Coefficients, balanced chemical equation

The number written in front of the chemical formulas in a balanced chemical equation— coefficients indicate the relative numbers of reactants and products in the reaction. 

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 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 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... 

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... 

The equilibrium composition of a reaction mixture is described by the equilibrium constant, which is equal to the activities of the products (raised to powers equal to their stoichiometric coefficients in the balanced chemical equation for the reaction) divided by the activities of the reactants (raised to powers equal to their stoichiometric coefficients). 

The drawings produced by students allow researchers to better conceptualize how some students interpreted a balanced chemical equations. This is especially useful in assessing their understanding of stoichiometric coefficients and the meaning of subscripts of chemical formulae. 

The stoichiometric coefficients in a balanced chemical equation must be chosen so that the atoms of each element are conserved. Many chemical equations can be balanced by inspection. Balancing by inspection means changing stoichiometric coefficients until the number of atoms of each element is the same on each side of the arrow. Usually, we can tell what changes need to be made by looking closely at the reaction and matching the numbers of atoms of each element on both sides of the equation. Consider the following example. 

To summarize, the amounts of different reagents that participate in a chemical reaction are related through the stoichiometric coefficients in the balanced chemical equation. To convert from moles of one reagent to moles of any other reagent, multiply by the stoichiometric ratio that leads to proper cancellation of units ... 

Entropy changes are important in every process, but chemists are particularly interested in the effects of entropy on chemical reactions. If a reaction occurs under standard conditions, its entropy change can be calculated from absolute entropies using the same reasoning used to calculate reaction enthalpies from standard enthalpies of formation. The products of the reaction have molar entropies, and so do the reactants. The total entropy of the products is the sum of the molar entropies of the products multiplied by their stoichiometric coefficients in the balanced chemical equation. The total entropy of the reactants is a similar sum for the reactants. Equation... 

The rates for different species participating in a chemical reaction are related by the stoichiometric coefficients of the balanced chemical equation. Equation provides the exact relationship. 

The coefficients of any balanced redox equation describe the stoichiometric ratios between chemical species, just as for other balanced chemical equations. Additionally, in redox reactions we can relate moles of chemical change to moles of electrons. Because electrons always cancel in a balanced redox equation, however, we need to look at half-reactions to determine the stoichiometric coefficients for the electrons. A balanced half-reaction provides the stoichiometric coefficients needed to compute the number of moles of electrons transferred for every mole of reagent. 

Fig. 8-1 The conversion of moles of one reagent to moles of another, using a ratio of the coefficients of the balanced chemical equation as a factor label...

Arts. The chemist can put in as little as is weighable or as much as the vessel will hold. For example, the fact that a reactant has a coefficient of 2 in the balanced chemical equation does not mean that the chemist must put two moles into the reaction vessel. The chemist might decide to add the reactants in the ratio of the balanced chemical equation, but even that is not required. And even in that case, the numbers of moles of each reactant might be twice the respective coefficients or one-tenth those values, etc. The equation merely states the reacting ratio. 

In this equation, e is the actual potential and f° is the standard potential, n is the number of electrons involved, and Q is a ratio of concentration terms. Q is equal to the ratio of concentrations of products to concentrations of reactants, each raised to the power corresponding to the coefficient in the balanced chemical equation. Pure solids and liquids and the solvent water are not included in Q their effective concentrations are assumed to be 1. Gas pressures in atmospheres are used instead of concentrations. For a general reaction... 

The square brackets refer to the concentration of the species inside. Note that the concentrations are multiplied or divided, not added or subtracted, and the concentrations of the products are in the numerator. The coefficients in the balanced chemical equation have become exponents in this mathematical equation. 

We deduce that to produce 0.20 M C it takes 0.20 M A and 0.20 M B. Moreover, we know that 0.20 M D was also produced. The magnitudes of the values in the second row of the table—the changes produced by the reaction—are always in the same ratio as the coefficients in the balanced chemical equation. 

The changes brought about by the chemical reaction arc a little different in this case. Twice as many moles per liter of A are used up as moles per liter of C are produced. Note that the magnitudes in the middle row of this table and the coefficients in the balanced chemical equation are in the same ratio. 

In which line of the table used to calculate the equilibrium concentrations are the values in the ratio of the coefficients of the balanced chemical equation Are other lines ... 

Each calculation uses the stoichiometric coefficients from the balanced chemical equation and the molar mass of the reactant. 

The molar ratios given by the stoichiometric coefficients in the balanced chemical equations are used in the solution. 

