The enthalpy of the reaction forming \(\mathrm{PbO}\) according to the following equation is \(438 \mathrm{~kJ}\). What heat energy (kJ) is released in formation of \(22.3 \mathrm{~g} \mathrm{PbO}(s)\) ? (Atomic weights : \(\mathrm{Pb}=207, \mathrm{O}=16.0\) ) $$ 2 \mathrm{~Pb}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{PbO}(s) $$ (a) \(21.9\) (b) \(28.7\) (c) \(14.6\) (d) \(34.2\)

Stoichiometry is like a recipe for chemistry, providing the precise measurements needed to obtain a desired chemical reaction. It tells us how much of each reactant is needed to react with others and what amount of products will form. In our exercise, stoichiometry helps us to understand the relationship between the reactants, lead (Pb) and oxygen (O2), and the product, lead oxide (PbO). The balanced chemical equation shows a 1:1:1 stoichiometric ratio between the reactant molecule and the product molecules. This is crucial in determining the amount of heat energy released during the formation of a certain amount of PbO. Knowing the stoichiometric coefficients, we can adjust the enthalpy change to match the amount of product formed.

For instance, if we know the total heat energy for the reaction when 2 moles of PbO are formed, we can use stoichiometry to find out how much energy is released for any other amount of PbO produced. This is done by comparing the moles of product in our question to the moles associated with the given enthality of reaction. Simply, if 2 moles release 438 kJ, we can calculate how many kJ 0.1 mole (from our example) will release.

Molar mass calculation is critical for converting between mass and moles of a substance, which is essential in the realm of chemical reactions. It represents the weight of one mole of a substance, usually measured in grams per mole. We calculate molar mass by adding together the atomic weights of all atoms in a molecule. In the example of PbO, the molar mass is calculated by adding the atomic weight of lead (Pb), which is 207 g/mol, and the atomic weight of oxygen (O), which is 16 g/mol, resulting in a molar mass for PbO of 223 g/mol.

This molar mass allows us to translate the 22.3 grams of PbO in the problem into moles, which is necessary to apply the stoichiometry of the reaction to determine the related energy change. Without accurately calculating molar mass, we couldn't bridge the gap between the mass of a substance and the number of moles required to determine the enthalpy change for the specific mass of product formed.

Heat energy calculation involves determining the amount of energy in the form of heat that is either absorbed or released during a chemical reaction. This is often expressed as the enthalpy of reaction and is given in units of joules (J) or kilojoules (kJ). In our example, the enthalpy change, or the heat energy change, for the reaction is given as 438 kJ for the formation of 2 moles of PbO. However, we don't have 2 moles in our problem; instead, we have calculated that we have 0.1 mole of PbO.

To find out the energy released for this amount, we perform a heat energy calculation. It's a simple proportion based on the stoichiometry of the reaction: if 2 moles of PbO correspond to 438 kJ, then the energy for 0.1 mole of PbO would be a tenth of the energy for 1 mole, multiplied by 2 since the energy value given is for 2 moles. These calculations are fundamental to understanding energy changes in chemical reactions, which have widespread implications in fields such as thermochemistry, industrial chemistry, and environmental science.