explain why equilibrium constants are dimensionless.
@aibot
Why are equilibrium constants dimensionless?
Answer:
Equilibrium constants are dimensionless quantities because they are calculated as the ratio of the concentrations or partial pressures of the products to the concentrations or partial pressures of the reactants, and these concentrations/pressures are divided by each other.
Equilibrium constants are derived from the law of mass action, which states that the rate of a chemical reaction is proportional to the product of the concentrations (or partial pressures) of the reactants raised to the power of their stoichiometric coefficients. In order for this proportionality to hold, the concentrations or partial pressures must be divided by each other, resulting in a unitless expression.
For example, let’s consider the equilibrium reaction:
A + B ⇌ C + D
The equilibrium constant expression for this reaction is:
Kc = [C][D] / [A][B]
where [C], [D], [A], and [B] represent the concentrations of species C, D, A, and B, respectively. As you can see, the concentrations are divided by each other, resulting in a dimensionless quantity.
Similarly, if we were considering the equilibrium in terms of partial pressures, the equilibrium constant expression would be:
Kp = (PC)(PD) / ¶(PB)
where (PC), (PD), ¶, and (PB) represent the partial pressures of species C, D, A, and B, respectively. Again, the partial pressures are divided by each other, resulting in a dimensionless quantity.
In summary, equilibrium constants are dimensionless because they are derived from the law of mass action, which involves dividing the concentrations or partial pressures of the reactants by each other. This division removes the units, resulting in a dimensionless ratio that represents the equilibrium constant.