Sure, let's analyze the given reaction step by step:
The reaction provided is:
[tex]\[ A(s) + 2B(g) \rightarrow 3C(g) + D(g) + \text{heat} \][/tex]
### Change in Enthalpy ([tex]\( \Delta H \)[/tex])
Enthalpy ([tex]\( \Delta H \)[/tex]) is a measure of the heat change during the reaction. Since the reaction releases heat (as indicated by the presence of "heat" in the products), we can infer that the reaction is exothermic.
Prediction: [tex]\( \Delta H \)[/tex] is negative. This means that the reaction releases energy.
### Change in Entropy ([tex]\( \Delta S \)[/tex])
Entropy ([tex]\( \Delta S \)[/tex]) is a measure of disorder or randomness in a system.
- Solids have low entropy because their particles are tightly packed in an orderly structure.
- Gases have high entropy because their particles are free to move and are more dispersed.
In this reaction:
- Reactants: 1 mole of solid A and 2 moles of gas B.
- Products: 4 moles of gas (3 moles of gas C and 1 mole of gas D).
Since the reaction produces more moles of gas than it consumes (4 moles of gas produced vs. 2 moles of gas consumed), the disorder or randomness in the system increases.
Prediction: [tex]\( \Delta S \)[/tex] is positive. This means there is an increase in entropy.
### Change in Gibbs Free Energy ([tex]\( \Delta G \)[/tex])
Gibbs Free Energy ([tex]\( \Delta G \)[/tex]) is a criterion for spontaneity. It is given by the equation:
[tex]\[ \Delta G = \Delta H - T\Delta S \][/tex]
For a reaction to be spontaneous, [tex]\( \Delta G \)[/tex] should be negative.
Given our predictions:
- [tex]\( \Delta H \)[/tex] is negative (exothermic reaction, heat released).
- [tex]\( \Delta S \)[/tex] is positive (increase in entropy, more gas produced).
Using the Gibbs Free Energy equation:
- Since [tex]\( \Delta H \)[/tex] is negative and [tex]\( \Delta S \)[/tex] is positive, the term [tex]\(-T\Delta S\)[/tex] (where [tex]\( T \)[/tex] is the temperature in Kelvin) will subtract a positive value (due to [tex]\( \Delta S > 0 \)[/tex]), making [tex]\( \Delta G \)[/tex] even more negative.
Conclusion: Given that [tex]\( \Delta H \)[/tex] is negative and [tex]\( \Delta S \)[/tex] is positive, [tex]\( \Delta G \)[/tex] will be negative at all temperatures. Hence, the reaction is spontaneous at all temperatures.
### Summary
- [tex]\( \Delta H \)[/tex] (Change in Enthalpy): Negative (exothermic reaction, heat released).
- [tex]\( \Delta S \)[/tex] (Change in Entropy): Positive (increase in entropy, more gas produced).
- [tex]\( \Delta G \)[/tex] (Change in Gibbs Free Energy): Negative at all temperatures.
Conclusion about Spontaneity: The reaction is spontaneous at all temperatures because the negative [tex]\( \Delta H \)[/tex] (enthalpy) and positive [tex]\( \Delta S \)[/tex] (entropy) ensure that [tex]\( \Delta G \)[/tex] is always negative.
