What does it mean when a reaction is spontaneous?
It just means the reaction is energetically downhill, i.e. energy is released and the system overall becomes more thermodynamically stable as a result.
Spontaneity is a measure of how energetically feasible the reaction is, assuming that it would occur quickly if it can occur. That is, if the kinetics are fast enough for us to observe in our lifetime, AND the reaction is spontaneous, then we can see it happen.
A common equation that is true at constant temperature is:
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A reaction that is spontaneous can happen without the need for outside energy, and it will proceed in the direction of reducing free energy to form products from reactants.
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A spontaneous reaction is a chemical reaction that occurs naturally without the need for external intervention. It proceeds on its own without requiring energy input from the surroundings. Spontaneous reactions tend to occur in the direction that leads to a decrease in the overall free energy of the system. This means that the products of the reaction have lower free energy than the reactants. In thermodynamic terms, spontaneous reactions have a negative change in Gibbs free energy (( \Delta G < 0 )).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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