(a) How much ethylene glycol must be added ( to \(20.0 \mathrm{~kg}\) of dimethyl terephthalate to produce a linear chain structure of poly(ethylene terephthalate) according to Equations \(15.9 ?\) (b) What is the mass of the resulting polymer?

Understanding stoichiometry is fundamental to chemistry. It is the calculation of the quantitative or measurable relationship between the reactants and products in a balanced chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a reaction, which is vital for the synthesis of compounds such as poly(ethylene terephthalate) (PET).

Stoichiometry relies on the law of conservation of mass, where the total mass of the reactants equals the total mass of the products. This is because matter is neither created nor destroyed during a chemical reaction. For example, when synthesizing PET, we use the stoichiometric ratio from the balanced equation to determine how much ethylene glycol is needed for a given amount of dimethyl terephthalate. If the balanced equation dictates a 1:1 ratio, then one mole of dimethyl terephthalate requires one mole of ethylene glycol to produce the desired amount of PET and byproduct, thereby illustrating the practical importance of stoichiometry in chemical synthesis.

The molar mass of a substance is the weight of 6.022 x 10²³ (Avogadro's number) atoms or molecules of that substance and is expressed in grams per mole (g/mol). Molar mass is an essential concept in stoichiometry as it converts between the mass of a substance and the number of moles, providing a bridge between the macroscopic and molecular worlds.

To calculate the molar mass of a compound, sum the atomic masses of all the atoms present in its molecular formula. For instance, in the synthesis of PET, determining the molar mass of both the reactants and products is a critical step that impacts all subsequent calculations, including how much of each reactant is needed and the final mass of the polymer produced. Accuracy in these calculations ensures the efficiency and sustainability of manufacturing processes, especially in industrial applications where large quantities are involved.

Chemical reactions need to be balanced to reflect the conservation of mass. In a balanced equation, the number of atoms for each element in the reactants equals the number of atoms in the products. Balancing chemical equations is not only a crucial skill in chemistry but is also particularly important in the synthesis of polymers like PET.

When synthesizing PET, the balanced chemical reaction guides stoichiometric calculations, ensuring the correct proportions of reactants are used. An unbalanced reaction could lead to excess of one reactant or a shortage of another, resulting in an incomplete reaction or wastage of materials. The balanced equation for PET synthesis, presented in the exercise solution, shows the reaction between dimethyl terephthalate and ethylene glycol forming the polymer and methanol as a side product. This balanced equation ensures a clear understanding of the reaction's specific requirements and the stoichiometry involved in producing a valuable material used in various applications such as fabric, packaging, and plastic bottles.