The breaking of a covalent bond is associated with the exchange of energy, delta-H, between the system and its surroundings. When covalent bonds break via homolytic cleavage, they produce two uncharged radicals, each of which bears an unpaired electron. The energy required to break a bond along homolytic cleavage is called the bond dissociation energy, BDE or D. The BDE measured at one-atmosphere pressure is denoted by delta-H naught. During a chemical reaction, reactants go through a high-energy transition state before the formation of products. This energy barrier between the reactants and products is called the activation energy, denoted by the symbols Ea or delta-G double dagger. Activation energy is expressed as the difference between the free energies of the transition state and the reactants. Since the energy of reactants is lower than the transition state, the value of activation energy is always positive. If a collision between reactants does not cross the activation energy barrier, they will not react with each other to form products. The number of successful collisions depends on the number of reactant molecules with a certain threshold value of activation energy. The size of the activation energy controls the reaction rate. A large value leads to a slow reaction, whereas a small value leads to a faster reaction, as a large number of reactant molecules possess the threshold energy necessary to produce a reaction. Sometimes, a catalyst is used to lower the activation energy and speed up the reaction rate. For example, yeast is used as a catalyst to brew beer, made by the fermentation of sugars to produce ethanol. Although the process is thermodynamically favorable, it has a large activation energy. Adding yeast to the mixture lowers the activation energy, and the process takes place at a faster rate, which is industrially economical.