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# Equations, Chemical

Chemical reactions convert reactants to products, whose properties differ from those of the reactants. Chemical equations are a compact and convenient way to represent chemical reactions. They have the general form

Reactant(s) Product(s)

The arrow in the equation means "changes to" or "forms." The reaction of gaseous nitrogen with hydrogen to produce ammonia, NH3, is represented by the chemical equation

Although there are thousands of chemical reactions, a significant number of them, especially those that are not organic reactions, can be classified according to four general patterns: combination, decomposition, displacement, and exchange.

1. Combination. A combination reaction is one in which two or more substances (the reactants) are combined directly to form a single product (the product). An example is the reaction in which sodium (Na) combines with chlorine (Cl2) to form sodium chloride, or table salt (NaCl).

2 Na + Cl2 2 NaCl

The physical states of reactants and products are included where necessary. The symbols used are: (s ) for solid, (l ) for liquid, (g ) for gas, and (aq ) for aqueous (water) solutions. In the case of sodium chloride formation, the equation is modified accordingly.

2 Na (s ) + Cl2 (g ) 2 NaCl (s )

2. Decomposition. A decomposition reaction can be considered to be the reverse of a combination reaction. In a decomposition reaction, one substance (the reactant) decomposes to form two or more products. For example, calcium carbonate (limestone) decomposes at high temperatures to calcium oxide (lime) and carbon dioxide. This reaction is used industrially to produce large quantities of lime.

3. Displacement. A displacement reaction (also called a single replacement reaction) occurs when an element reacts with a compound to form a new compound and release a different element. An example is the reaction that releases silicon (Si) from silicon dioxide (sand), SiO2, via its reaction with carbon. Carbon monoxide, CO, is the reaction's other product. When further purified, the silicon can be used in computer chips.

SiO2 (s ) + 2 C (s ) Si (s ) + 2 CO (g )

4. Exchange. During an exchange reaction, "partners" in compounds exchange their partners. One type of exchange reaction is called a neutralization reaction, the reaction between an acid and a base. The reaction of sodium hydroxide (lye), NaOH, with hydrochloric acid, HCl, to produce NaCl and water is such a reaction. In this case, Na+ switches partners from OH to Cl, and H+ from Cl to OH.

NaOH (aq ) + HCl (aq ) NaCl (aq ) + H2O (l )

Organic chemical reactions, those in which carbon plays a predominant role, are very important in biochemical systems and industrial processes. These reactions can also be represented by balanced chemical equations, a few examples of which are given.

The fermentation of glucose to produce ethyl alcohol (ethanol)

The synthesis of acetylsalicylic acid (aspirin) from the reaction of salicylic acid with acetic anhydride

The formation of a triglyceride (a fat), such as the biochemical synthesis of tristearin via the reaction of stearic acid with glycerol:

Matter is conserved in chemical reactions: The total mass of the products equals the total mass of the reactants. Chemical equations reflect this conservation. It is why chemical equations must be balanced. Atoms have mass, and the numbers of each kind of atom on each side of the equation must be the same. Coefficients, the numbers to the left of the formulas, are used to balance equations. Many equations can be balanced directly by simply adjusting the coefficients, as illustrated in the equations given above. Other equations are more difficult to balance, such as that for the decomposition of nitroglycerine (an explosive)

4 C3H5(NO3)3 (l ) 12 CO2 (g ) + 10 H2O (l ) + 6 N2 (g ) + O2 (g )

and this complicated reaction involving several reactants and products

4 CuSCN + 7 KIO3 + 14 HCl 4 CuSO4 + 7 KCl + 4 HCN + 7 ICl + 5 H2O

Balanced chemical equations provide a significant amount of information. Consider the equation for photosynthesis, the natural process by which green plants form glucose, C6H12O6, and oxygen from the reaction of carbon dioxide with water.

This balanced equation and its coefficients can be interpreted as indicating that six carbon dioxide molecules and six water molecules react to form one molecule of glucose and six oxygen molecules, each containing two oxygen atoms. A coefficient multiplies the term following it. The "6 CO2" denotes six CO2 molecules containing a total of six carbon atoms and twelve oxygen atoms.

Applying these concepts to the remainder of the balanced equation yields information that confirms that the equation is balancedthe atom counts for both sides of the equation are the same.

 Reactants Products Carbon atoms = 6 Carbon atoms = 6 Hydrogen atoms = 12 Hydrogen atoms = 12 Oxygen atoms = 12 + 6 = 18 Oxygen atoms = 6 + 12 = 18

Coefficients also apply to a larger scale, in which the counting unit is the mole (there are 6.02 × 1023 molecules per mole of a compound), rather than individual molecules. Thus, this balanced equation also represents the reaction of six moles of glucose with six moles of water to produce one mole of glucose and six moles of oxygen.