The Law of Conservation of Mass states that the total mass remains unchanged. This means that the total mass of the atoms of each element represented in the reactants must appear as products. In order to indicate this, we must balance the reaction. When balancing chemical equations, it is important to realize that you cannot change the formulas of the reactants and products the only things you may change are the coefficients in front of the reactants and products. The coefficients indicate how many of each chemical species react or form. A balanced equation has the same number of each type of atom present on both sides of the equation and the coefficients are present in the lowest whole number ratio. For example, iron metal reacts with oxygen gas to form rust, iron(III) oxide. We may represent this reaction by the following balanced equation ... 

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

We calculate the mole-to-coefficient ratio of each reactant by dividing the moles of that reactant by its coefficient in the balanced chemical equation. The reactant that has the smallest mole-to-coefficient ratio is the limiting reactant. Many of us use this method. 

Divide each by the coefficient in the balanced chemical equation. The smallest result is the limiting reactant ... 

In this chapter, you learned how to balance simple chemical equations by inspection. Then you examined the mass/mole/particle relationships. A mole has 6.022 x 1023 particles (Avogadro s number) and the mass of a substance expressed in grams. We can interpret the coefficients in the balanced chemical equation as a mole relationship as well as a particle one. Using these relationships, we can determine how much reactant is needed and how much product can be formed—the stoichiometry of the reaction. The limiting reactant is the one that is consumed completely it determines the amount of product formed. The percent yield gives an indication of the efficiency of the reaction. Mass data allows us to determine the percentage of each element in a compound and the empirical and molecular formulas. 

Where the lower case letters are the coefficients in the balanced chemical equation, the upper case letters stand for the reactant, and product chemical species and initial rates are used, then the rate equation (rate law) is ... 

This reaction quotient is a fraction. The numerator is the product of the chemical species on the right hand side of the equilibrium arrow, each one raised to the power of that species coefficient in the balanced chemical equation. The denominator is the product of the chemical species on the left hand side of the equilibrium arrow, each one raised to the power of that species coefficient in the balanced chemical equation. It is called Qc, in this case, since molar concentrations are being used. If this was a gas phase reaction, gas pressures could be used and it would become a Qp. 

The equilibrium constant expression associated with systems of slightly soluble salts is the solubility product constant, Ksp. It is the product of the ionic concentrations, each one raised to the power of the coefficient in the balanced chemical equation. It contains no denominator since the concentration of a solid is, by convention, 1, and for this reason it does not appear in the equilibrium constant expression. The Ksp expression for the PbS04 system is ... 

We will need the moles of HN02 in all the remaining steps in this problem. The moles of NaOH will be changing as we add more. The coefficients in the reaction are all ones, thus, we can simply compare the moles to find the limiting reactant. The sodium hydroxide, with the smaller number of moles is limiting. We can add the mole information to the balanced chemical equation. (The water, being neutral, will not be tracked.)... 

However, if reaction is not of a simple stoichiometry but involves different number of moles of reactants or products, the rate should be divided by corresponding stoichiometric coefficient in the balanced chemical equation for normalizing it and making it comparable. For example, for a general reaction aA + bB — cC + dD... 

A balanced chemical equation provides many types of information. It shows which chemical species are the reactants and which species are the products. It may also indicate in which state of matter the reactants and products exist. Special conditions of temperature, catalysts, etc., may be placed over or under the reaction arrow. And, very importantly, the coefficients (the integers in front of the chemical species) indicate the number of each reactant that is used and the number of each product that is formed. These coefficients may stand for individual atoms/molecules or they may represent large numbers of them called moles (see the Stoichiometry chapter for a discussion of moles). The basic idea behind the balancing of equations is the Law of Conservation of Matter, which says that in ordinary chemical reactions matter is neither created nor destroyed. The number of each type of reactant atom has to equal the number of each type of product atom. This requires adjusting the reactant and product coefficients—balancing the equation. When finished, the coefficients should be in the lowest possible whole-number ratio. 

In balancing chemical equations don t change the subscripts in the chemical formula, just the coefficients. 

Answer all three of the following questions. Each question will have two parts—writing the balanced chemical equation and answering a question about the reaction. Coefficients in the balanced chemical equation must be in the lowest whole-number ratio. Do not include formulas for substances that remain unchanged during the reaction. Unless otherwise noted, assume all the reactions occur in aqueous solution. If a substance is extensively ionized and therefore is present as ions in solution, write its formula as ions. 

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