Question

Which of the following statements is (are) true? Correct the false statements. a. When a base is dissolved in water, the lowest possible pH of the solution is \(7.0 .\) b. When an acid is dissolved in water, the lowest possible pH is \(0 .\) c. A strong acid solution will have a lower pH than a weak acid solution. d. A \(0.0010-M \mathrm{Ba}(\mathrm{OH})_{2}\) solution has a pOH that is twice the pOH value of a \(0.0010-M \mathrm{KOH}\) solution.

Short answer

Answer: a. False. When a base is dissolved in water, the lowest possible pH of the solution is greater than 7. b. True. When an acid is dissolved in water, the lowest possible pH is 0. c. True. A strong acid solution will have a lower pH than a weak acid solution. d. False. A 0.0010 M Ba(OH)2 solution has a pOH value that is slightly lower compared to the pOH value of a 0.0010 M KOH solution.

Step-by-step solution

Statement a: Analyzing Base in Water pH

A base dissolved in water will always lead to a pH greater than 7. A pH of 7 indicates a neutral pH, where the concentrations of hydrogen ions (H+) and hydroxide ions (OH-) are equal. Adding a base to water will increase the OH- concentration, leading to a higher pH. Therefore, the lowest possible pH for a base dissolved in water cannot be 7.0. Corrected Statement a: When a base is dissolved in water, the lowest possible pH of the solution is 7.0. (False)

Statement b: Analyzing Acid in Water pH

When an acid is dissolved in water, depending on the strength of the acid, the resulting pH value will be lower than 7. The strongest possible acid will have the highest H+ concentration, resulting in the lowest pH value. If the concentration of hydrogen ions is \(10^{0} \mathrm{M}\) then the pH will be 0 (since pH = -log[H+]). Therefore, when an acid is dissolved in water, the lowest possible pH is 0. Statement b: When an acid is dissolved in water, the lowest possible pH is 0. (True)

Statement c: Comparing Strong Acid and Weak Acid pH

A strong acid completely dissociates in water, thus releasing more hydrogen ions (H+) and having a lower pH than a weak acid, which partially dissociates in water. Therefore, a strong acid solution will have a lower pH than a weak acid solution. Statement c: A strong acid solution will have a lower pH than a weak acid solution. (True)

Statement d: Comparing pOH values of Ba(OH)2 and KOH solutions

First, we need to understand that when a base is added to water, it increases the concentration of OH- ions. In this case, Ba(OH)2 is a strong base, and it has two OH- ions for each molecule. So, when 0.0010 M Ba(OH)2 is added to water, it produces 2 × 0.0010 M = 0.0020 M of OH- ions. The pOH is defined as -log[OH-]. The pOH for 0.0020 M of OH- ions is -log(0.002) ≈ 2.7. Now, for the KOH solution which also has 0.0010 M concentration, it has only one OH- ion for each molecule. Therefore, the pOH of this solution would be -log(0.0010) ≈ 3.0. Comparing the pOH values, it is not true that the pOH of the Ba(OH)2 solution is twice the pOH value of the KOH solution. They are different by around 0.3 pOH units. So, the statement is false. Corrected statement d: A 0.0010 M Ba(OH)2 solution has a pOH value that is slightly lower compared to the pOH value of a 0.0010 M KOH solution. (False)

Key concepts

Acid-Base Chemistry

Acid-base chemistry is a fundamental part of understanding the behavior of chemical substances in solution. Acids and bases are substances that can donate or accept hydrogen ions ( H+ ) respectively when dissolved in water. Understanding the role of acids and bases helps us predict reactions and the strength of substances.

• Acids: Substances that increase the concentration of hydrogen ions in a solution. They have a pH of less than 7.
• Bases: Substances that increase the concentration of hydroxide ions ( OH^- ) in a solution. They have a pH greater than 7.

The pH scale, ranging from 0 to 14, measures how acidic or basic a solution is. The middle point of 7 represents a neutral pH, equivalent to pure water at room temperature. An acidic solution shifts the scale to the left (lower pH), while a basic solution moves it to the right (higher pH).
Understanding the basics of acid-base theory can help apply these concepts to various chemical equilibrium scenarios, including titrations and buffers.

Strong and Weak Acids

Acids can be either strong or weak, and this classification depends on how completely they dissociate in water.
Strong Acids

• These acids fully dissociate in water, meaning they completely release their hydrogen ions ( H+ ).
• An example is hydrochloric acid ( HCl ), which dissociates fully into H+ and Cl^- ions.
• Strong acids have a low pH, often near 0, depending on their concentration.

Weak Acids

• Unlike strong acids, weak acids only partially dissociate in water.
• An example is acetic acid ( CH_3COOH ), which does not fully release its hydrogen ion, hence resulting in a higher pH than strong acids.
• Weak acids have higher pH values compared to strong acids, but still below 7.

The dissociation extent in water greatly affects the pH, which explains why a strong acid solution has a lower pH than that of a weak acid.

Chemical Solutions

Chemical solutions are homogeneous mixtures made of two or more substances. In acid-base chemistry, solutions typically consist of an acid or a base dissolved in water (the solvent). Here’s what happens:

• The component that gets dissolved (the solute, such as an acid or base) interacts with water molecules.
• The resulting solution shows characteristic pH behavior based on the nature of the solute.

The concentration of the solution is a crucial aspect determining its properties. For example, in a 0.0010 M solution of barium hydroxide ( Ba(OH)_2 ), the OH^- ion concentration ultimately influences the pOH (potential of hydroxide), a concept complementary to pH.
Therefore, understanding the nature and concentration of the solute can help predict the behavior and potential reactions within the solution. This is especially important when considering reactions between acids and bases, which engage in neutralization reactions to produce water and other compounds.

Dissociation in Water

Dissociation refers to the process by which molecules split into smaller particles, such as ions, when dissolved in water. This is a crucial concept for both acids and bases that interact with water.
Acid Dissociation

• When acids dissolve in water, they release hydrogen ions ( H+ ) into the solution.
• The level of dissociation indicates the strength of the acid; strong acids dissociate completely, contributing to a lower pH.

Base Dissociation

• Bases dissociate to release hydroxide ions ( OH^- ) in water.
• The dissociation level affects the solution's basicity, meaning a strong base also has greater dissociation, which produces a higher pOH.

The dissociation process is key to understanding how acids and bases interact in water, impacting their strength and the resulting solution’s pH or pOH. Knowing this helps predict and explain the outcome of chemical reactions such as neutralization, as well as determining the correct pH balance in various scenarios.