foundations

Three letters, one equation, the universe's decision rule. ΔG = ΔH - TΔS Every chemist knows this formula. Most memorize it for exams and forget the meaning. But this equation encodes the competition between energy and entropy, with temperature as referee. Understanding it—really understanding it—means understanding why

In the 1870s, Josiah Willard Gibbs was a professor at Yale with no salary. He taught for free, published in obscure journals, and created the theoretical framework that would become the foundation of chemistry, materials science, and biochemistry. His key insight: reactions don't just want to minimize energy.

Every second, your body hydrolyzes 10^21 ATP molecules. By day's end, you've turned over roughly your body weight in ATP. This single molecule powers everything—muscle contraction, nerve impulses, protein synthesis, cell division. ATP isn't the most energy-rich molecule. It's not

Every reaction has a destination. Not where all reactants become products, and not where nothing happens. The destination is equilibrium—the point where forward and reverse reactions balance perfectly. At equilibrium, ΔG = 0. The system has found its free energy minimum. No driving force remains in either direction. This isn&

Temperature appears in ΔG = ΔH - TΔS as a simple multiplier. But its influence is deeper than that. The Gibbs-Helmholtz equation reveals how temperature changes shift the free energy landscape. It shows why reactions that are non-spontaneous at one temperature become spontaneous at another. And it connects the temperature derivative

Water freezes at 0°C. This seems like a fact about water, but it's really a fact about free energy. At that precise temperature, the free energy curves of ice and liquid water cross. Above, liquid wins. Below, ice wins. At exactly 0°C, they tie. Phase transitions