# How does concentration effect dynamic equilibrium?

Jun 18, 2015

The Law of Mass Action states that when a system (e.g., chemical reaction) is at equilibrium, the ratio of products and reactant concentrations is equal to the equilibrium constant for that reaction. If we change the concentration of any species (e.g., by adding reactant to the mixture), then the reaction will shift toward reactants or products in order to restore the ratio of concentrations to the equilibrium value.

#### Explanation:

Example:
When $N {O}_{2}$ is in equilibrium with its dimer, ${N}_{2} {O}_{4}$, the ratio of concentrations (expressed in mol/L) is equal to 4.7 at room temperature.

$2 N {O}_{2} \leftrightarrow {N}_{2} {O}_{4}$

${K}_{c} = \frac{\left[{N}_{2} {O}_{4}\right]}{{\left[N {O}_{2}\right]}^{2}} = 4.7$

So, if the concentration of $N {O}_{2}$ is 0.02M, then we know that the equilibrium concentration of ${N}_{2} {O}_{4}$ must be $4.7 {\left(0.02\right)}^{2} = 1.88 \times {10}^{-} 3 M$

If the system is in a 1L container at constant volume and temperature and we add 0.03 mol of $N {O}_{2}$, then for a short time the concentration of $N {O}_{2}$ is increased to 0.05M. The non-equilibrium ratio of concentrations is
$Q = \frac{\left[{N}_{2} {O}_{4}\right]}{{\left[N {O}_{2}\right]}^{2}} = \frac{1.88 \times {10}^{-} 3}{{\left(0.05\right)}^{2}} = 0.75$
which is smaller than the equilibrium ratio of 4.7. In order to restore equilibrium, the reaction shifts toward products, consuming $N {O}_{2}$ and producing ${N}_{2} {O}_{4}$ until the equilibrium rations are restored:

${K}_{c} = \frac{\left[{N}_{2} {O}_{4}\right]}{{\left[N {O}_{2}\right]}^{2}} = \frac{0.00188 + x}{{\left(0.05 - 2 x\right)}^{2}} = 4.7$

Solving this quadratic equation for the change in concentration, $x$, gives $x = 5.37 \times {10}^{-} 3 M$. The new equilibrium concentrations will be
$\left[{N}_{2} {O}_{4}\right] = 0.00188 + 0.00537 = 0.00725 M$
$\left[N {O}_{2}\right] = 0.05 - 2 \left(0.00537\right) = 0.0392 M$
and the new ratio is
$\frac{\left[{N}_{2} {O}_{4}\right]}{{\left[N {O}_{2}\right]}^{2}} = 4.72$, which is equal to the equilibrium constant within the rounding error of the significant digits of the calculation.