Why is the reaction quotient Q always equal to one at standard state?

Question

I understand that at equilibrium, $Q$ is equal to $K$. This should not depend how I express concentrations (as amount of substance concentrations $c$ or as partial pressures $p$ or as molality $b$ or as mole fraction $x$) and which units I use (e.g. partial pressure in Pa or in atm) as long as I am consistent.

Various expressions rely on $Q$ being dimensionless (because we take its logarithm) and on being equal to one when all species are at standard state. For example, the equation for calculating the change in Gibbs free energy for a reaction should result in the standard Gibbs free energy for the standard state:

$$\Delta_r G = \Delta_r G^\circ + R T \ln Q = \Delta_r G^\circ \text{(for standard state)}$$

This requires that $Q = 1$ at standard state. The Nernst equation is another (related) example.

What I am wondering about is why $Q$ is always equal to one at standard state, no matter how I express concentrations when calculating reaction quotients.

For example, if I have a reaction like $\ce{A(g) + B(g) -> C(g)}$, doesn't the value of $Q$ change if I switch from concentration $c$ to partial pressure $p$, or use units of atm instead of Pa when measuring partial pressures? Come to think of it, doesn't the value of the equilibrium constant $K$ change as well when I change measures or units of concentration?

Answer 1

As already said in the comments, you cannot use any unit you want in the reaction quotient; it has to be formulated in terms of activity (for solutes) or fugacity (for gases).

The "standard state" of a chemical species is a reference state in which the properties of the chemical species are defined. This standard state is a theoretical state, it does not need to be practically reachable by the chemical species. By definition, solutes in standard state have an activity of 1, and gas have a fugacity of 1. Therefore, whatever you reaction, if all the species are assumed to be in standard state, the reaction quotient will be a product of 1s, that is, 1.