# What is the relationship between equilibrium constant and delta G?

DeltaG tells us whether a reaction is spontaneous or not. If delta G is negative, the reaction is spontaneous, and if delta G is positive, the reaction is not spontaneous. There is a relationship between deltaG and equilibrium constant, K. It is given by the formula **deltaG=-RTlnK**, where R is the gas constant (8.314J K−1 mol−1), T is the temperature in Kelvin, and K is the equilibrium constant.

Can we figure out if the reaction is spontaneous or not just from equilibrium constant K? Yes!

If we plug in ln of a number less than zero on our calculator, we will get a negative number. This, in turn, will turn delta G into a positive number and therefore when **k<0, deltaG>0**, and the reaction is non spontaneous.

For values of k above 1, delta G is less than zero, making the reaction spontaneous. For k=1, lnk=0, making delta G=0.

Note: If a reaction is spontaneous in one direction, it will be non spontaneous in the opposite direction and vice versa.

Some other important formulas for deltaG are:

deltaG = deltaH-TdeltaS, where deltaH is enthalpy and delta S is change in entropy, and T is the temperature in Kelvin. Note that enthalpy or entropy alone does not tell us whether a reaction is spontaneous or not. It is delta G that we need to use to figure out the spontaneity of the reaction.

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