A reaction is said to be unimolecular if, on the microscopic level, rearrangement of the structure of a single moleculeA set of atoms joined by covalent bonds and having no net charge. produces the appropriate productA substance produced by a chemical reaction. molecules. An example of a unimolecular processAn elementary step in a reaction mechanism in which a single molecule reacts to form products; formally no species collide in such a step, but the energy needed to overcome an activation barrier is provided to the single molecule through prior collisions. is conversion of cisDescribes the relationship between two atoms or groups of atoms, each attached to one of two doubly bonded carbon atoms and located on the same side of the double bond. Also refers to groups located adjacent to each other in an octahedral or square planar coordination complex.-2-butene to transDescribes the relationship between two atoms or groups of atoms, each attached to one of two doubly bonded carbon atoms and located on the opposite side of the double bond. Also refers to groups located opposite to each other in an octahedral or square planar coordination complex.-2-butene (in the absence of any catalystA substance that increases the rate of a chemical reaction but that undergoes no net change during the reaction.):
All that is required for this reaction to occur is a twist or rotation around the double bondAttraction between two atoms (nuclei and core electrons) that results from sharing two pairs of electrons between the atoms; a bond with bond order = 2., interchanging the methyl groupThose elements that comprise a single column of the periodic table. Also called family. with the hydrogen atomThe smallest particle of an element that can be involved in chemical combination with another element; an atom consists of protons and neutrons in a tiny, very dense nucleus, surrounded by electrons, which occupy most of its volume. on the right-hand side. Only one cis-2-butene molecule need be involved as a reactantA substance consumed by a chemical reaction. in this process.
Rotating part of a molecule about a double bond is not easy, however, -because it involves a distortion of the electronA negatively charged, sub-atomic particle with charge of 1.602 x 10-19 coulombs and mass of9.109 x 1023 kilograms; electrons have both wave and particle properties; electrons occupy most of the volume of an atom but represent only a tiny fraction of an atom's mass. clouds forming the double bond. This barrier to rotation was described in orbital descriptions of multiple bonds. A considerable increase in energyA system's capacity to do work. is required to twist one end of cis-2-butene around the other. This is shown in Fig. 1, where the energy has been plotted as a function of the angle of rotation. The maximum energy is reached when one end of the molecule has been rotated by 90° with respect to the other.
This conformationIn an ion or molecule, one of many spatial arrangements of atoms that differ by rotation about single bonds, but that do not differ in which atoms are attached to each other. is 262 kJ mol–1 higher than the energy of the original planar molecule. From this maximum it is downhill energetically on either side; so if the molecule has twisted this far, it should keep on twisting, eventually becoming trans-2-butene when the angle of rotation reaches 180°. Trans-2-butene is slightly lower in energy than cis-2-butene, as indicated the enthalpyA thermodynamic state function, symbol H, that equals internal energy plus pressure x volume; the change in enthalpy corresponds to the energy transferred as a result of a temperature difference (heat transfer) when a reaction occurs at constant pressure. change of – 4 kJ mol–1 for the overall reaction.
Figure 1 shows that the barrier to rotation around a double bond is an energy barrier. At least 262 kJ mol–1 must be supplied to transform cis-2-butene into trans-2-butene by a rotation such as we have described. The minimum quantity of energy required to surmount an energy barrier during a chemical reactionA process in which one or more substances, the reactant or reactants, change into one or more different substances, the products; chemical change involves rearrangement, combination, or separation of atoms. Also called chemical change. is called the activation energyThe energy barrier over which a reaction must progress in order for reactants to form products; the minimum energy that reactants must have if they are to be converted to products., and the molecular species at the top of the barrier is called the activated complexIn the mechanism of a reaction, a species that lies at an energy peak and that can change either into products or into reactants; also called a transition state. or the transition state. Quantities associated with this activated complex are usually denoted by a double dagger (‡). For example, the activation energy is given the symbol E‡.
In the sample of gaseous cis-2-butene at room temperatureA physical property that indicates whether one object can transfer thermal energy to another object., only a tiny fraction of molecules have enough energy to surmount the activation-energy barrier. (Recall from figure 2 in the section on molecular speed distribution in gases that only a very small fraction of all gas molecules are traveling at very high speeds and hence have large kinetic energies. The same applies to the energy a molecule has because it is vibrating or rotating.) Not only do few molecules have enough energy to overcome the activation-energy barrier, but fewer still have that energy concentratedIncreased the concentration of a mixture or solution (verb). Having a large concentration (adjective). so that it can cause the atomic movements needed for the reaction to occur. In the case of cis-2-butene for example, very few of the high-energy molecules have their energy distributed so that most of it is causing a twist around the double bond. Thus over a given periodThose elements from a single row of the periodic table. of time only a very small fraction of the cis-2-butene molecules will be converted to trans-2-butene.
Now suppose that we double the concentrationA measure of the ratio of the quantity of a substance to the quantity of solvent, solution, or ore. Also, the process of making something more concentrated. of a sample of cis-2-butene. This means that there will be twice as many molecules in each cubic decimeter. At a given temperature the fraction of the molecules which can react during a given time interval will be the same, but with twice as many molecules there will be twice as many conversions to trans-2-butene. Therefore in a period of 1 s the change in the amount of substanceA material that is either an element or that has a fixed ratio of elements in its chemical formula. per unitA particular measure of a physical quantity that is used to express the magnitude of the physical quantity; for example, the meter is the unit of the physical quantity, length. volume will be twice as great, and this means that the reaction rate is twice as great.
What we have just said applies to any unimolecular process. The reaction rate must always be directly proportional to the concentration of the reacting species. That is, for a general unimolecular process, A → products, the rate equationAn equation that describes the rate of a reaction as a function of the rate constant and the concentrations of reactants (and any other substances that affect the rate, such as products or catalysts); also called rate law. must be first order in A:
- Rate = kcA