# What is the meaning of K in the thermodynamic equation for equilibrium constant?

I just studied the formula for equilibrium constant in thermodynamics. But when an equilibrium is established $$\Delta G$$ is always $$0$$ as told by my teacher. Then $$k$$ has to be always $$1$$ whenever an equilibrium is established. But that does not happen always as equilibrium constant is not always $$1$$. I want to know where I am going wrong here. And this $$k$$ is $$k_\mathrm p$$ or $$k_\mathrm c$$ ? Any help will be really appreciated. Thanks in advance.

You are confused between $$\Delta G$$ and $$\Delta G^{\varnothing}$$, the standard free energy change.

The equation you are describing is actually:

$$\Delta G^{\varnothing} = -RT \ln K$$

These numbers are fixed for some reference temperature and pressure.

The specific $$\Delta G$$ you are referring to is a function of $$Q$$, the reaction quotient, which describes the position of your equilibrium. Its value, relative to $$K$$, will determine whether $$\Delta G$$ is positive, negative, or zero.

Specifically,

$$\Delta G = \Delta G^{\varnothing} + RT \ln Q$$

$$Q$$ is computed the same as $$K$$ except that you plug in the actual concentrations you have, not the values at equilibrium.

There are three cases to consider:

1. $$Q = K$$. This corresponds to $$\Delta G = 0$$. We are equilibrium.
2. $$Q > K$$. $$\Delta G > 0$$. We are favoring products to much. We need to shift the reaction back to decrease the value of $$Q$$.
3. $$Q < K$$. $$\Delta G < 0$$. We are favoring reactants to much. We need to shift the reaction forward to increase the value of $$Q$$.
• Thank you Sir. But I am still confused about this k . Is it kp or kc? – Avinash Sharma Oct 9 '18 at 2:30
• Technically, it is neither, but it's closer to $K_{\mathrm{c}}$ than $K_{\mathrm{p}}$. – Zhe Oct 9 '18 at 13:20