The value of \(\Delta E_{\mathrm{ryn}}\) for an exothermic reaction is always negative. (a) Why is this so in terms of \(E_{\text {reactants }}\) versus \(E_{\text {products }} ?\) (b) Why is this so in terms of bonds broken in the reactants versus bonds formed in the products?

An exothermic reaction is defined as a reaction that releases energy (usually in the form of heat) to its surroundings. In an exothermic reaction, the energy of the reactants (the initial substances) is higher than the energy of the products (the final substances). Mathematically, we can represent this difference in energy as follows: \[\Delta E_{ryn} = E_{products} - E_{reactants}\] Since the energy of the reactants is greater than the energy of the products, the value of ∆Eryn will be negative. This is because the reactants have lost energy during the reaction. So, when the reactants transform into products in an exothermic reaction, the overall system energy decreases, which makes ∆Eryn negative.

In a chemical reaction, bonds between atoms in the reactants are broken and new bonds are formed in the products. Energy is required to break a bond, while energy is released when a bond is formed. For an exothermic reaction, the amount of energy released when new bonds are formed in the products is greater than the amount of energy required to break the bonds in the reactants. Let's represent the energy required to break the bonds in the reactants as \(E_{bonds \, broken}\) and the energy released when bonds are formed in the products as \(E_{bonds \,formed}\). Since more energy is released in bond formation than is needed to break the bonds, we have: \[E_{bonds \,formed} > E_{bonds \,broken}\] To find the overall energy change in the reaction, we subtract the energy required to break the bonds in the reactants from the energy released during bond formation in the products: \[\Delta E_{ryn} = E_{bonds \,formed} - E_{bonds \,broken}\] In an exothermic reaction, this value would be negative because more energy is released during bond formation than is required to break the bonds in the reactants. As a result, ∆Eryn for an exothermic reaction is always negative.