Equation, Chemical

Equation, Chemical

Conventions and symbols

A few examples

Applications

Chemical equations reveal the chemical species involved in a particular reaction, the charges and weight relationships among them, and how much heat of reaction results. Equations tell us the beginning compounds, called reactants, and the ending compounds, called products, and which direction the reaction is going. Equations are widely used in chemical engineering, they serve as the basis for chemical synthesis, reactor design, process control, and cost estimate. This allows chemical process engineers to prepare ahead of time for on-line production.

It is fairly difficult to take a few chemical compounds and derive chemical equations from them, because many variables need to be determined before the correct equations can be specified. However, to look at a chemical equation and know what it really means is not as difficult. To achieve this, there are certain conventions and symbols which we always have to keep in mind. Now let’s start with a general chemical equation, aA + bB Δ→ cC + dD↑, to explain those conventions and symbols, and few examples will then be given and discussed.

Conventions and symbols

In general, the reactants (A and B) are always placed on the left-hand side of the equation, and the products (C and D) are shown on the right. The symbol “→” indicates the direction in which the reaction proceeds. If the reaction is reversible, the symbol should be used to show that the reaction can proceed in both the forward and reverse directions. Δ means that heat is added during the reaction, and not equal implies that D escapes while produced. Sometimes, Δ is replaced by “light” (to initiate reactions) or “flame” (for combustion reactions.) Instead of showing the symbol Δ, at the same place we may just indicate the operating temperature or what enzymes and catalysts are need to speed the reaction.

Each chemical species involved in an equation is represented by chemical formula associated with stoichiometric coefficients. For instance, a, b, c, and d are the stoichiometric coefficients for A, B, C, and D, respectively. Stoichiometric coefficients can be integers, vulgar fractions, (e.g. 3/4) or decimal fractions (e.g. 0.5). They define the moleratio (not mass ratio) that permits us to calculate the moles of one substance as related to the moles of another substance in the chemical equation. In the present case, we know that a moles of A react with b moles of B to form c moles of C and d moles of D.

The chemical equation needs to be balanced, that is, the same number of atoms of each “element” (not compounds) must be shown on the right-hand side as on the left-hand side. If the equation is based on an oxidation-reduction reaction which involves electron transfer, the charges should also be balanced. In other words, the oxidizing agent gains the same number of electrons as are lost by the reducing agent. For this reason, we must know the oxidation numbers for elements and ions in chemical compounds. An element can also have more than one oxidation number, for instance, Fe²⁺ and Fe³⁺ for iron.

Under certain conditions, the information on phase, temperature, and pressure should be included in the equation. For instance, H₂O can exist as solid, liquid, and vapor (gas) that can be represented by H₂O(s), H₂O(l), and H₂O(g), respectively. If we have an infinitely dilute solution, say HCl, it can be denoted as HCl(aq). For solubility problems, A underlined (A ) means that A is a solid or precipitated phase. In many cases, the heat of reaction, ΔH, is also given; a positive number implies an endothermic reaction (where heat is absorbed), and a negative number implies an exothermic reaction (where heat is given off). Unless otherwise specified, the heat of reaction is normally obtained for all the chemical species involved in the reaction at the standard state of 77°F (25°C) and 1 atmosphere total pressure, the so-called “standard heat of reaction” and denoted by ΔH°.

A few examples

NaOH + HCl→ NaCl + H₂O means that (1) 1 mole of NaOH reacts with 1 mole of HCl to form 1 mole of NaCl and 1 mole of H₂ O, (2) 40 g (that is, molecular weight) of NaOH react with 36.5 g of HCl to form 58.5 g of NaCl and 18 g of H₂O, or (3) 6.02× 10²³ molecules (1 mole) of NaOH react with 6.02× 10²³ molecules of HCl to form 6.02× 10²³ of NaCl and 6.02× 10²³ of H₂ O. Notice that on both sides of the equation, we have one chlorine atom, two hydrogen atoms, one oxygen atom, and one sodium atom. This equation, then, is properly balanced.

For the reaction between permanganate (MnO₄)ion and ferrous (Fe²⁺) ion in an acid solution, an expression is given like this, KMnO₄ + FeSO₄ + H₂ SO₄ → Fe₂ (SO₄ )₃ + K₂SO₄ + MnSO₄ + H₂O. Obviously this equation is not balanced. To remedy this, first, the equation can be rewritten as MnO₄ + Fe²⁺ + H⁺→ Fe³⁺ + Mn²⁺ + H₂O if one recognizes that potassium (K⁺) and sulfate (SO₄ ) ions do not enter into the reaction. Secondly, the oxidation number of manganese (Mn) is changed from +7 in MnO₄^- to +2 in Mn²⁺, that is, Mn gains 5 electrons during the reaction. Similarly, one electron is lost from Fe²⁺ to Fe³⁺. To make the number of electrons lost from one substance equal to the number of electrons gained by another in oxidation-reduction reactions, we need to use the least common multiple of 1 and 5, which is 5. So we have MnO₄ + 5Fe²⁺ + H⁺→ 5Fe³⁺ + Mn²⁺ + H₂O. Thirdly, the equation has to be balanced for the number of atoms of individual elements, too. Thus a final expression is obtained as MnO₄^- +5Fe²⁺+8H⁺→ 5Fe³⁺ +Mn²⁺+H₂O. Lastly we can add the potassium and sulfate back into the complete equation, 2KMnO₄+10FeSO₄ +8H₂ SO₄ → 5Fe₂ (SO₄ )₃ +K₂ SO₄ +2MnSO₄ +8H₂O. At this stage, we do not have to worry about charge balances, but atom conservation needs to be checked again and corrected.

Derivation of equations for oxidation-reduction reactions sometimes can be simplified by using a series of half reactions, whose expressions can be found in special tables of many textbooks. For example, with half-reactions of Zn→ Zn²⁺ + 2e and Fe²⁺ +2e→ Fe, by summing them up we can obtain the equation, Zn + Fe²⁺→ Zn²⁺ + Fe. Since 2e is found both on the right and left sides of the equations and does not react with anything else, it can be dropped from the combined equation.

For those reactions in which we are interested for their heats of reaction, knowing how to derive the final equations from relevant formation reactions is very useful. For example, when the formation reactions at temperature of 77°F (25°C; 298K) are given as (1) C(s) + O₂ (g)→ CO₂(g), ΔH_f ° = -94, 501 cal, (2) C(s) + 0.5 O₂ (g)→ CO(g), ΔH_f ° = -26, 416 cal, and (3) H₂(g) + 0.5 O₂ (g)→ H₂O, ΔH_f ° = -57, 798 cal, we can obtain the equation, CO₂(g) + H₂ (g)→ CO(g) + H₂O(g), ΔH_f ° = 9, 837 cal, by reversing (1), that is, CO₂ (g)→ C(s) + O₂ (g), ΔH_f ° = 94, 501 cal, and adding it to (2) and (3). Therefore, the result shows an endothermic reaction with the heat of reaction of 9, 837 cal at 77°F(25°C; 298K).

Applications

Because the stoichiometric coefficients are unique for a given reaction, chemical equations can provide us with more information than we might expect. They tell

KEY TERMS

Heat of formation, ΔH_f°— The heat involved for the formation of 1 mole of a compound that is formed from the elements which make up the compound.

Standard potential— The electrochemical potential (volts) with respect to the standard state which is a measure for the driving force of a reaction.

Stoichiometry— Deals with combining weights of elements and compounds.

us whether or not the conversion of specific products from given reactants is feasible. They also tell us that explosive or inflammable products could be formed if the reaction was performed under certain conditions.

Pang-Jen Kung