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Chapter: Modern Analytical Chemistry: Basic Tools of Analytical Chemistry

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Stoichiometric Calculations

A balanced chemical reaction indicates the quantitative relationships between the moles of reactants and products.

Stoichiometric Calculations

A balanced chemical reaction indicates the quantitative relationships between the moles of reactants and products. These stoichiometric relationships provide the basis for many analytical calculations. Consider, for example, the problem of deter- mining the amount of oxalic acid, H2C2O4, in rhubarb. One method for this analy- sis uses the following reaction in which we oxidize oxalic acid to CO2.

2Fe3+(aq) + H2C2O4(aq) + 2H2O(l) → 2Fe2+(aq) + 2CO2(g) + 2H3O+(aq      ….2.2

The balanced chemical reaction provides the stoichiometric relationship between the moles of Fe3+ used and the moles of oxalic acid in the sample being analyzed— specifically, one mole of oxalic acid reacts with two moles of Fe3+. As shown in Example 2.6, the balanced chemical reaction can be used to determine the amount of oxalic acid in a sample, provided that information about the number of moles of Fe3+ is known.


In the analysis described in Example 2.6 oxalic acid already was present in the desired form. In many analytical methods the compound to be determined must be converted to another form prior to analysis. For example, one method for the quan- titative analysis of tetraethylthiuram disulfide (C10H20N2S4), the active ingredient in the drug Antabuse (disulfiram), requires oxidizing the S to SO2, bubbling the SO2 through H2O2 to produce H2SO4, followed by an acid–base titration of the H2SO4 with NaOH. Although we can write and balance chemical reactions for each of these steps, it often is easier to apply the principle of the conservation of reaction units.

A reaction unit is that part of a chemical species involved in a reaction. Con- sider, for example, the general unbalanced chemical reaction

A + B → Products

Conservation of reaction units requires that the number of reaction units associated with the reactant A equal the number of reaction units associated with the reactant

B. Translating the previous statement into mathematical form gives

 

Number of reaction units per A x moles A= number of reaction units per B x moles B   ……………….. 2.3

 

If we know the moles of A and the number of reaction units associated with A and B, then we can calculate the moles of B. Note that a conservation of reaction units, as defined by equation 2.3, can only be applied between two species. There are five important principles involving a conservation of reaction units: mass, charge, pro- tons, electron pairs, and electrons.

Conservation of Mass

The easiest principle to appreciate is conservation of mass. Except for nuclear reac- tions, an element’s total mass at the end of a reaction must be the same as that pres- ent at the beginning of the reaction; thus, an element serves as the most fundamen- tal reaction unit. Consider, for example, the combustion of butane to produce CO2 and H2O, for which the unbalanced reaction is

C4H10(g) + O2(g) → CO2(g) + H2O(g)

All the carbon in CO2 comes from the butane, thus we can select carbon as a reac- tion unit. Since there are four carbon atoms in butane, and one carbon atom in CO2, we write

4 x moles C4H10 = 1 x moles CO2

Hydrogen also can be selected as a reaction unit since all the hydrogen in butane ends up in the H2O produced during combustion. Thus, we can write

10 x moles C4H10 = 2 x moles H2O

Hydrogen also can be selected as a reaction unit since all the hydrogen in butane ends up in the H2O produced during combustion. Thus, we can write

10 x moles C4H10 = 2 x moles H2O

Although the mass of oxygen is conserved during the reaction, we cannot apply equation 2.3 because the O2 used during combustion does not end up in a single product.

Conservation of mass also can, with care, be applied to groups of atoms. For example, the ammonium ion, NH4+, can be precipitated as Fe(NH4) (SO4) . 6H2O.

Selecting NH4+ as the reaction unit gives

2 x moles Fe(NH4)2(SO4)2 · 6H2O = 1 x moles NH4+

Conservation of Charge

The stoichiometry between two reactants in a precipitation reaction is governed by a conservation of charge, requiring that the total cation charge and the total anion charge in the precipitate be equal. The reaction units in a precipitation reaction, therefore, are the absolute values of the charges on the cation and anion that make up the precipitate. Applying equation 2.3 to a precipitate of Ca3(PO4)2 formed from the reaction of Ca2+ and PO43–, we write

2 x moles Ca2+ = 3 x moles PO43–

Conservation of Protons

In an acid–base reaction, the reaction unit is the proton. For an acid, the num- ber of reaction units is given by the number of protons that can be donated to the base; and for a base, the number of reaction units is the number of protons that the base can accept from the acid. In the reaction between H3PO4 and NaOH, for example, the weak acid H3PO4 can donate all three of its pro- tons to NaOH, whereas the strong base NaOH can accept one proton. Thus, we write

3 x moles H3PO4 = 1 x moles NaOH

Care must be exercised in determining the number of reaction units associ- ated with the acid and base. The number of reaction units for an acid, for in- stance, depends not on how many acidic protons are present, but on how many of the protons are capable of reacting with the chosen base. In the reaction be- tween H3PO4 and NH3

H3PO4(aq) + 2NH3(aq) < = = = = > HPO4–(aq) + 2NH4+(aq)

a conservation of protons requires that

2 x moles H3PO4 = moles of NH3

Conservation of Electron Pairs

In a complexation reaction, the reaction unit is an electron pair. For the metal, the number of reaction units is the number of coordination sites available for binding ligands. For the ligand, the number of reaction units is equivalent to the number of electron pairs that can be donated to the metal. One of the most important analyti- cal complexation reactions is that between the ligand ethylenediaminetetracetic acid (EDTA), which can donate 6 electron pairs and 6 coordinate metal ions, such as Cu2+; thus

6 x mole Cu2+ = 6 x moles EDTA

Conservation of Electrons

In a redox reaction, the reaction unit is an electron transferred from a reducing agent to an oxidizing agent. The number of reaction units for a reducing agent is equal to the number of electrons released during its oxidation. For an oxidizing agent, the number of reaction units is given by the number of electrons needed to cause its reduction. In the reaction between Fe3+ and oxalic acid (reaction 2.2), for example, Fe3+ undergoes a 1-electron reduction. Each carbon atom in oxalic acid is initially present in a +3 oxidation state, whereas the carbon atom in CO2 is in a +4 oxidation state. Thus, we can write

1 x moles Fe3+ = 2 x moles of H2C2O4

Note that the moles of oxalic acid are multiplied by 2 since there are two carbon atoms, each of which undergoes a 1-electron oxidation.

Using Conservation Principles in Stoichiometry Problems

As shown in the following examples, the application of conservation principles sim- plifies stoichiometric calculations.


 

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