Question

Consider a \(0.10-M \mathrm{H}_{2} \mathrm{CO}_{3}\) solution and a \(0.10-M \mathrm{H}_{2} \mathrm{SO}_{4}\) solution. 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\(M\) b. The \(\left[\mathrm{H}^{+}\right]\) is 0.10\(M .\) c. The \(\left[\mathrm{H}^{+}\right]\) is between 0.10\(M\) and 0.20 \(\mathrm{M}\) d. The \(\left[\mathrm{H}^{+}\right]\) is 0.20 \(\mathrm{M}\)

Short answer

For the 0.10 M H₂CO₃ solution, the [H⁺] is less than 0.10 M (option a) because it is a weak acid and only partially dissociates. For the 0.10 M H₂SO₄ solution, the [H⁺] is 0.20 M (option d) because it is a strong acid and completely dissociates, contributing 2 H⁺ ions per molecule.

Step-by-step solution

Acid Dissociation and Types of Acids

We are dealing with two acids, H₂CO₃ (carbonic acid) and H₂SO₄ (sulfuric acid). To find the [H⁺] of each solution, we need to understand how each acid dissociates in water. Carbonic acid (H₂CO₃) is a weak acid, which means it only partially dissociates in water: \(H_{2}CO_{3} \rightleftharpoons H^{+} + HCO_{3}^{-}\) Sulfuric acid (H₂SO₄) is a strong acid, which means it completely dissociates in water: \(H_{2}SO_{4} \rightarrow 2H^{+} + SO_{4}^{2-}\)

Comparison of [H⁺] Concentrations

For the 0.10 M H₂CO₃ solution: Since H₂CO₃ is a weak acid, it only partially dissociates, meaning that the [H⁺] will not reach 0.10 M. Thus, the [H⁺] is less than 0.10 M for the H₂CO₃ solution, which corresponds to option a. For the 0.10 M H₂SO₄ solution: Since H₂SO₄ is a strong acid, each molecule of H₂SO₄ will contribute 2 H⁺ ions to the solution. Therefore, the [H⁺] would be double the initial concentration, which is 2*(0.10 M) = 0.20 M. This corresponds to option d. So the best answer for this exercise is a combination of option a for the H₂CO₃ solution and option d for the H₂SO₄ solution.

Key concepts

Weak Acid

A weak acid is an acid that doesn't completely dissociate in water. When placed in an aqueous solution, it only partially releases its hydrogen ions (H⁺). This means that not all the acid molecules break apart, leading to a relatively low concentration of hydrogen ions in the solution compared to the initial acid concentration.

For example, carbonic acid (H₂CO₃) is a classic case of a weak acid. Its dissociation in water can be represented by the equation: \(H_{2}CO_{3} \rightleftharpoons H^{+} + HCO_{3}^{-}\). This equation explains that H₂CO₃ does not completely convert into hydrogen and bicarbonate ions; instead, it establishes an equilibrium where both the acid and its ions are present.

Because weak acids do not fully dissociate, the hydrogen ion concentration ([H⁺]) is less than the concentration of the acid itself. So, a 0.10 M carbonic acid solution will have an [H⁺] that is less than 0.10 M, aligning with option a from the exercise. Understanding the nature of weak acids is crucial for predicting the behavior of many biological and chemical systems.

Strong Acid

Strong acids are known for their complete dissociation in water. When a strong acid is dissolved in an aqueous solution, it fully releases its hydrogen ions (H⁺), leaving no undissociated acid molecules behind. This total ionization results in a high concentration of hydrogen ions compared to the concentration of the acid.

Sulfuric acid (H₂SO₄) is an excellent example of a strong acid. Its dissociation, especially the first dissociation step, is complete: \(H_{2}SO_{4} \rightarrow 2H^{+} + SO_{4}^{2-}\). Notice here that each molecule of sulfuric acid releases two hydrogen ions. Due to this complete dissociation, the hydrogen ion concentration in a 0.10 M H₂SO₄ solution is 0.20 M, because each H₂SO₄ releases two H⁺ ions. This fact corresponds to option d in the exercise. Knowing about strong acids' characteristics helps in accurately determining solution behaviors, crucial for fields ranging from industrial chemistry to biochemistry.

Hydrogen Ion Concentration

Hydrogen ion concentration ([H⁺]) is a key parameter that determines a solution's acidity level. It directly influences the pH of the solution, which is calculated as \(pH = -\log[H^{+}]\). The concentration of hydrogen ions is an indicator of how acidic or basic a solution is—lower [H⁺] values mean a more basic solution, while higher [H⁺] values indicate a more acidic environment.

It's important to recognize that the degree of dissociation of an acid in a solution determines the [H⁺]. In the case of weak acids like carbonic acid, the partial dissociation results in lower [H⁺] compared to the initial acid concentration. Meanwhile, strong acids like sulfuric acid contribute more [H⁺] due to their complete dissociation.

In practical applications, monitoring the hydrogen ion concentration is crucial for processes like fermentation in food production and maintaining physiological pH in human bodies. Understanding these differences between weak and strong acids is fundamental in analyzing various chemical reactions and their resulting acidity.