Calculations with Balanced Chemical Equations

SECTION 3.6 Calculations with Balanced Chemical Equations... 

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. 

The following plot shows how the partial pressures of reactant and products vary with time for the decomposition of compound A into compounds B and C. All three compounds are gases. Use this plot to do the following (a) Write a balanced chemical equation for the reaction, (h) Calculate the equilibrium constant for the reaction, (c) Calculate the value of Kc for the reaction at 25°C. 

Tables of amounts are useful in stoichiometry calculations for precipitation reactions. For example, a precipitate of Fe (OH) forms when 50.0 mL of 1.50 M NaOH is mixed with 35.0 mL of 1.00 M FeCl3 solution. We need a balanced chemical equation and amounts in moles to calculate how much precipitate forms. The balanced chemical equation is the net reaction for formation of Fe (OH)3 Fe (ag) + 3 OH (a g) Fe (OH)3 (. )...

As another illustration of the use of Equation, we calculate the enthalpy of combustion of methane, the principal component of natural gas. We begin with the balanced chemical equation ... 

First determine [H30+], with calculation based, on the balanced chemical equation. 

We first balance the chemical equation and then calculate the value of AG° with data from Appendix D, and finally calculate the value of with the use of AG° = -RT nK. 

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 have seen how analytical calculations in titrimetric analysis involve stoichiometry (Sections 4.5 and 4.6). We know that a balanced chemical equation is needed for basic stoichiometry. With redox reactions, balancing equations by inspection can be quite challenging, if not impossible. Thus, several special schemes have been derived for balancing redox equations. The ion-electron method for balancing redox equations takes into account the electrons that are transferred, since these must also be balanced. That is, the electrons given up must be equal to the electrons taken on. A review of the ion-electron method of balancing equations will therefore present a simple means of balancing redox equations. 

The relationship above gives a way of converting from grams to moles to particles, and vice versa. If you have any one of the three quantities, you can calculate the other two. This becomes extremely useful in working with chemical equations, as we will see later, because the coefficients in the balanced chemical equation are not only the number of individual atoms or molecules at the microscopic level, but also the number of moles at the macroscopic level. 

Each of these dissociation reactions also specifies a definite equilibrium concentration of each product at a given temperature consequently, the reactions are written as equilibrium reactions. In the calculation of the heat of reaction of low-temperature combustion experiments the products could be specified from the chemical stoichiometry but with dissociation, the specification of the product concentrations becomes much more complex and the s in the flame temperature equation [Eq. (1.11)] are as unknown as the flame temperature itself. In order to solve the equation for the n s and T2, it is apparent that one needs more than mass balance equations. The necessary equations are found in the equilibrium relationships that exist among the product composition in the equilibrium system. 

When dealing with normality and equivalents, it is not necessary to have balanced chemical equations on which to base your calculations. 

The sequence of conversions in Figure 18.20 is used to calculate the mass or volume of product produced by passing a known current through a cell for a fixed period of time. The key is to think of the electrons as a "reactant" in a balanced chemical equation and then to proceed as with any other stoichiometry problem. Worked Example 18.10 illustrates the calculations. Alternatively, we can calculate the current (or time) required to produce a given amount of product by working through the sequence in Figure 18.20 in the reverse direction, as shown in Worked Example 18.11. 

In writing chemical equations and biochemical equations it is important to be careful with names of reactants. Chemical reactions are written in terms of species. In chemical reaction equations, atoms of all elements and electric charges must balance. Biochemical reaction equations are written in terms of reactants, that is in terms of sums of species, H+ is not included as a reactant and electric charges are not shown or balanced. In biochemical reaction equations, atoms of all elements other than hydrogen must balance. The names of the reactants that must be used in making calculations with this data base are given later. 

You can see that a balanced chemical equation is a powerful tool. It allows chemists to predict the amount of products that will result from a reaction involving a known amount of reactants. As well, chemists can use a balanced equation to calculate the amount of reactants they will need to produce a desired amount of products. They can also use it to predict the amount of one reactant they will need to react completely with another reactant. 

Suppose that a solution of an acid reacts with a solution of a base. You can determine the concentration of one solution if you know the concentration of the other. (This assumes that the volumes of both are accurately measured.) Use the concentration and volume of one solution to determine the amount (in moles) of reactant that it contains. The balanced chemical equation for the reaction describes the mole ratio in which the compounds combine. In the following Sample Problems and Practice Problems, you will see how to do these calculations. 

Stoichiometry establishes the quantities of reactants (used) and products (obtained) based on a balanced chemical equation. With a balanced equation, you can compare reactants and products, and determine the amount of products that might be formed or the amount or reactants needed to produce a certain amount of a product. However, when comparing different compounds in a reaction, you must always compare in moles (i.e., the coefficients). The different types of stoichiometric calculations are summarized in Figure 5.1. 

The coefficients in a balanced equation give the ratio of moles of each substance in the reaction to moles of any other substance. They also give the ratio of formula units of each substance to formula units of any other substance. The balanced chemical equation is the cornerstone from which we can calculate how much of one substance reacts with or is produced by a certain quantity of another substance (Chapter 10). 

The balanced chemical equation gives the mole ratios of all the substances in the reaction, just as an empirical formula gives the ratios of atoms of the elements in a compound. As with chemical formulas, these ratios can be used as factors in calculations involving any two of the substances. 

Net ionic equations (Chapter 9), like all other balanced chemical equations, give the mole ratios of reactants and products. Therefore, any calculations that require mole ratios may be done with net ionic equations as well as with total equations. However, a net ionic equation does not yield mass data directly because part of each soluble ionic compound is not given. For example, we can tell how many moles of silver ion are required to produce a certain number of moles of a product. 

The number of moles of gas involved a chemical reaction, calculated from the ideal gas law, can be used with the balanced chemical equation to determine the number of moles of any other reactant or product in the reaction. Also, the number of moles of any gas, calculated from the balanced chemical equation, can be used with other data in the ideal gas law to calculate the volume, temperature, or pressure of the gas. 

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