International A Level (IAL) Chemistry (YCH11) -Concise Summary Notes- All Topics
12.9 Feasibility of Reactions: Balance of Entropy and Effect of Temperature
The feasibility (spontaneity) of a reaction depends on the total entropy change, which is influenced by both the entropy change of the system and the surroundings. Temperature also plays a crucial role in determining the relative contributions of these factors.
(i) Balance between \( \mathrm{\Delta S_{system}} \) and \( \mathrm{\Delta S_{surroundings}} \)
A reaction is feasible when the total entropy change is positive, i.e. \( \mathrm{\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} > 0} \).
The feasibility depends on the balance between:
- \( \mathrm{\Delta S_{system}} \): change in disorder of the reacting system.
- \( \mathrm{\Delta S_{surroundings}} \): change in entropy due to heat transfer.
Since:
\( \mathrm{\Delta S_{surroundings} = -\frac{\Delta H}{T}} \)
- Exothermic reactions (\( \mathrm{\Delta H < 0} \)) give a positive \( \mathrm{\Delta S_{surroundings}} \).
- Endothermic reactions (\( \mathrm{\Delta H > 0} \)) give a negative \( \mathrm{\Delta S_{surroundings}} \).
Therefore:
- Even if a reaction is endothermic, it can still be feasible if \( \mathrm{\Delta S_{system}} \) is sufficiently positive to outweigh the negative \( \mathrm{\Delta S_{surroundings}} \).
- This explains why some endothermic reactions occur spontaneously at room temperature.
(ii) Effect of Temperature on Feasibility
Temperature affects feasibility because it changes the magnitude of \( \mathrm{\Delta S_{surroundings}} \).
From:
\( \mathrm{\Delta S_{surroundings} = -\frac{\Delta H}{T}} \)
- As temperature increases, the value of \( \mathrm{\frac{\Delta H}{T}} \) decreases.
- Therefore, the magnitude of \( \mathrm{\Delta S_{surroundings}} \) becomes smaller.
- This reduces the contribution of the surroundings to \( \mathrm{\Delta S_{total}} \).
Implications:
- For endothermic reactions, increasing temperature makes \( \mathrm{\Delta S_{surroundings}} \) less negative, so the reaction becomes more feasible.
- For exothermic reactions, increasing temperature reduces the positive contribution of \( \mathrm{\Delta S_{surroundings}} \), so feasibility may decrease.
Calculation of Temperature for Feasibility
At the point of feasibility (equilibrium):
\( \mathrm{\Delta S_{total} = 0} \)
Therefore:
\( \mathrm{\Delta S_{system} = \frac{\Delta H}{T}} \Rightarrow T = \frac{\Delta H}{\Delta S_{system}} \)
This allows the temperature at which a reaction becomes feasible to be calculated.
Alternative Expression (Optional)
\( \mathrm{\Delta G = \Delta H – T\Delta S_{system}} \)
- \( \mathrm{\Delta G < 0} \): reaction is feasible.
- \( \mathrm{\Delta G = 0} \): equilibrium.
This equation is equivalent to the entropy approach but is not required.
Key Features
- Feasibility depends on total entropy change, not just enthalpy or system entropy alone.
- Temperature affects the contribution of the surroundings.
- Endothermic reactions can be feasible at high temperature.
- The balance between \( \mathrm{\Delta S_{system}} \) and \( \mathrm{\Delta S_{surroundings}} \) determines spontaneity.
Example 1:
Explain why an endothermic reaction with a positive \( \mathrm{\Delta S_{system}} \) can be spontaneous at high temperature.
▶️ Answer/Explanation
In an endothermic reaction, \( \mathrm{\Delta H > 0} \), so \( \mathrm{\Delta S_{surroundings}} \) is negative.
However, if \( \mathrm{\Delta S_{system}} \) is positive, it increases the total entropy.
At higher temperatures, the magnitude of \( \mathrm{\Delta S_{surroundings}} \) becomes smaller.
Therefore, the positive \( \mathrm{\Delta S_{system}} \) can outweigh the negative \( \mathrm{\Delta S_{surroundings}} \), making \( \mathrm{\Delta S_{total} > 0} \).
Hence, the reaction becomes spontaneous at high temperature.
Example 2:
A reaction has \( \mathrm{\Delta H = +40\ kJ\ mol^{-1}} \) and \( \mathrm{\Delta S_{system} = +100\ J\ mol^{-1}K^{-1}} \). Calculate the minimum temperature at which the reaction is feasible.
▶️ Answer/Explanation
Convert \( \mathrm{\Delta H} \): \( \mathrm{40\ kJ = 40000\ J} \)
At feasibility: \( \mathrm{T = \frac{\Delta H}{\Delta S_{system}}} \)
\( \mathrm{T = \frac{40000}{100} = 400\ K} \)
Therefore, the reaction is feasible at temperatures above \( \mathrm{400\ K} \).
12.10 Feasibility when One Entropy Change is Negative
The feasibility of a reaction depends on the total entropy change, not on the sign of individual entropy changes. A reaction can still be spontaneous even if either the entropy change of the system or the surroundings is negative, provided that the overall entropy change is positive.
Key Idea
A reaction is feasible as long as \( \mathrm{\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} > 0} \), even if one term is negative.
Understanding the Balance
- The total entropy change depends on the combined effect of both system and surroundings.
- A negative contribution from one can be outweighed by a larger positive contribution from the other.
- Therefore, it is the overall balance that determines spontaneity.
Case 1: \( \mathrm{\Delta S_{system} < 0} \), \( \mathrm{\Delta S_{surroundings} > 0} \)
- The system becomes more ordered.
- Typically occurs in exothermic reactions where heat is released.
- The surroundings gain entropy due to heat transfer.
- If the increase in surroundings entropy is greater, the reaction is spontaneous.
Case 2: \( \mathrm{\Delta S_{system} > 0} \), \( \mathrm{\Delta S_{surroundings} < 0} \)
- The system becomes more disordered.
- Typically occurs in endothermic reactions where heat is absorbed.
- The surroundings lose entropy.
- If the increase in system entropy is greater, the reaction is spontaneous.
Key Insight
- Neither \( \mathrm{\Delta S_{system}} \) nor \( \mathrm{\Delta S_{surroundings}} \) alone determines feasibility.
- The sign and magnitude of both must be considered together.
Key Features
- A reaction can be spontaneous even if one entropy change is negative.
- Total entropy must be positive for feasibility.
- Balance between system and surroundings is essential.
- Temperature influences the relative contributions.
Example 1:
Explain why an exothermic reaction with a negative \( \mathrm{\Delta S_{system}} \) can still be spontaneous.
▶️ Answer/Explanation
In an exothermic reaction, heat is released to the surroundings, so \( \mathrm{\Delta S_{surroundings}} \) is positive.
Even if the system becomes more ordered and \( \mathrm{\Delta S_{system}} \) is negative, the increase in entropy of the surroundings may be larger.
If the total entropy change is positive, the reaction is spontaneous.
Example 2:
A reaction has \( \mathrm{\Delta S_{system} = +150\ J\ mol^{-1}K^{-1}} \) and \( \mathrm{\Delta S_{surroundings} = -100\ J\ mol^{-1}K^{-1}} \). Determine whether the reaction is spontaneous.
▶️ Answer/Explanation
\( \mathrm{\Delta S_{total} = 150 + (-100) = 50\ J\ mol^{-1}K^{-1}} \)
Since \( \mathrm{\Delta S_{total} > 0} \), the reaction is spontaneous.
This shows that a negative entropy change in the surroundings does not prevent feasibility if the total entropy change is positive.