Which of the following concentrations would be practically...

Which of the following concentrations would be practically equal in a calculation of the equilibrium concentrations in a $0.134-M$ solution of $\mathrm{H}_{2} \mathrm{CO}_{3},$ a diprotic acid: $\left[\mathrm{OH}^{-}\right],\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right],\left[\mathrm{HCO}_{3}-\right]$ $\left[\mathrm{CO}_{3}^{2-}\right] ?$ No calculations are needed to answer this question.

Key Concepts

Use of Equilibrium Approximations

When solving equilibrium problems with weak acids, approximations are often made by assuming that species present only in trace amounts (due to very small equilibrium constants) are negligible. This simplification allows one to identify which concentrations are effectively non?contributing and, in some cases, reveals that two very low concentrations—such as those of hydroxide ions and a scarcely produced conjugate base—can be practically equal in magnitude.

Autoionization of Water

The self-ionization of water, described by its equilibrium constant Kw, relates the concentrations of hydrogen and hydroxide ions. In an acidic solution, the concentration of hydroxide ions is determined by the relationship [OH?] = Kw/[H?]. Because of the low pH in such solutions, [OH?] is very small, often approaching the magnitude of other minor species formed by very weak secondary equilibria.

Diprotic Acid Dissociation

Diprotic acids release two protons in successive steps. The first deprotonation typically has a much larger equilibrium constant (Ka1) than the second deprotonation (Ka2), which means the first dissociation proceeds to a much greater extent than the second. In equilibrium calculations, this stepwise behavior significantly affects the distribution of species in solution.

Equilibrium Constant Comparison

Comparing the magnitudes of the acid dissociation constants and the water ionization constant (Kw) is essential in equilibrium calculations. For a weak, diprotic acid, the large difference between the first and second dissociation constants means that while most acid remains in the undissociated form, the concentrations of species from the second dissociation are extremely small. This comparison can lead to the insight that certain species, though formed through different processes, can have numerically similar equilibrium concentrations when their governing constants are of similar orders of magnitude.

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