Temperature and Thermodynamic Favorability

Delta G tells you whether a reaction is thermodynamically favored: negative means yes, positive means no. It's built from two pieces, delta H and delta S, combined as delta G = delta H - T delta S. Delta H barely changes with temperature, but the T delta S term scales directly with T. So temperature acts like a dial that controls how much the entropy term matters compared to the enthalpy term.

Sort the four sign combinations and you get three outcomes. Delta H negative, delta S positive: delta G is negative at every temperature, always favored. Delta H positive, delta S negative: delta G is positive at every temperature, never favored. The other two combinations are sometimes: delta H negative and delta S negative is favored only at low T, where T delta S stays small enough not to overturn a negative delta H; delta H positive and delta S positive is favored only at high T, where T delta S finally grows large enough to beat delta H. The crossover temperature, where delta G equals zero, is found by solving delta H = T delta S, giving T = delta H / delta S.

This is why calcium carbonate sits quietly on a shelf but decomposes into CaO and CO₂ when you heat it in a kiln: delta H and delta S are both positive, so the reaction needs a high T delta S term to win out. Graphing delta G against T gives a straight line, delta H as the y-intercept and -delta S as the slope, and the x-intercept is that crossover temperature. This same balance of enthalpy against entropy reappears later as cell voltage in electrochemistry, just told in different units.