Rates of Spontaneous Processes
The phrase as fast as possible points up a major difficulty in dealing with spontaneousCapable of proceeding without an outside source of energy; refers to a reaction in which the products are thermodynamically favored (product-favored reaction). processes. Some of them occur quite rapidly, but others are so slow as to be imperceptible. A rapid spontaneous process occurs when 2 mol H2O is mixed with 2 mol “heavy water,” D2O, made from the isotopeOne of two or more samples of an element whose atoms differ in the number of neutrons found in the nucleus. deuteriumThe isotope of hydrogen having one neutron in its nucleus., 21H, or D. The two species start to transfer protons and deuterons (D+ ions) as soon as they are stirred together, and we rapidly obtain a mixtureA combination of two or more substances in which the substances retain their chemical identity. consisting of 2 mol H—O—D and 1 mol each of H—O—H and D—O—D. Assuming that deuterium atomsThe 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. behave the same chemically as ordinary hydrogen atoms, this is what the laws of probability would predict. There are four equally likely possibilities for a randomly selected water moleculeA set of atoms joined by covalent bonds and having no net charge.:
Two of the four possibilities have the molecular formulaThe chemical formula of a substance written using the subscripts that reflect the number of each kind of atom present in a molecule of the substance. For example, the simplest formula for ethane is CH3, but the molecular formula is C2H6 because there are 2 C atoms and 6 H atoms in a molecule of ethane. HDO, and so the probability of finding an HDO molecule in our mixture is 1/2. Half the molecules (2 mol) will be HDO. Similarly 1/4 of the 4 mol water will be H2O and 1/4 will be D2O.
The shift from the improbable situation of 2 mol H2O + 2 mol D2O to the more probable 2 mol HDO + 1 mol H2O + 1 mol D2O occurs rapidly because of the ease with which protons and deuterons can transfer from one water molecule to another. When such a shuffling process is slow, however, the situation is quite different. For example, we would expect that mixing 2 mol H2 with 2 mol D2 would produce 2 mol HD and a mole each of H2 and D2. At room temperatureA physical property that indicates whether one object can transfer thermal energy to another object., though, nothing happens, even over a periodThose elements from a single row of the periodic table. of days, because there is no easy way for H or D atoms to swap partners. Reshuffling requires breaking an H—H or a D—D bond, and this takes some 400 kJ mol–1. The molecules are stuck in a situation of low probability because there is no pathway by which they can attain higher probability. If such a pathway is provided, by raising the temperature or adding a catalystA substance that increases the rate of a chemical reaction but that undergoes no net change during the reaction., the molecules start exchanging H and D and move toward the most probable situation.
The moral of this story is that saying a reaction is spontaneous is not the same as saying it will occur if the reactants are mixed. Rather, it means the reaction can occur but may be so slow that nothing seems to happen. In the case of a slow spontaneous reaction it is worthwhile to look for a catalyst, but if we know the reaction is nonspontaneous, there is no point in even mixing the reactants, let alone searching for a catalyst. A nonspontaneous reaction cannot occur of itself without outside intervention.