Consider a \(0.10 \mathrm{M} \mathrm{H}_{2} \mathrm{CO}_{3}\) solution and a \(0.10 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) solu- tion. Without doing any detailed calculations, choose one of the following statements that best describes the \(\left[\mathrm{H}^{+}\right]\) of each solution and explain your answer. a. The \(\left[\mathrm{H}^{+}\right]\) is less than \(0.10 \mathrm{M}\). b. The \(\left[\mathrm{H}^{+}\right]\) is \(0.10 \mathrm{M}\). c. The \(\left[\mathrm{H}^{+}\right]\) is between \(0.10 \mathrm{M}\) and \(0.20 \mathrm{M}\). d. The \(\left[\mathrm{H}^{+}\right]\) is \(0.20 \mathrm{M}\).

Understanding acid strength is crucial when studying chemistry, particularly in the context of how acids react in solution. Acid strength refers to the tendency of an acid to donate protons (hydrogen ions, \( \text{H}^+ \)) when in an aqueous solution. Strong acids, like sulfuric acid (\( \text{H}_2\text{SO}_4 \)), dissociate completely in water, releasing all of their hydrogen ions. This characteristic leads to high hydrogen ion concentrations in the solution.

Conversely, weak acids like carbonic acid (\( \text{H}_2\text{CO}_3 \)) only partially dissociate, meaning only a fraction of the available hydrogen ions is released into the solution. As a result, weak acids lead to lower hydrogen ion concentrations. It is worth noting that the extent of ionization greatly impacts the pH of the solution and its reactivity with other substances.

Ionization of acids is the process by which an acid releases hydrogen ions into a solution. The ionization process is commonly represented by a chemical equilibrium between the non-ionized acid and the ions produced. For a generic acid, \( HA \), the ionization reaction can be written as:\[ HA \leftrightarrow \text{H}^+ + A^- \]

In water, strong acids fully ionize, shifting the equilibrium far towards the products, resulting in a large concentration of \( \text{H}^+ \). On the other hand, weak acids only partially ionize, which means that at equilibrium, there is a significant amount of the non-ionized acid remaining alongside the ions. This difference in ionization levels is a fundamental concept when predicting the behavior of acids in various chemical reactions.

Hydrogen ion concentration, often represented as \( [\text{H}^+] \), is a measure of the amount of hydrogen ions present in a solution. It serves as an essential indicator of a solution's acidity. The higher the concentration of hydrogen ions, the more acidic the solution is, which corresponds to a lower pH value.

To illustrate, a 0.10 M solution of a strong acid would tend to have a higher \( \text{H}^+ \) concentration, potentially approaching 0.10 M (or higher if the acid can provide more than one \( \text{H}^+ \) per molecule). In contrast, a 0.10 M solution of a weak acid will have a lower \( \text{H}^+ \) concentration because not all of the acid molecules will ionize. Understanding this concept is vital when determining the pH of a solution and its corresponding chemical behavior.

The distinction between weak and strong acids is an important concept in chemistry. It primarily involves the degree of ionization that acids undergo in aqueous solution.

Strong acids, such as \( \text{H}_2\text{SO}_4 \), ionize completely, which means they release all their available hydrogen ions into the solution, enhancing their reactivity. In the exercise, sulfuric acid's full ionization in the first dissociation step, along with the partial ionization of the bisulfate ion (\( \text{HSO}_4^- \)), leads to an \( \text{H}^+ \) concentration that is between 0.10 M and 0.20 M.

In contrast, weak acids like \( \text{H}_2\text{CO}_3 \) only partially ionize in solution. This partial ionization leads to lower hydrogen ion concentrations, as not all of the acid molecules contribute to \( \text{H}^+ \) ions. Consequently, the \( \text{H}^+ \) concentration for a weak acid solution like \( \text{H}_2\text{CO}_3 \) is less than 0.10 M, which also highlights the importance of understanding the nature of the acid when anticipating its ion concentration and its effect on pH.