Equations, balancing chemical

In balancing equations, start with the most complicated molecule. 

Most chemical equations can be balanced by inspection, that is, by trial and error. It is always best to start with the most complicated molecules (those containing the greatest number of atoms). For example, consider the reaction of ethanol with oxygen, given by the unbalanced equation 

Notice that the carbon and hydrogen atoms are not balanced. There are two carbon atoms on the left and one on the right, and there are six hydrogens on the left and two on the right. We need to find the correct numbers of reactants and products so that we have the same number of all types of atoms among the reactants and products. We will balance the equation by inspection (a systematic trial-and-error procedure). 

The most complicated molecule here is C2FI5OFI. We will begin by balancing the products that contain the atoms in C2FI5OFI. Since C2FI5OFI contains two carbon atoms, we place the coefficient 2 before the CO2 to balance the carbon atoms  

Since C2FI5OFI contains six hydrogen atoms, the hydrogen atoms can be balanced by placing a 3 before the FI2O  

Such chemical equations must obey certain rules  

The reactants are written to the left-hand side, LHS, the products 

Each side of the equation must have the same number of each kind of atoms, i.e. the equation must balance. 

The overall ionic charges must be the same on each side of the equation. 

The products involve 3C1, while the reactants involve only ICl 

If you carry out a chemical reaction and carefully sum up the masses of all the reactants, and then you compare the sum to the sum of the masses of all the products, you see that they re the same. In fact, a law in chemistry, the law of conservation of mass, states, In an ordinary chemical reaction, matter is neither created nor destroyed. This means that you neither gain nor lose any atoms during the reaction. They may be combined differently, but they re still there. 

A chemical equation represents the reaction, and that chemical equation nee to obey the law of conservation of mass. You use that chemical equation to calculate how much of each element you need and how much of each element will be produced. You need to have the same number of each kind of element on both sides of the equation. The equation should bcdance. 

Before you start balancing an equation, you need to know the reactants and the products for that reaction. You can t change the compounds, and you can t ch inge the subscripts, because that would change the compounds. So the only thing you can do to balance the equation is put in coefficients, whole numbers in front of the compounds or elements in the equation. 

Coefficients tell you how many atoms or molecules you have. For example, if you write 2 H O, it means you have two water molecules  

Each water molecule is composed of two hydrogen atoms and one oxygen atom. So with 2 H2O, you have a total of four hydrogen atoms and two oxygen atoms. 

2 Given an unbalanced chemical equation, balance it by inspection. 

The balancing procedure in the preceding section is sometimes called balancing by inspection. It is a trial-and-error method that succeeds in nearly all the reactions you are likely to encounter in a general chemistry course. Most equations can be balanced 

Step 2 Insert coefficients that balance the elements that appear in compounds. Use fractional coefficients, if necessary. Do not balance element-only formulas, such as Na or O2, at this time. We call these uncombined elements. Choosing elements in the following order is usually easiest  

Step 3 Place coefficients in front of formulas of uncombined elements that balance those elements. Use fractional coefficients, if necessary. 

Step 4 Clear fractions, if any, by multiplying all coefficients by the lowest common denominator. Remove any 1 coefficients that remain. 

Balancing Chemical Equations Use with Chapter 10, Section 10.1 

Each chemical equation below contains at least one error. Identify the error or errors and then write the correct chemical equation for the reaction. 

Copyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc. 

From this discussion you can see that a balanced chemical equation gives you a great deal of information. 

An unbalanced chemical equation is of limited use. Whenever you see an equation, you should ask yourself whether it is balanced. The principle that lies at the heart of the balancing process is that atoms are conserved in a chemical reaction. The same number of each type of atom must be found among the reactants and products. Also, remember that the identities of the reactants and products of a reaction are determined by experimental observation. For example, when liquid ethanol is burned in the presence of sufficient oxygen gas, the products will always be carbon dioxide and water. When the equation for this reaction is balanced, the identities of the reactants and products must not be changed. The formulas of the compounds must never be changed when balancing a chemical equation. That is, the subscripts in a formula cannot be changed, nor can atoms be added or subtracted from a formula. 

Chromate and dichromate compounds are suspected carcinogens (cancer-inducing agents) and should be handled carefully. 

