Spontaneous reactions occur without any net input of energy. Many factors influence whether a reaction is spontaneous, including whether the reaction is exothermic or endothermic. Exothermic reactions that result in increased disorder, or entropy, will always be spontaneous. On the other hand, endothermic reactions that result in an increase in order are never spontaneous. Nevertheless, a number of reactions that involve dissolving or mixing certain compounds are both spontaneous and endothermic.
Enthalpy and Entropy
Changes in enthalpy and entropy are two quantities that affect the spontaneity of a reaction. The change in enthalpy of a reaction can be generally understood as the change in heat of a reaction. If this change is negative, the system gives off heat energy; the reaction is exothermic. If the change in enthalpy is positive, the system absorbs heat energy; the reaction is endothermic. Another factor that affects spontaneity is a reaction's change in entropy. Entropy is a term used to describe randomness or disorder. If there is an increase in disorder, the change in entropy is positive. If there is a decrease in disorder, the change in entropy is negative.
Gibbs Free Energy
The quantity that defines whether a reaction is spontaneous is called the Gibbs free energy. Gibbs free energy is calculated by subtracting the product of a system's temperature and the change in entropy from the system's change in enthalpy. (The word "system" can be replaced by the word "reaction.") If this result is negative, the reaction is spontaneous. Therefore, in order for an endothermic reaction to be spontaneous, the product of the temperature and change in entropy must be greater than the change in enthalpy.
Dissolving Ammonium Nitrate
When the salt ammonium nitrate dissolves in water, it consumes heat from its surroundings; this is an endothermic process. The container and surroundings can feel very cold to the touch when this happens. For this reason, ammonium nitrate is used in cold packs. In this process, the change in enthalpy is positive. However, the change in entropy is also positive; the system becomes more disordered. This change in entropy is large enough that the mathematical product of the temperature and change in entropy in the Gibbs free energy equation is larger than the change in enthalpy. Therefore, the Gibbs free energy is negative, and the reaction is spontaneous.
Barium Hydroxide and Ammonium Thiocyanate
The reaction between solid barium hydroxide octahydrate and solid ammonium thiocyanate is endothermic and spontaneous. Two of the products in this reaction are ammonia gas and liquid water. These phase changes from solid to both gas and liquid give the reaction a positive change in entropy. The system's disorder increases due to these changes -- gases and liquids have more disorder than solids. Again, this increase in disorder overcomes the change in enthalpy, and the reaction is spontaneous.