Conservation of Mass: Its Proper Place Richard S. Treptow Chicago State University. Chicago. IL 60628 Accurding tu rhr theory of rdafiviry, rhere is no essential distincrim between mas4 and energy. Enprgy has mass and mars represents energy. Instead of two conservation laws we have only one, that of mass-energy. A. Einstein and L. Infeld' In an earlier paper I argue that relativity in no way compromises the law of conservation of m a s ~ It . ~does require, however, that we he careful in how we interpret the law. In this paper, I show how mass conservation inevitably follows from energy conservation. A scheme is proposed for introducing these two important laws into the chemistry curriculum. Relativity tells us that mass and energy are equivalent. They are alternate measures of the same thing, called massenergy. I t follows that anything we know about energy we also know about mass. If a body loses energy to its surroundings it also loses mass. Let us consider a chemical reaction in a bomb calorimeter (see figure). Suppose the reaction is the combustion of henzoic acid,
whose molar heat ofcombusrion at constant volume is 3.23 X 10". The reaction occurs with transfer of heat from the bomh (system) to the calorimeter (surroundings). Since energy is conserved we can write AE,
lo6J
= -USE,,, = -3.23 X
According to E = mc2, dividing through by c2converts energy units into mass units. Hence, Am,,,
= -Am,,,
= -3.59 X
10-'g
Mass is transferred from the homh to the water as surely as energy is. Although neither the homh nor the water has constant mass, the entire assembly does. Mass conservation is mandated by energy conservation. The illustration shows that relativity reduces two formerly separate conservation laws to one:
that the mass of a system is constant. Rather, it affirms that any change in a system's mass must be compensated by a change in the mass of its surroundings. Corollary A is of little use to chemists because mass changes that occur in chemical processes are too small to he detectahle. Corollary A has no meaningful test or application in chemistry. Corollary B is much more useful. I t states that any energy change in a system is accompanied by a change of opposite sign in its surroundings. Chemists commonly determine the energy of a reaction by measuring the energy change of its surroundings. Corollary B is better known as the first law of thermodynamics. Chemists do make much use of the fact that chemical processes occur with no detectable change in the mass of the system. For such purposes I propose 'The Principlr of MarsCunvtancv. Within thelimitpof deterutbilits, the pnhcrsof n chemirsl reaction have thesame massap the
reactants. This statement could well be called Lauoisier's ~ r i n c i o l e since it summarizes the historic observations that launched chemistrv on the idea of mass conservation. It affirms that for practkal purposes the mass of an atom does not change durina chemical reactions. Despite its usefulness, we should cmsider mass constancy to he a principle, not a law. It has certain limt~ationswhich preclude it from beinp classified as a law of nature. In parti&lar, i t applies only to chemical reactions, and it speaks merely of what is detectable and not what is absolutely true. The full scheme outlined above may be too elaborate for the general chemistry student. Beginners have need only for the law of energy conservation and the principle of mass constancy. If these two concepts are properly introduced in general chemistry, they will serve as the groundwork for full disclosure inmore advanced courses. In any case, the equivalence of mass and energy is too profound to be missingfrom a chemist's education.
The Law of Mass-Energy Conservation. Mass-energy cannot be created or destroyed. Mass-energy is the sole conserved property, whether we measure i t joules or grams.3 Despite the inseparability of mass and energy, we usually treat these two entities independently. For such purposes, two corollaries are useful: Corollary A. The Law of Mass Conservation. Mass cannot be created or destroyed. Corollary B. The Law of Energy Conservation. Energy cannot he created or destroyed. Corollary A must be carefully interpreted. I t does not say
'
Einstein, A,; Infeld. L. "The Evolution of Physics": Cambridge University: Cambridge, 1947;pp 202-209. * Treptow, R. S. J. Chem. Educ. 1986, 63,103. Some authors mistakenly phrase the law of mass-energy conservation as "The sum of mass and energy in the universe is constant." Such phrasing is incorrect. it suggests the possibility of mass being converted into energy, which never happens. Recall that mass and energy measure the same thing; taking their sum is an exercise in double counting. 1052
Journal of Chemical Education
closed system to its calorimeter, but total massenergy is conserved. Massenergy passes from a
surroundings in a bomb
