Moles of Reaction

James Richard Fromm

Chemical reactions are reactions between chemical species in which bonds holding atoms together are broken and formed. Atoms are conserved - neither lost nor gained but simply rearranged. A chemical reaction which is written to show this is called a balanced chemical reaction. In a balanced chemical reaction, all atoms appearing on the initial or reactant side must be balanced by an equal number of atoms of the same element appearing on the final or product side. As a consequence, the equation is also balanced in terms of mass; the total mass of reactants must equal the mass of products. Chemical reactions, if fully balanced or full reactions, are also balanced with respect to electrical charge. (When studying electrochemical reactions, it is sometimes useful to write half-reactions in which electrical charge is balanced by electrons, as we will do in other sections.)

Balanced chemical reactions are normally written with the correct molecular formula for each molecular substance. The empirical formula is used for ionic crystals. Ions themselves are written in the form of the ionic crystal if it is present as a solid, as in the example NaCl(s) or NaCl(c). Ions are written as the individual ions when they are not associated in crystals, either in the gas phase as Na+(g) or in solution as Na+(aq).

The mole is a unit of number, even though it is a very large number, and so balanced chemical reactions have a double meaning--one at the level of individual molecules and one at the level of moles of molecules. They describe the behavior of one molecule, a dozen molecules, or one mole of molecules equally well. Chemists use exactly the same form of a balanced chemical reaction to describe the reaction at the molecular level and at the molar level.

Balanced Chemical Reactions

A chemical reaction which is not balanced contains only qualitative information. While it is true that the unbalanced reaction

CO(g) + O2(g) rarrow.gif (63 bytes) CO2(g)

does specify the reactants and products, it contains far less information than does the balanced reaction,

2CO(g) + O2(g) rarrow.gif (63 bytes) 2CO2(g).

A balanced chemical reaction shows explicitly the ratios of moles between the products and reactants, while the unbalanced chemical reaction does not. As a consequence, chemists always prefer to write balanced chemical reactions.

Balanced chemical reactions are usually written with the lowest integral number of molecules possible on each side, as in the above example. However, if a chemist needed to use or calculate some property per mole of CO(g) it would be more convenient to use the form

CO(g) + 0.5O2(g) rarrow.gif (63 bytes) CO2(g).

The two forms are equivalent in terms of the ratio of moles of one substance to moles of another. The ratios of moles of substances involved in any balanced chemical reaction are identical to the ratios of moles in any multiple or submultiple of the balanced chemical reaction.

Many useful chemical properties are extensive properties. Extensive properties are directly proportional to amount of substance. The amount of energy produced by an automobile engine depends directly on the amount of fuel consumed, as do the mass and volume of air required and the mass and volume of exhaust produced. Chemists usually express these extensive properties in an intensive way, either as per mole of some specified substance or per mole of some specified reaction. The amount of carbon dioxide produced in the combustion of carbon monoxide is one mole of CO2 per mole of carbon monoxide or two moles of CO2 per mole of oxygen. It is also one mole of CO2 per mole of the reaction

CO(g) +0.5O2(g) rarrow.gif (63 bytes) CO2(g)

or two moles of CO2 per mole of reaction

2CO(g) + O2(g) rarrow.gif (63 bytes) 2CO2(g).

A chemist should not express any of the extensive properties simply as "per mole" or "per mole reaction" without specifying the substance or balanced reaction referred to. Failure to be specific in this regard is probably the most significant reason for major errors in chemical stoichiometric calculations, both for students and experienced chemists.

Example. We can compute the number of moles of silver metal producible from 1.25 moles of silver sulfide, Ag2S, and compare it with the number of grams of silver metal producible from 1.25 grams of silver sulfide. The balanced equation for the reaction could be

Ag2S(s) rarrow.gif (63 bytes) 2Ag + S.

Since two moles of silver metal are produced for each mole of silver sulfide, 1.25 moles of silver sulfide would produce 2.50 moles of silver metal. The molar mass of silver is 107.868 and that of sulfur is 32.06, so the molar mass of Ag2S is 247.796. The mass of silver which would be produced is then (1.25)(2)(107.868)/247.796 or 1.088 g.

Mass Relationships in Balanced Reactions

Moles are the fundamental units of amount of substance, but amount of substance is not usually measured directly. Chemists far more frequently measure the mass of a product or reactant and then calculate the amount of substance from the molar mass of the compound, since amount of substance is the ratio mass/molar mass:

n = m/M.

The interrelations between masses and amounts are most easily followed visually using a mole map, a simple version of which is shown in the Figure below. The mass of any reactant or product can be used to calculate the amount of that substance involved; from the amount of that substance the amount of any other reactant or product involved can be calculated, and then the mass of the other reactant or product can be calculated if desired.

Example. We can calculate the mass of carbon monoxide which can be burned to carbon dioxide by 14.32 g of oxygen. The calculation proceeds from mass of oxygen to amount of oxygen to amount of carbon monoxide to mass of carbon dioxide. The amount of oxygen is 14.32/32 = 0.4475 mol; the amount of carbon monoxide is 0.4475 x 2 = 0.895 mol; the mass of carbon monoxide is therefore 0.895 x 28 = 25.06 g.

When chemical reactions are carried out, the amount of a product may not be as great as one would expect from the overall balanced reaction, either because other reactions called side reactions take place to some extent or because the reaction in question does not proceed to completion under the conditions of a particular experiment. This is often expressed in terms of the yield of a chemical reaction, which is the ratio of the amount of substance actually obtained to the amount of substance which would have been obtained according to the balanced reaction. Since the molar mass of the substance is used to obtain both the actual amount and the theoretical amount, the ratio of mass obtained to mass expected is identical to the ratio of amount obtained to amount expected. The yield can be expressed as the per cent yield or percentage yield, which is simply the actual yield expressed as a percentage.

Example. We can calculate the percentage yield obtained experimentally when 18.92 g of carbon dioxide are produced from 15.46 g of carbon monoxide. The amount of carbon monoxide present is 15.46/28 = 0.5521 mol; the amount of carbon dioxide should be 0.5521 mol; the mass of carbon dioxide produced should be 0.5521 x 44 = 24.29 g; the actual yield is 18.92 g/24.29 g = 0.7788 and the percentage yield is 77.88%.

Relationships which give quantitative information about amount of substance do not all rely upon measurement of mass. A more elaborate mole map showing many of these is given in the Figure below. This form of the mole map will be useful in many later sections.

Copyright 1997 James R. Fromm