Chapter 11: Using Balanced Chemical Equations

Stoichiometry and Mole to Mole Conversions

Stoichiometry is the study of the numerical relationship between the amounts of reactants and products in a balanced chemical equation. These relationships allow for the determination of equivalent molar amounts. For example, in the synthesis of urea, $2NH_3(g) + CO_2(g) \rightarrow (NH_2)_2CO(aq) + H_2O(l)$, the balanced equation dictates that $5.25$ moles of ammonia ($NH_3$) will produce $2.63$ moles of urea and require $2.63$ moles of carbon dioxide ($CO_2$) based on the stoichiometric ratios.

Mass to Mass Conversions

While chemical equations provide relationships in moles, laboratory measurements are typically conducted in mass. Mass to mass calculations require converting the starting mass to moles using molar mass, applying the stoichiometric mole ratio, and converting the resulting moles back to mass. Heating ammonium nitrate ($NH_4NO_3$) follows the equation $NH_4NO_3(s) \rightarrow N_2O(g) + 2H_2O(g)$. To produce $10.0\,g$ of nitrous oxide ($N_2O$), one must heat $18.2\,g$ of $NH_4NO_3$, which also produces $8.18\,g$ of water ($H_2O$).

Limiting Reactants and Percent Yield

The limiting reactant is the substance used up first in a reaction, thereby limiting the amount of product formed. Excess reactants are those remaining after the limiting reactant is consumed. The theoretical yield is the maximum obtainable product predicted by stoichiometry. In practice, the actual yield is usually lower. The efficiency of a reaction is measured by percent yield: $\text{Percent Yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$. For example, the synthesis of aspirin from salicylic acid and acetic anhydride involves determining which reactant limits the theoretical yield of acetylsalicylic acid ($C_9H_8O_4$).

Aqueous Reactions and Molarity

Stoichiometry for reactions in solution utilizes molarity ($M$) and volume ($V$) to determine the number of moles ($\text{moles} = M \times V$). These calculations are essential for precipitation reactions, such as adding silver nitrate ($AgNO_3$) to precipitate chloride ions as silver chloride ($AgCl$). Molarity is also used in neutralization reactions to determine the volume of a base like $NaOH$ needed to neutralize various acids including $HCl$, $H_2SO_4$, and $H_3PO_4$. In the analysis of Gatorade, triiodide ($I_3^-$) is reacted with vitamin C ($C_6H_8O_6$) in a $1:1$ ratio to determine the mass of ascorbic acid present.

Gases in Chemical Reactions

Gas stoichiometry combines the ideal gas equation ($PV = nRT$) with balanced equations to calculate the volume of gaseous reactants or products. For reactions involving multiple gases, volume ratios are equivalent to mole ratios if temperature and pressure remain constant. For instance, the volume of nitrogen ($N_2$) gas generated by the decomposition of sodium azide ($2NaN_3(s) \rightarrow 2Na(s) + 3N_2(g)$) in an air bag can be predicted using its molar mass ($65.02\,g/mol$) and the ideal gas law at specific conditions like $1.00\,atm$ and $358\,K$.

Chemical Reactions and Heat

The heat of reaction specifies the exact amount of energy consumed or produced during a chemical change. Endothermic reactions, such as photosynthesis ($6H_2O(l) + 6CO_2(g) \rightarrow C_6H_{12}O_6(s) + 6O_2(g)$), have a positive heat of reaction ($+2803\,kJ$). Exothermic reactions, like the combustion of methane ($CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$), have a negative heat of reaction ($-560.5\,kJ$). The total solar energy required for photosynthesis is directly proportional to the mass of glucose produced, determined by converting grams to moles and multiplying by the heat of reaction.