What if a friend was balancing chemical equations by changing the values of the subscripts instead of using the coefficients How would you explain to your friend that this was the wrong thing to do  

Sample Problem D Solid aluminum carbide, AI C3, reacts with water to produce methane gas and solid aluminum hydroxide. Write a balanced chemical equation for this reaction. 

The reactants are aluminum carbide and water. The products are methane and aluminum hydroxide. The formula equation is written as follows. 

Begin balancing the formula equation by counting either aluminum atoms or carbon atoms. (Remember that hydrogen and oxygen atoms are balanced last.) There are four A1 atoms on the left. To balance A1 atoms, place the coefficient 4 before Al(OH)3 on the right 

Now balance the carbon atoms. With three C atoms on the left, the coefficient 3 must be placed before CH on the right 

Balance oxygen atoms next because oxygen, unlike hydrogen, appears only once on each side of the equation. There is one O atom on the left and 12 O atoms in the four Al(OH)3 formula units on the right Placing the coefficient 12 before H2O balances the O atoms. 

EXERCISE 6.1 Identify the reactants and products and write the unbalanced equation (including symbols for states) for each of the following chemical reactions. 

Trial and error is often useful for solving problems. It s okay to make a few wrong turns before you get to the right answer. 

OBJECTIVE To learn how to write a balanced equation for a chemical reaction. 

As indicated in the preceding section, a correctly written chemical equation has equal numbers of atoms of each element on both sides of the equatiotL Balancing a chemical equation is accomplished by placing the correct number in front of each formula in the chemical equation. However, the following must be remembered  

Only the numbers in front of the chemical formulas may be changed to balance a chemical equation. The chemical formulas themselves (subscript numbers) may not be changed in balancing the equation. 

Balancing an equation is best accomplished by considering one element at a time, balancing it by changing the numbers preceding the formulas in which it is contained, then successively balancing other elements in the formulas contained in the equation. 

If you look carefully at the reactions we ve been writing, you ll notice more than just the formulas and the states of the substances in the equation. Numerical information about the relative amounts of the substances involved is also evident. For example, we included the number 2 in front of both the H2(g) and H20(g) in the equation for the reaction between hydrogen and oxygen. Why are these numbers there, and what do they mean If you ve studied chemistry before in high school, you probably remember that these coefficients are often needed to balance a chemical equation. 

If we also consider nudear reactions, we must acknowledge that matter and energy can be interconverted. 

Propane, C3H8, is used as a fuel for gas barbecue grills, where it burns in a controlled fashion. But if a mixture of propane and air is ignited in a closed space, like a gas pipeline, an explosion can easily result. In either of these cases, the propane combines with oxygen, O2, to form carbon dioxide and water. Write a balanced chemical equation describing this reaction. 

This problem requires two steps. First we must read the problem and determine which substances are reactants and which are products. This will allow us to write an unbalanced skeleton equation. Then we must proceed to balance the equation, making sure that the same number of atoms of each element appears on both sides. 

Step 1 The problem notes that propane bums or explodes by combining with oxygen. The reactants are therefore C3H8 and O2. We are also told that the products are CO2 and H2O. So we have enough information to write the unbalanced equation. (Here we will write blanks in front of each formula to emphasize that we still need to determine the coefficients.) 

A balanced equation has the same number of atoms of each element on both sides of the arrow. Because atoms are neither destroyed nor created in chemical reactions, every atom must be accounted for. If there are 10 carbon atoms in the reactants, there must be 10 carbon atoms in the products. Because every atom is accounted for, a balanced equation always obeys the Law of Conservation of Mass. It is important that you know how to balance chemical equations. Most equations are not difficult to balance, but you have to pay attention to the details of counting atoms. 

Equations are balanced by placing whole-number coefficients in front of one or more species in the equation, using the smallest set of numbers that does the job. The following equation describing the reaction of aluminum with oxygen is correctly balanced. Inspecting the equation shows the same number of aluminum and oxygen atoms on both sides of the equation. 

Choosing the right coefficients is done by trial and error, but if you carefully check the numbers of atoms each time a coefficient is changed, you can reduce the trial and eliminate the error. The equation describing the combustion of methane, the principal component of natural gas, follows. Counting the atoms of each element on both sides of the equation shows it is not a balanced equation. 

