Can a reaction with positive Gibbs free energy change ever occur?

If you have an endothermic reaction with a negative entropy change, is it still possible to induce the reaction in some way despite the fact that the Gibbs free energy change is positive or all temperatures?

Yes, $\Delta G = -RT\ln K$.

If a reaction is endothermic with a negative entropy change, $\Delta G$ is positive.

That $\Delta G$ is positive only means that $K<1$.

$\Delta G$ would need to approach infinity for $K$ to approach zero.

Therefore, at equilibrium, there will always be some products in principle no matter how unfavorable the reaction.

As a practical matter, the reaction would need to be only slightly endothermic and having only a slight negative entropy change to get a significant amount of product.

However, if the small amount of product is continuously removed from the system, as for example by precipitation from a liquid phase, or gas bubbling out of a liquid phase, or by liquid-liquid extraction, one can keep the reaction going forward.

• Thank you for your reply! Is K the equilibrium constant in this equation? I have not come across this equation before... – Meep Feb 17 '15 at 17:17
• The equation is actually the definition of standard equilibrium constant, so it is a very important equation: goldbook.iupac.org/S05915.html – DavePhD Feb 17 '15 at 17:31