Dynamic equilibrium.

Step 1 of 5

Two rates

Two reactions run in the flask at once: pairing, $\mathrm{2NO_2 \rightarrow N_2O_4}$⁠, and splitting, $\mathrm{N_2O_4 \rightarrow 2NO_2}$⁠. Each has its own rate. By collision theory, the pairing rate goes as $[\mathrm{NO_2}]^2$⁠, because each pairing needs two $\mathrm{NO_2}$⁠ molecules to meet, and the splitting rate goes as $[\mathrm{N_2O_4}]$⁠.

In the top chart beside the Scene the orange line is pairing and the blue line is splitting.

Step 2 of 5

The molecules never stop

When the rates are equal, each second exactly as many pairs form as split, so no concentration changes. That state is called dynamic equilibrium: “equilibrium” because nothing changes, and “dynamic” because everything keeps moving.

Step 3 of 5

What is equal

The word “equilibrium” sometimes misleads: it sounds as if something in the flask were split half and half. Compare the two charts beside the Scene, and see exactly what meets and what only stops changing.

Step 4 of 5

The equilibrium constant

At equilibrium $k_f[\mathrm{NO_2}]^2 = k_b[\mathrm{N_2O_4}]$$k_f[\mathrm{NO_2}]^2 =$$k_b[\mathrm{N_2O_4}]$⁠, so the ratio

$K = \frac{[\mathrm{N_2O_4}]}{[\mathrm{NO_2}]^2} = \frac{k_f}{k_b}$$K =$$\frac{[\mathrm{N_2O_4}]}{[\mathrm{NO_2}]^2} =$$\frac{k_f}{k_b}$⁠

is a fixed number that depends only on the temperature: the equilibrium constant. In the expression the products go on top and the reactants underneath, each concentration to the power of its coefficient in the equation. Here Temperature is fixed at 348 K, 75 °C.

Step 5 of 5

Which way the mix moves

You can work out the same expression at any moment, even before equilibrium. Then it is called the reaction quotient, $Q$⁠. The line under the bottom chart compares $Q$⁠ with $K$⁠. Here Time is fixed at an early moment, before the flask has settled.