Oxidation-reduction (redox) reactions are an important, general kind of reaction, one involving the transfer of electrons. Oxidation is the loss of an electron or electrons from an element, ion, or compound. Reduction is the gain of an electron or electrons from an element, ion, or compound. The two processes occur simultaneously; electrons released during oxidation are gained in a reduction process. In every redox reaction, a reactant is oxidized (loses electrons) and a reactant is reduced (gains electrons). During a redox reaction there is a change in oxidation numbersevidence of a redox reaction. An oxidation number compares the charge of an uncombined atom, one not in a compound, with its actual or relative charge when it is part of a compound. Oxidation numbers are zero, positive, or negative.

These guidelines are used to determine oxidation numbers.

• Atoms of pure elements, that is, atoms not combined with any other element, have an oxidation number of zero. For example, sodium in metallic sodium, Na; oxygen in molecular oxygen, O2; and chlorine in molecular chlorine, Cl2, each have an oxidation number of 0.
• Monatomic ions have an oxidation number equal to the charge of the ion. Thus, a sodium ion, Na+, has an oxidation number of +1; that of chlorine in a chloride ion, Cl, is 1.
• Generally, hydrogen atoms in compounds have an oxidation number of +1; oxygen atoms in compounds are typically 2.
• The sum of oxidation numbers in a neutral compound is zero. Water, H2O, is an example. Hydrogen: 2 H × (+1/H) = +2; oxygen: 1 O × (2/O) = 2; (+2) + (2) = 0
• The sum of oxidation numbers of the atoms in a polyatomic ion equals the charge on the ion. For example, the sulfate ion, SO42, a polyatomic ion, has a net charge of 2. Each oxygen in a sulfate ion has an oxidation number of 2, and four oxygens add up to 8. For the sulfate ion to have a net 2 charge, sulfur must have a +6 oxidation number: 2 = 4(2) +6.

Oxidation numbers and their changes can be used to identify the reaction of sodium with chlorine to form NaCl as a redox reaction.

2 Na + Cl2 2 NaCl

 Reactant Products Oxidation number Oxidation number Na = 0 Na+ = +1 Cl = 0 Cl− = −1

During this reaction, reactant sodium atoms (oxidation number 0) are converted to sodium ions (oxidation number +1); reactant chlorine atoms (oxidation number 0) are transformed to chloride ions (oxidation number 1). Because there is a change in the oxidation numbers of the reactants during the reaction, this is a redox reaction. The definitions of oxidation and reduction can be broadened a bit using oxidation numbers: Oxidation is an increase in oxidation number; reduction is a decrease in oxidation number. The gain in oxidation number occurs because electrons are lost during oxidation; the gain of electrons during reduction causes a decrease in the oxidation number. This can be shown by using so-called half-reactions for each process.

Oxidation half-reaction: Na Na+ + e

Reduction half-reaction: Cl2 + 2 e 2 Cl

Notice in the balanced equation that two moles of Na were used to react with the two moles of chlorine atoms in one mole of Cl2. Each mole of Na lost one mole of electrons; each mole of chlorine atoms gained a mole of electrons. Two moles of electrons were transferred to form two moles of NaCl. The overall reaction is the sum of the two half-reactions; the moles of electrons cancel, and the sodium ions and chloride ions combine to form sodium chloride. Note that the sum of the oxidation numbers in sodium chloride is zero: (+1) + (1) = 0.

Oxidation half-reaction: 2 Na 2 Na+ + 2 e

Reduction half-reaction: Cl2 + 2 e 2 Cl

Overall reaction: 2 Na + Cl2 2 NaCl

Oxidation-reduction reactions, even complex ones, can be balanced using either the half-reaction method or the oxidation number method. The half-reaction method will be discussed first, using the reaction of iron with chlorine to produce iron chloride.

Fe + Cl2 FeCl3 (unbalanced equation)

## Half-Reaction Method

Step 1. Divide the reaction into two half-reactions; one corresponding to oxidation, the other, reduction.

Oxidation: Fe Fe3+

Reduction: Cl2 + Cl

Step 2. Balance each half-reaction for mass and then charge. The iron half-reaction is balanced with respect to mass because there is one iron on each side. However, the charge is not balanced; the left side has a charge of zero, the right side has a charge of +3. Charge is balanced by adding three electrons to the right side.

