D22.2 All-Reactant or All-Product Starting Point

At a given temperature, the same equilibrium concentrations would be achieved whether a reaction begins with only reactants present or only products present (the total number of atoms of each kind is the same in either case). This characteristic of equilibrium can help us simply certain equilibrium calculations.

Let’s use an example to consider this characteristic of equilibrium in more detail. What are the equilibrium concentrations of the various aqueous species in a solution of 0.150 M HF at 25 °C? The reaction in question is:

One way to determine the equilibrium concentrations is to start with only reactants. In other words, you make an assumption that the initial concentrations are [HF]₀ = 0.150 M and [H⁺]₀ = [F^–]₀ = 0. This is called the “all-reactant” starting point.

Alternatively, we could solve the problem assuming that all the HF ionizes first, and then the system comes to equilibrium. In other words, [HF]₀ = 0 and [H⁺]₀ = [F^–]₀ = 0.150 M. This is called the “all-product” starting point.

The two approaches give the same results, and show that starting with all-products leads to the same equilibrium conditions as starting with all-reactants.

Note that this is true only if the temperature is the same and the same total number of atoms of each kind is present in both cases. Here, we either started with all reactants, 0.150 M HF (which contains 0.150 mol/L hydrogen atoms and 0.150 mol/L fluorine atoms), or with all products, 0.150 M H⁺ and 0.150 M F^– (which also contains 0.150 mol/L hydrogen atoms and 0.150 mol/L fluorine atoms). Had we started with 0.140 M H⁺ and 0.160 M F^–, the equilibrium concentrations would not be the same.

For the HF(aq) ⇌ H⁺(aq) + F^–(aq) reaction at 25 °C, the equilibrium constant is small: K_c = 6.80 × 10^-4. This reaction is reactant-favored. In Activity: All-reactant Starting Point, the change in concentration is x_all-reactant = 0.00977 M, while in Activity: All-product Starting Point, the change in concentration is x_all-product = 0.140 M. Because the process is reactant-favored, the all-reactant initial concentrations are much closer to the equilibrium concentrations than the all-product initial concentrations. Therefore, the all-reactants situation involves only small changes in concentrations to reach equilibrium (x is small). Recognizing this allows us to make approximations that can significantly simplify the calculations in equilibrium problems.

We know that when K_c << 1, the equilibrium is significantly reactant-favored, and when K_c >> 1, the equilibrium is significantly product-favored. If the ICE table can be set up so that the “initial” concentrations are close to equilibrium (either all-reactant or all-product, depending on the size of K_c), then any change in concentration that is small compared to the initial concentrations can be neglected. “Small” is defined as resulting in an error that does not change the answer within the number of significant figures involved.