The concentration of a species in a chemical reaction can change over time as the reaction progresses. However, at steady state, the concentration of the species remains constant. This means that the rate of formation of the species is equal to the rate of its consumption.
In order to understand why the concentration remains constant at steady state, let’s consider a simple reaction mechanism involving species A, B, and C. The reaction is as follows:
A -> B -> C
In this mechanism, species A is converted into species B, which is then converted into species C. We can write the rate equation for the formation of species B as:
Rate of formation of B = k1[A] – k2[B]
Here, k1 is the rate constant for the conversion of A to B, and k2 is the rate constant for the conversion of B to C. The first term on the right-hand side represents the rate of formation of B, while the second term represents the rate of consumption of B.
At steady state, the rate of formation of B is equal to the rate of its consumption. This can be mathematically expressed as:
K1[A] – k2[B] = 0
Rearranging this equation, we get:
K1[A] = k2[B]
From this equation, it is clear that the concentration of B remains constant at steady state, as long as the concentrations of A and the rate constants k1 and k2 are constant.
To illustrate this concept, let’s consider a real-life example. Imagine you are baking cookies and following a recipe that requires the conversion of flour (A) into dough (B), which is then converted into baked cookies (C). As you mix the ingredients, the concentration of flour decreases while the concentration of dough increases. However, once the dough is formed, its concentration remains constant as long as you are continuously baking cookies at a steady rate. The rate at which you are consuming dough (to make cookies) is equal to the rate at which you are forming dough (from flour), resulting in a constant concentration of dough.
At steady state, the concentration of a species remains constant because its rate of formation is equal to its rate of consumption. This concept is important in the derivation of rate laws using the steady-state approximation.