Fe Fe3+ + 3 e

The chlorine half-reaction is unbalanced in terms of mass and charge. Mass balance is achieved by using a coefficient of 2 on the right side.

Cl2 2 Cl

Charge is then balanced by adding two electrons to the left side.

Cl2 + 2 e 2 Cl

The two half-reactions indicate that three electrons are lost per Fe atom during oxidation, and that two electrons are gained as each Cl2 molecule is reduced.

Step 3. Combine the two half-reactions in such a way as to balance the electrons lost and gained. The oxidation half-reaction lost three electrons; the reduction half-reaction gained two electrons. Therefore, to balance electrons lost and gained, multiply the oxidation half-reaction by 2 and the reduction half-reaction by 3. Add the resulting half-reactions to get the final balanced equation for the formation of FeCl3. Note that, in doing so, the electrons cancel (as they should if the final equation is balanced).

2 [Fe Fe3+ + 3 e] 2 Fe 2 Fe3+ + 6 e

3 [Cl2 + 2 e 2 Cl] 3 Cl2 + 6 e 6Cl

The Fe3+ and Cl ions combine to form FeCl3 and the overall balanced equation is

2 Fe + 3 Cl2 2 FeCl3

The half-reaction method can be applied to more complex redox reactions, such as the reaction of permanganate ion, MnO4, with Fe2+ in acidic solution.

MnO4 (aq ) + Fe2+ (aq ) Mn2+ (aq ) Fe3+ (aq ) (unbalanced equation)

Step 1. Oxidation: Fe2+ (aq ) Fe3+ (aq )
Reduction: MnO4 (aq ) Mn2+ (aq )

Step 2. Mass and charge balance are achieved this way:

The iron is balanced by adding one electron on the right

Fe2+ (aq ) Fe3+ (aq ) e

To balance oxygen, we use H2O on the right side; to balance hydrogen, we use H+ on the left side (recall that the reaction is taking place in acidic solution)

8 H+ (aq ) + MnO4 (aq ) Mn2+ (aq ) + 4 H2O (l )

The reduction half-reaction has a net charge of +7 on the left [(8+) + (1)] and +2 on the right [(+2) + 0]. Adding 5 electrons to the left side balances the charge.

8 H+ (aq ) + MnO4 (aq ) + 5 e Mn2+ (aq ) + 4 H2O (l )

Step 3. Equalize the electrons transferred. Multiply the oxidation half-reaction by 5. Add the half-reactions, canceling the electrons.

5 Fe2+ (aq ) 5 Fe3+ (aq ) + 5 e

8 H+ (aq ) + MnO4 (aq ) + 5 e Mn2+ (aq ) + 4 H2O(l )

Balanced equation: 5 Fe2+ (aq ) + 8 H+ (aq ) + MnO4 (aq ) 5 Fe3+ (aq ) + Mn2+ (aq ) + 4 H2O (l )

## Oxidation Number Method

MnO4 (aq ) + Fe2+ (aq ) + H+ (aq ) Mn2+ (aq ) + Fe3+ (aq ) H2O (l ) (unbalanced equation)

As in the half-reaction method, H2O is used to balance oxygen, and H+ is used to balance hydrogen.

Step 1. Identify the oxidation number of each element on each side of the equation. Determine which has undergone oxidation and which has undergone reduction. This is indicated in Table 1.

 Element Oxidation Number as Reactant Oxidation Number as Product Change in Oxidation Number Oxidation or Reduction Mn +7 +2 Decrease by 5 Reduction O −2 −2 0 Neither Fe +2 +3 Increase by 1 Oxidation H +1 +1 0 Neither

Step 2. Use coefficients so that the total increase in oxidation number equals the total decrease. In this case, the total decrease is 5 (Mn+7 becomes Mn2+), and the total increase must also be 5; each iron must be multiplied by 5: (5 Fe2+ becomes 5 Fe3+). Balance hydrogen and oxygen in the usual manner. The balanced equation is

MnO4 (aq ) + 5 Fe2+ (aq ) + 8 H+ (aq ) Mn2+ (aq ) + 5 Fe3+ (aq ) + 4 H2O (l )

## Bibliography

Daub, G. William, and Seese, William S. (1996). Basic Chemistry, 7th edition. Upper Saddle River, NJ: Prentice Hall.

Ebbing, Darrell D., and Wentworth, R. A. D. (1998). Fundamentals of Introductory Chemistry, 2nd edition. Boston: Houghton Mifflin.

Goldberg, David E. (2001). Fundamentals of Chemistry, 3rd edition. Boston: McGraw-Hill.