On the left side, we start with 1 molecule of CH4, 1 C atom, and 4 H atoms. On the right side of the equation, there is 1 C atom in 1 C02 molecule (C is balanced), but only 2 H atoms in 1 HzO molecule. Hydrogen can be balanced by placing a 2 in front of HzO. This doubles both H and O, (2 HzO = 4 H and 2 O). Let s check the results. 

There are an identical number of atoms of each element on both sides of the arrow The equation is balanced  

Propane gas, C3H3, from the tank burns by reacting with oxygen, 02,in air to give carbon dioxide, C02,and water, H2O. 

When the coefficients in a chemical equation are correctly given, the numbers of atoms of each element are equal on both sides of the arrow. The equation is then said to be balanced. That a chemical equation should be balanced follows from atomic theory. A chemical reaction involves simply a recombination of the atoms none are destroyed and none are created. Consider the burning of natural gas, which is composed mostly of methane, CH4. Using atomic theory, you describe this as the chemical reaction of one molecule of methane, CH4, with two molecules of oxygen, O2, to form one molecule of carbon dioxide, CO2, and two molecules of water, H2O. 

Before you can write a balanced chemical equation for a reaction, you must determine by experiment those substances that are reactants and those that are products. You must also determine the formulas of each substance. Once you know these things, you can write the balanced chemical equation. 

This equation is not balanced because the coefficients that give the relative number of molecules involved have not yet been deteamined. To balance the equation, you select coefficients that will make the numbers of atoms of each element equal on both sides of the equation. 

Because there are three carbon atoms on the left side of the equation (CsHg), you must have three carbon atoms on the right. This is achieved by writing 3 for the coefficient of CO2. 

As we saw in the previous section, an unbalanced chemical equation is not an accurate representation of the reaction that occurs. Whenever you see an equation for a reaction, you should ask yourself whether it is balanced. 

That is, atoms are neither created nor destroyed. They are just grouped differently. The same number of each type of atom is found among the reactants and among the products. 

Chemists determine the identity of the reactants and products of a reaction by experimental observation. For example, when methane (natural gas) is burned in the presence of sufficient oxygen gas, the products are always carbon dioxide and water. 

The identities (formulas) of the compounds must never be changed in balancing a chemical equation. 

As we saw in the previous section, an unbalanced chemical equation is not an accurate representation of the reaction that occurs. Whenever you see an equation for a reaction, you should ask yourself whether it is balanced. The principle that lies at the heart of the balancing process is that atoms are conserved in a chemical reaction. That is, atoms are neither created nor destroyed. They are just grouped differently. The same number of 

Most chemical equations can be balanced by trial and error—that is, by inspection. Keep trying until you find the numbers of reactants and products that give the same number of each type of atom on both sides of the arrow. For example, consider the reaction of hydrogen gas and oxygen gas to form liquid water. First, we write the unbalanced equation from the description of the reaction. 

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Wnte a balanced chemical equation for the combustion of each of the following compounds... 

Write properly balanced chemical equations for the oxidation to COg and water of (a) myristic acid, (b) stearic acid, (c) a-linolenic acid, and (d) arachidonic acid. 

A chemist who carries out a reaction in the laboratory needs to know how much product can be obtained from a given amount of starting materials (reactants). To do this, he or she starts by writing a balanced chemical equation. 

Chemical reactions are represented by chemical equations, which identify reactants and products. Formulas of reactants appear on the left side of the equation those of products are written on the right In a balanced chemical equation, there are the same number of atoms of a given element on both sides. The same situation holds for a chemical reaction that you carry out in the laboratory atoms are conserved. For that reason, any calculation involving a reaction must be based on the balanced equation for that reaction. 

The emphasis is on writing and balancing chemical equations for these reactions. All of these reactions involve ions in solution. The corresponding equations are given a special name net ionic equations. They can be used to do stoichiometric calculations similar to those discussed in Chapter 3. 

A chemical equation that shows the enthalpy relation between products and reactants is called a thermochemical equation. This type of equation contains, at the right of the balanced chemical equation, the appropriate value and sign for AH. 

Throughout Section 11.3, balanced chemical equations are written in such a way that the coefficient of die reactant is 1. In general, if the coefficient of the reactant is a, where a may be 2 or 3 or..., then k in each integrated rate equation must be replaced by the product ak. (See Problem 101.)... 

In taking these sums, the standard molar entropies are multiplied by the number of moles specified in the balanced chemical equation. 

