Question

Which of the following statements are true regarding a \(1.0-M\) solution of a strong acid \(\mathrm{HA}\) at \(25^{\circ} \mathrm{C} ?\) (Choose all that apply.) (a) \(\left[\mathrm{A}^{-}\right]>\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) (b) The \(\mathrm{pH}\) is 0.00 . (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \mathrm{M}\) (d) \([\mathrm{HA}]=1.0 \mathrm{M}\)

Short answer

Statements (b) and (c) are true.

Step-by-step solution

Understanding Strong Acid Dissociation

A strong acid like \( \mathrm{HA} \) completely dissociates in water. This means that for a \( 1.0 \mathrm{M} \) solution of \( \mathrm{HA} \), the concentration of \( \mathrm{H}_3\mathrm{O}^+ \) ions produced is also \( 1.0 \mathrm{M} \). Thus, the equation can be represented as: \[ \mathrm{HA}(aq) \rightarrow \mathrm{H}_3\mathrm{O}^+(aq) + \mathrm{A}^-(aq) \] Since it completely dissociates, \( [\mathrm{A}^-] = [\mathrm{H}_3\mathrm{O}^+] \).

Evaluating Statement (a)

Statement (a) claims \( \left[\mathrm{A}^{-}\right] > \left[\mathrm{H}_{3} \mathrm{O}^{+}\right] \). However, since \( \mathrm{HA} \) fully dissociates, \( \left[\mathrm{A}^{-}\right] = \left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = 1.0 \mathrm{M} \). Therefore, statement (a) is false.

Evaluating Statement (b)

The \( \mathrm{pH} \) of a solution is calculated using the formula: \( \mathrm{pH} = -\log_{10} \left[ \mathrm{H}_{3} \mathrm{O}^{+} \right] \). Since \( \left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = 1.0 \mathrm{M} \), \( \mathrm{pH} = -\log_{10}(1.0) = 0 \). Therefore, statement (b) is true.

Evaluating Statement (c)

Statement (c) claims that \( \left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = 1.0 \mathrm{M} \). As discussed in Step 1, for a strong acid like \( \mathrm{HA} \), \( \left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = 1.0 \mathrm{M} \) since the acid completely dissociates. Therefore, statement (c) is true.

Evaluating Statement (d)

Statement (d) claims that \( [\mathrm{HA}] = 1.0 \mathrm{M} \). However, because \( \mathrm{HA} \) completely dissociates in water, there are actually no \( \mathrm{HA} \) molecules in solution, meaning \( [\mathrm{HA}] = 0 \). Therefore, this statement is false.

Key concepts

pH calculation

Calculating the pH of a solution is a fundamental skill in acid-base chemistry that allows us to determine the acidity or alkalinity of the solution. The pH is calculated using the formula: \[ \text{pH} = -\log_{10} \left[ \text{H}_3\text{O}^+ \right] \]This calculation requires knowledge of the concentration of hydronium ions, \([\text{H}_3\text{O}^+]\), in the solution. For a strong acid like HCl or HNO₃, which dissociates completely in water, the pH can be directly determined from the initial acid concentration. In a 1.0 M solution of a strong acid, \([\text{H}_3\text{O}^+] = 1.0\text{ M}\), resulting in a pH of 0.Remember that the scale of pH is logarithmic, meaning each whole number change on the scale represents a tenfold change in acidity or basicity. As such, a pH of 0 implies a very high concentration of hydronium ions, marking the solution as highly acidic.

concentration of hydronium ions

The concentration of hydronium ions in a solution is crucial for determining both the solution's pH and its chemical behavior. When dealing with strong acids, understanding their complete dissociation becomes pivotal. Strong acids such as hydrochloric acid (HCl) release hydronium ions, \(\text{H}_3\text{O}^+,\) upon dissociation in water. For a 1.0 M solution of a strong acid, the concentration of hydronium ions is equal to the initial concentration of the acid.This is because strong acids dissociate entirely:\[ \text{HA}(\text{aq}) \rightarrow \text{H}_3\text{O}^+(\text{aq}) + \text{A}^-(\text{aq}) \]Therefore, if you start with a 1.0 M solution of a strong acid, it will fully convert to produce 1.0 M \(\text{H}_3\text{O}^+\) ions. This complete dissociation simplifies calculations as it directly sets the concentration of hydronium ions and helps us easily compute the pH.

complete dissociation

Complete dissociation is a characteristic feature of strong acids and bases. In the case of our strong acid \(\text{HA},\) we know it dissociates entirely in water. This results in all the acid molecules converting to hydronium ions \(\text{H}_3\text{O}^+\) and their respective conjugate base \(\text{A}^-\). Complete dissociation is crucial because it directly affects the concentration of ions in solution, influencing both pH and overall reaction tendencies.This is the fundamental equation illustrating complete dissociation:\[ \text{HA}(\text{aq}) \rightarrow \text{H}_3\text{O}^+(\text{aq}) + \text{A}^-(\text{aq}) \]Complete dissociation means that there are no undissociated \(\text{HA}\) molecules left in the solution, setting \([\text{HA}] = 0\) and \([\text{H}_3\text{O}^+] = [\text{A}^-] = 1.0\text{ M}\)\ for a 1.0 M solution. Understanding this concept is key to correctly predicting and explaining various chemical behaviors and properties in acid-base chemistry.

acid-base chemistry

Acid-base chemistry is a broad field that revolves around the behavior and interactions between acids and bases in different environments. Inherent in this is the understanding of strong and weak acids, dissociation, and the role of hydronium ions. Strong acids are notable for their complete dissociation, as observed with hydrochloric acid (HCl) or nitric acid (HNO₃), drastically affecting the solution's pH and reactivity.In acid-base reactions, the transfer of protons (\(\text{H}^+\) ions) is a central theme. Strong acids tend to readily donate these protons to water, resulting in increased \(\text{H}_3\text{O}^+\) concentration, whereas bases tend to accept protons, reducing the \(\text{H}_3\text{O}^+\) concentration and increasing pH.Key concepts in acid-base chemistry involve recognizing how the strength of an acid or base determines its dissociation and hence its impact on the solution:\

• Strong Acids and Bases: Completely dissociate, altering pH significantly.
• Weak Acids and Bases: Partially dissociate, requiring equilibrium calculations for pH.

Understanding acid-base chemistry is essential in predicting outcomes in both natural processes and industrial applications.