Myers, R. T.; Oldham, K. B.; and Tocci, S. (1999). Holt Chemistry: Visualizing Matter, 2nd edition. Austin, TX: Holt, Rinehart and Winston.

### Internet Resources

Bellevue Community College, Science Division. "Balancing Chemical Equations." Available from <http://www.scidiv.bcc.ctc.edu/wv/6/0006-002-balancing.html>.

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# Equation, chemical

A chemical equation is a shorthand method for representing the changes that take place during a chemical reaction. In describing the formation of water from its elements, a chemist could say, for example, that "two molecules of hydrogen gas combine with one molecule of oxygen to form two molecules of water." Or she could write the following chemical equation that contains the same information in a much more compact form:

2 H2 + O2 2 H2O

At the minimum, a chemical equation contains the chemical symbols and formulas for the elements and compounds involved in the reaction and the + and signs that indicate reactants and products. The term reactants refers to the substances present at the beginning of the reaction, and the term products refers to the substances formed in the reaction.

In the example above, the reactants are represented by the symbols H for hydrogen and O for oxygen. The product is represented by the formula H2O for water. The + sign indicates that hydrogen (H) has combined with oxygen (O) in the reaction. The indicates that the two have reacted with each other to form water.

## Balancing chemical equations

One of the fundamental laws of chemistry is the law of conservation of matter. That law says that matter can be neither created nor destroyed in an ordinary chemical reaction. In terms of the above reaction, the law means that there must be the same number of hydrogen atoms and oxygen atoms at the beginning of the reaction and at the end of the reaction.

The coefficients in the chemical equation assure that this condition is true. The coefficients are the numbers in front of the chemical symbols or formulas: 2 H2 and 2 H2O. One of the skills that beginning chemistry students need to learn is how to select the correct coefficients in order to make sure the equation obeys the law of conservation of matter. Choosing those coefficients is called balancing the chemical equation.

## Words to Know

Balancing an equation: The process of selecting coefficients for symbols and formulas in a chemical equation to make sure that the law of conservation of matter is not violated.

Chemical reaction: Any chemical change in which one new substance is formed.

Chemical symbol: A letter or pair of letters that represent a specific quantity of a chemical element.

Coefficient: A number selected for use in balancing a chemical equation. Coefficients are placed in front of the chemical symbols and formulas in an equation.

Products: The substances formed in a chemical reaction.

Reactants: The substances present at the beginning of a chemical reaction.

Most chemical equations contain other symbols (in addition to chemical symbols) that provide further information about the reaction. The subscript 2 in the symbols for hydrogen and oxygen (H2 and O2), for example, tells that each molecule of hydrogen and oxygen consists of two atoms of the element.

Other symbols are often used to indicate the physical state of the substances in the reaction. The same reaction for the formation of water can also be represented as:

2 H2 (g) + O2 (g) 2 H2O (l)

The symbols g and l tell us that hydrogen and oxygen are gases and water is a liquid. Other symbols used for this purpose include (s) for solids and (aq) for substances dissolved in water (the aq ueous condition). Upward and downward pointing arrows ( and ) can also be used to indicate the formation of gases and precipitates (solids), respectively, during a chemical reaction.

Finally, symbols can also be used to indicate the gain or loss of heat in a chemical reaction. Nearly all reactions are accompanied by such changes, and they can be represented by means of the symbol ΔH. In the case of the reaction above, for example, the complete reactions could be written as:

2 H2 (g) + O2 (g) 2 H2O (l)

ΔH = 571.6 kJ

In this case, the added information, ΔH = 571.6 kJ tells us that 571.6 kilojoules of heat energy were given off during the formation of water from its elements. (A joule is the metric unit of measurement for energy. One kilojoule is 1,000 joules.)

## Applications

The use of chemical equations is absolutely essential in dealing with any discussion of chemical reactions. It would be completely unreasonable for chemists to describe chemical reactions in English sentences, as indicated in the first paragraph of this entry. Thus, all reports of chemical research, books and articles on chemical topics, and any other written commentaries on chemistry all include chemical equations.

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## chemical equation

chemical equation, group of symbols representing a chemical reaction.

Basic Notation Used in Equations

The chemical equation 2H2+O2→2H2O represents the reaction of hydrogen and oxygen to form water. The arrow points in the direction of the reaction—from the reactants (substances that react) toward the product or products. In this case the reactants are hydrogen (written H2 because each molecule consists of two atoms of hydrogen) and oxygen (written O2 because each molecule consists of two atoms of oxygen) and the product is water. The coefficient 2 before the H2 indicates that two molecules of hydrogen take part in the reaction, and the 2 before the H2O indicates that two molecules of water are produced. When no number is written, as in front of the O2, a one is assumed; one molecule of oxygen takes part in the reaction. The equation shows that two molecules of hydrogen react with one molecule of oxygen to form two molecules of water. Because of the relationship between molecules and the mole, the equation also shows that two moles of hydrogen react with one mole of oxygen to form two moles of water. The same sort of relationship holds with the gram-formula weight.