Strategy Start by writing a balanced chemical equation for the reaction involved. Then use Equation 17.1 in combination with Table 17.1 to calculate the difference in entropy between products and reactants. For (b) note that you are asked to calculate AS° for one gram of methane. 

However, the two ions NOf (ag) and Na+(agj do not play an active role in the reaction, nor do they influence the reaction that does occur [reaction (70)]. Consequently, they are not included in the equation for the reaction. The balanced chemical equation should show only species which actually participate in the reaction. These species are called the predominant reacting species. 

More quantitative evidence can be obtained by carrying out the reaction between an excess of sodium and a weighed amount of ethanol and measuring the amount of hydrogen gas evolved. When this is done it is found that 46 grams of ethanol (one mole) will produce only mole of hydrogen gas. We can therefore write a balanced chemical equation for the reaction of sodium with ethanol ... 

For the reaction between solid sodium and water, the complete, balanced chemical equation is therefore... 

In other words, the stoichiometric coefficients multiplying the chemical formulas in any balanced chemical equation tell us the relative number of moles of each substance that reacts or is produced in the reaction. 

A balanced chemical equation symbolizes both the qualitative and the quantitative changes that take place in a chemical reaction. The stoichiometric coefficients tell us the relative numbers of moles of reactants and products taking part in the reaction. 

Although normally the coefficients in a balanced chemical equation are the smallest possible whole numbers, a chemical equation can be multiplied through by a factor and still be a valid equation. At times it is convenient to use fractional coefficients for example, we could write... 

Sometimes we need to construct a balanced chemical equation from the description of a reaction. For example, methane, CH4, is the principal ingredient of natural gas (Fig. H.3). It burns in oxygen to form carbon dioxide and water, both formed initially as gases. To write the balanced equation for the reaction, we first write the skeletal equation ... 

Self-Test H.1A When aluminum is melted and heated with solid barium oxide, a vigorous reaction takes place, and elemental molten barium and solid aluminum oxide are formed. Write the balanced chemical equation for the reaction. 

Self-Test H.1B Write the balanced chemical equation for the reaction of solid magnesium nitride with aqueous sulfuric acid to form aqueous magnesium sulfate and aqueous ammonium sulfate. 

H.7 Write a balanced chemical equation for each of the following reactions, (a) Calcium metal reacts with water to produce hydrogen gas and aqueous calcium hydroxide. 

P, with the remainder oxygen. The mass spectrum of compound B yields a molar mass of 97.99 g-mol. Write the molecular formula of compound B. (c) Compound B reacts with an aqueous solution of calcium hydroxide to form compound C, a white precipitate. Write balanced chemical equations for the reactions in parts (a), (b), and (c). 

J.I4 The oxides of nonmetallic elements are called acidic oxides because they form acidic solutions in water. Write the balanced chemical equations for the reaction of one mole of each acidic oxide with one mole of water molecules to form an oxoacid and name the acid formed (a) C02 (b) SO,. 

J 3 Write and balance chemical equations for simple redox reactions (Self-Test K.4). 

Sometimes we need to know how much product to expect from a reaction, or how much reactant we need to make a desired amount of product. The quantitative aspect of chemical reactions is the part of chemistry called reaction stoichiometry. The key to reaction stoichiometry is the balanced chemical equation. Recall from Section H that a stoichiometric coefficient in a chemical equation tells us the relative amount (number of moles) of a substance that reacts or is produced. Thus, the stoichiometric coefficients in... 

The balanced chemical equation for a reaction is used to set up the mole ratio, a factor that is used to convert the amount of one substance into the amount of another. 

Step 2 Use the mole ratio derived from the stoichiometric coefficients in the balanced chemical equation to convert from the amount of one substance (A) into the amount in moles of the other substance (B). For aA - / B or aA + hY> — cC, use... 

L.25 Barium bromide, BaBrv, can be converted into BaCl2 by treatment with chlorine. It is found that 3.25 g of BaBrv reacts completely with an excess of chlorine to yield 2.27 g of BaCl2. Determine the value of x and write the balanced chemical equation for the production of BaCl2 from BaBr,.. 

Write a balanced chemical equation for the formation reaction of (a) HCl(g) (b) C6H6(1) (c) CuS04-5H20(s) (d) CaCOj(s, calcite). For each reaction, determine AH°, AS0, and AG° from data in Appendix 2A. 

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