# Number of gas molecules in activated state vs normal state

I have a simple bimolecular reaction

$$\ce{A + M <=>[k_2][k_1] A^* + M}\tag{1}$$

where $$\ce{A}$$ is a molecule which collides with another molecule $$\ce{M}$$. $$\ce{A^*}$$ is the $$\ce{A}$$ molecule in the activated state. $$k_2$$ is the reaction rate constant in the forward direction and $$k_1$$ is the reaction rate constant in the reverse direction.

The activated complex then forms the product by the following reaction where $$k_3$$ is the reaction rate constant.

$$\ce{A^* ->[k_3] P}\tag{2}$$

For this mechanism it's said that at low pressures $$k_3 > k_2$$ and vice versa at high pressures. Now according to Le Chatelier's principle at low pressures the system moves to produce more gas molecules and vice versa.

Now at low pressures, by low pressures I mean lowering the pressure from a set pressure, $$P$$, reaction step 1 will move to produce more gas molecules. But when we are comparing $$\ce{A}$$ and $$\ce{A^*}$$, which one will have more gas molecules i.e how to deduce in which direction will the step 1 move in response to stresses in terms of more pressure and less pressure?

• A*/A will probably follow the Boltzman distribution E=E0.exp(-Ea/kT), eventually shifted due reaction entropy change. As both (1) and (2) are supposed to be in equilibrium, (2) would have zero net effect on (1). If (2) has not reach equilibrium by P production yet, the ration A*/A would be even smaller. Sep 7 at 7:34
• Sorry Poutnik step 2 is not supposed to be in equilibrium. I have edited the question. Sep 7 at 8:16
• So IMHO [A*]/[A] < [A*]/[A](eq) < 1 // BTW are you sure you mean by K1,K2,K3 equilibrium constants and not kinetic rate constants ? Sep 7 at 9:21
• Instead of K3 K3, use should rather use \$K_3\$ $K_3$ to follow the proper typography. // You can find useful Notation basics and How can I format math/chemistry expressions on Chemistry SE. Sep 7 at 9:32
• Yes I meant kinetic reaction rate constant. I have edited in the question. What do you mean by IMHO [A*]/[A] < [A*]/[A](eq) < 1? Can you please clarify? Sep 7 at 9:36