Explain in terms of energy why a chemical reaction could never turn lead into gold.

At its core, the energy conservation principle states that within a closed system, the total amount of energy remains constant—it is conserved. This means that energy can neither be created nor destroyed, but it can transform from one form to another. For instance, in chemical reactions, this principle is observed when the energy stored in chemical bonds is released or absorbed. However, the total energy balance before and after the reaction is the same.
Simple examples of energy transformation are a battery powering a light bulb, turning chemical energy into light and heat energy, or photosynthesis, where plants convert solar energy into chemical energy. Understanding this principle is crucial because it limits the possible outcomes of chemical processes, indicating that no chemical reaction could provide the enormous energy required to change the core structure of an atom and thereby transmute elements like lead into gold.

The atomic number is a fundamental characteristic that distinguishes one element from another. It is defined as the number of protons present in the nucleus of an atom. The atomic number, therefore, determines the identity of an element. For instance, hydrogen, the simplest element, has just one proton and an atomic number of 1, while carbon has six protons and an atomic number of 6.
Since each element has its unique atomic number, elements can be listed in order based on their atomic number in the periodic table. This number also coincides with the number of electrons in a neutral atom, which dictates the atom's chemical behavior. However, in chemical reactions, the atomic number of an element remains unchanged, as the reactions only affect the electronic configurations or the way atoms combine, not the nuclei themselves.

Transmutation involves changing the identity of an element by altering its atomic number, typically through nuclear reactions and not chemical reactions. Historically, alchemists sought to transmute base metals into noble metals like gold, a process now known to require changing the nucleus of an atom.
In modern science, transmutation is achieved through processes such as radioactive decay where unstable isotopes naturally transform into more stable elements, or in nuclear reactors where neutron capture can result in an element changing into another. An element's atomic number can increase or decrease through these nuclear processes due to the gain or loss of protons in the nucleus. This sort of nuclear alchemy requires extreme conditions and energies that eclipse anything achievable through mere chemical reactions.

While often confused due to their fundamental role in changing substances, nuclear and chemical processes are vastly different in terms of the changes they produce and the energies involved.
Chemical processes revolve around the interactions of electrons to form and break chemical bonds, shaping the properties and behaviors of molecules. These reactions are governed by the rules of classical chemistry, often observable in everyday life, like when iron rusts or when baking soda reacts with vinegar.
On the other hand, nuclear processes involve changes to the nucleus of atoms, including the protons and neutrons that compose it. These shifts can alter the very identity of an element through transmutation. Nuclear reactions, such as those powering the sun or occurring in atomic bombs, involve energies millions of times greater than those in chemical processes. It is due to the immense energy threshold to effect nuclear change that transmuting elements like lead into gold through chemistry is unfeasible. Nuclear reactions also disregard the conservation of mass that typically holds in chemical reactions, adhering instead to the conservation of mass-energy as described by Einstein's famous equation, E=mc².