Question

A solution of \(0.10 M \mathrm{HCl}\) has a \(\mathrm{pH}=1.00\), whereas a solution of \(0.10 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) has a \(\mathrm{pH}=2.88\). Explain.

Short answer

The strong acid HCl fully dissociates, giving pH 1.00; CH₃COOH is weaker, only partially dissociating, resulting in pH 2.88.

Step-by-step solution

Understanding Molarity

The molarity of a solution refers to the concentration of a given solute in a solution. Both solutions in this problem, HCl and CH₃COOH, have a molarity of 0.10 M, meaning there are 0.10 moles of HCl or CH₃COOH per liter of solution.

Identifying the Type of Acid

Hydrochloric acid (HCl) is a strong acid, while acetic acid (CH₃COOH) is a weak acid. A strong acid completely dissociates in solution, while a weak acid only partially dissociates.

Analyzing Dissociation in Solution

Since HCl is a strong acid, it fully dissociates into H⁺ and Cl⁻ ions in solution, resulting in a high concentration of H⁺ ions, approximately equal to the initial concentration, 0.10 M. On the other hand, CH₃COOH, being a weak acid, only partially dissociates, leading to much fewer H⁺ ions.

Calculating the pH

The pH is calculated using the formula: \( \mathrm{pH} = -\log[\mathrm{H^+}] \). For the 0.10 M HCl solution, the concentration of H⁺ ions is approximately 0.10 M, so \( \mathrm{pH} = -\log(0.10) = 1.00 \). For the 0.10 M CH₃COOH solution, the concentration of H⁺ is less because it is a weak acid, explaining a higher \( \mathrm{pH} = 2.88 \).

Concluding Explanation

The difference in pH values arises from the difference in the extent of dissociation of the acids. The strong HCl acid dissociates completely, resulting in a lower pH, while the weak CH₃COOH only partially dissociates, leading to a higher pH.

Key concepts

Molarity

The term "molarity" is crucial in understanding solutions. It measures how concentrated a solution is. More specifically, it tells us how many moles of a solute are dissolved in a liter of solution. For instance, if you have a 0.10 M solution, it means there are 0.10 moles of solute per liter of the entire solution.
In the given problem, both hydrochloric acid (HCl) and acetic acid (CH₃COOH) have a molarity of 0.10 M. This means the concentration of each solute in their respective solutions is the same. However, this does not equate to the same behavior, especially regarding their roles in pH.

• Molarity is denoted by the capital letter M, followed by the solute concentration.
• It's useful for predicting quantitative reactions in solutions.
• Understanding molarity helps in grasping how other solution properties change with concentration.

By understanding molarity, we can compare the behavior of different solutions from a concentration standpoint.

Strong vs Weak Acids

In chemistry, it's vital to distinguish between strong and weak acids. Strong acids, like HCl, dissociate completely in water, meaning they break up into their ions entirely. On the other hand, weak acids such as CH₃COOH only partially dissociate in water.
This dissociation level largely affects the acid's properties and reactivity. The completely dissociated HCl will make more hydrogen ions available in the solution than partially dissociated CH₃COOH.

• Strong acids fully ionize in solution, meaning a higher concentration of H⁺ ions.
• Weak acids only partially ionize, leading to fewer available H⁺ ions.
• The extent of dissociation affects the pH of the solution significantly.

Understanding the difference between strong and weak acids is essential for grasping why they behave differently in similar conditions.

Dissociation in Solutions

Dissociation refers to the process by which molecules separate into smaller particles, such as ions, when dissolved in a solvent like water. A strong acid like HCl dissociates completely in solution. This means nearly all HCl molecules break into H⁺ and Cl⁻ ions.
Acetic acid (CH₃COOH), a weak acid, only partially dissociates, resulting in an equilibrium between the undissociated and dissociated forms. The extent of dissociation is a crucial factor impacting the concentration of hydrogen ions in the solution, hence the pH.

• Complete dissociation occurs when an acid or base separates into ions entirely.
• Partial dissociation is typical of weak acids or bases.
• Equilibrium in weak acids shows a balance between molecules that have dissociated and those that haven't.

Grasping how acids dissociate in water helps explain why their pH levels differ, even at the same concentration.

pH Calculation

The pH scale is a measure of how acidic or basic a solution is, ranging from 0 (very acidic) to 14 (very basic), with 7 being neutral. The formula for calculating pH is: \[ \mathrm{pH} = -\log[\mathrm{H^+}] \]This equation shows that pH is directly linked to the concentration of hydrogen ions in the solution.
In the problem, a 0.10 M solution of HCl, being a strong acid, has a pH of 1.00 because it dissociates completely, making the concentration of H⁺ ions equal to the molarity. For CH₃COOH, a weaker acid, the concentration of hydrogen ions is less than 0.10 M due to its partial dissociation, resulting in a pH of 2.88.

• pH is inversely related to hydrogen ion concentration.
• Stronger acids tend to have lower pH values.
• pH calculations are crucial for evaluating solution characteristics.

Knowing how to calculate and interpret pH helps in understanding the properties and potential reactions of different solutions.