# 3: Using Chemical Equations in Calculations

The following sections are concerned with the amounts of substances which participate in chemical reactions, the quantities of heat given off or absorbed when reactions occur, and the volumes of solutions which react exactly with one another. These seemingly unrelated subjects are discussed together because many of the calculations involving them are almost identical in form. The same is true of the density calculations and of the calculations involving molar mass and the Avogadro constant.

• 3.1: Prelude to Chemical Equations
An incredible variety of problems can be solved using conversion factors . Sometimes only one factor is needed, but quite often several are applied in sequence. In solving such problems, it is necessary first to think your way through, perhaps by writing down a road map showing the relationships among the quantities given in the problem. Then you can apply conversion factors, making sure that the units cancel, and calculate the result.
• 3.2: Equations and Mass Relationships
A balanced chemical equation not only tells how many molecules of each kind are involved in a reaction, it also indicates the amount of each substance that is involved. The stoichiometric ratio measures one element (or compound) against another.
• 3.3: The Limiting Reagent
The substance A material that is either an element or that has a fixed ratio of elements in its chemical formula. which is used up first is the limiting reagent. The reactant (of two or more reactants) present in an amount such that it would be completely consumed if the reaction proceeded to completion. Also called limiting reactant..
• 3.4: Percent Yield
Even though none of the reactants is completely consumed, no further increase in the amounts of the products occurs. We say that such a reaction does not go to completion. When a mixture of products is produced or a reaction does not go to completion, the effectiveness of the reaction is usually evaluated in terms of percent yield of the desired product. A theoretical yield is calculated by assuming that all the limiting reagent is converted to product.
• 3.5: Analysis of Compounds
Up to this point we have obtained all stoichiometric ratios from the coefficients of balanced chemical equations. Chemical formulas also indicate relative amounts of substance, however, and stoichiometric ratios may be derived from them, too.
• 3.6: Thermochemistry
When a chemical reaction occurs, there is usually a change in temperature of the chemicals themselves and of the beaker or flask in which the reaction is carried out. If the temperature increases, the reaction is exothermic—energy is given off as heat when the container and its contents cool back to room temperature. (Heat is energy transferred from one place to another solely because of a difference in temperature.)
• 3.7: Energy
• 3.8: Thermochemical Equations
• 3.9: Hess' Law
• 3.10: Standard Enthalpies of Formation
• 3.11: Solution Concentrations
In the laboratory, in your body, and in the outside environment, the majority of chemical reactions take place in solutions. Macroscopically a solution is defined as a homogeneous mixture of two or more substances, that is, a mixture which appears to be uniform throughout. On the microscopic scale a solution involves the random arrangement of one kind of atom or molecule with respect to another.
• 3.12: Diluting and Mixing Solutions
• 3.13: Titrations
A titration is a volumetric technique in which a solution of one reactant (the titrant) is added to a solution of a second reactant (the "analyte") until the equivalence point is reached. The equivalence point is the point at which titrant has been added in exactly the right quantity to react stoichiometrically with the analyte. If either the titrant or analyte is colored, the equivalence point is evident from the disappearance of color as the reactants are consumed.