Methodology for Writing an Equation

There are three steps involved in writing a chemical equation. The first step is to decide which substances are the reactants and which are the products. For example, natural gas (cooking gas) burns in air, providing heat and producing no visible products. The natural gas is principally methane, and the portion of the air that reacts (supports combustion) is oxygen. These are the reactants. Products of the reaction are heat and two invisible gases, carbon dioxide and water vapor. We can now write the word equation methane + oxygen → carbon dioxide + water vapor + heat. The next step is to determine the correct formula for each substance and substitute it for the name. The equation now becomes CH4+O2→CO2+H2O. (A notation for heat is often omitted.)

The final step is to balance this equation. As the equation is now written, three oxygen atoms are produced from two, and four hydrogen atoms become only two. This cannot occur, since atoms are not created or destroyed in chemical reactions. The equation is already balanced for carbon, since there is one carbon atom on the reactant side and one carbon atom on the product side. There are four hydrogen atoms in the methane molecule on the reactant side, so there must be four hydrogen atoms in water molecules on the product side (since water is the only product containing hydrogen); thus there must be two water molecules, each containing two hydrogen atoms. The equation can now be written CH4+O2→CO2+2H2O. It is not yet balanced, since there are only two oxygen atoms shown as reactants and four as products. The equation is completely balanced by showing two oxygen molecules (four atoms) as reactants: CH4+2O2→CO2+2H2O.

Additional Symbols Used in Chemical Equations

There are a number of other symbols used in chemical equations. A symbol written above or below the reaction arrow indicates special reaction conditions. For example, when mercuric oxide is heated it decomposes into mercury metal and oxygen gas; this reaction is shown by the equation 2HgO →Δ 2Hg + O2↑. The Greek letter delta under the arrow represents the heating. The upward-pointing arrow after the O2 indicates that this product is gaseous and escapes. When a precipitate is formed by a reaction, the substance that precipitates is often followed by a downward-pointing arrow, e.g., AgNO3 + NaCl →H2O AgCl↓ + NaNO3. The H2O above the arrow shows that the reaction takes place in the presence of water—in this case, in water solution. The formulas AgNO3, NaCl, and NaNO3 do not represent molecules, since these substances are almost completely ionized in water solution (see ion).

When chemical equilibrium occurs in a reaction, the double arrow (⇌) is used instead of the single arrow. For example, liquid water dissociates to form hydronium ions (H3O+) and hydroxide ions (OH-). These ions exist in equilibrium with water molecules. The equation is 2H2O ⇌H2O H3O+ + OH-. The sign = is sometimes used in place of the double arrow.

Bibliography

See J. B. Dence, Mathematical Techniques in Chemistry (1975).

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# Chemical Equations

Chemistry is a part of forensic science . By studying the reactions that occur during various tests, the forensic scientist can receive clues about the nature of the compound under study. Often, knowledge of the nature of the chemical reactions is helpful. This knowledge comes from the chemical equation that describes the reaction.

Chemical equations reveal the chemical species involved in a particular reaction, the charges and weight relationships among them, and how much heat a reaction generates. Equations define the beginning compounds, called reactants, and the ending compounds, called products, and which direction the reaction is going.

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.

In general, reactants are placed on the left-hand side of the equation, and the reaction products 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 heat escapes while produced. Sometimes, Δ is replaced by "light" (to initiate reactions) or "flame" (for combustion reactions.) Instead of showing the symbol D, at the same place we may just indicate the operating temperature or what enzymes and catalysts are needed to speed the reaction.

Each chemical species involved in an equation is represented by chemical formula associated with stoichiometric coefficients (numerical measures showing relationships between reactants and products in a chemical reaction). For instance, a, b, c, and d are the stoichiometric coefficients for A, B, C, and D, respectively.

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.

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

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## chemical equation

chemical equation Set of symbols used to represent a chemical reaction. Equations show how atoms are rearranged as a result of a reaction, with reactants on the left-hand side and products on the right-hand side. For example, the formation of magnesium oxide when magnesium burns in oxygen is represented by 2Mg + O2 Æ 2MgO. The number of atoms of an element on the left-hand side of an equation must equal the number on the right.

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## equation, chemical

chemical equation: see chemical equation.