Problem 28 - Chemistry

Question

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

Step-by-Step Solution

Answer

a. False. Corrected statement: When a base is dissolved in water, the lowest possible pH of the solution is greater than 7.0. b. True. c. True. d. False. Corrected statement: A 0.0010 M \(Ba(OH)_2\) solution has a lower pOH value than a 0.0010 M KOH solution.

Step 1: Statement a

When a base is dissolved in water, the lowest possible pH of the solution is 7.0. This statement is false. When a base is dissolved in water, it will increase the concentration of hydroxide ions, making the solution basic, and a solution with pH 7.0 is considered neutral. Therefore, the pH of solutions with a dissolved base will always be greater than 7.0. Corrected statement: When a base is dissolved in water, the lowest possible pH of the solution is greater than 7.0.

Step 2: Statement b

When an acid is dissolved in water, the lowest possible pH is 0. This statement is true. When an acid is dissolved in water, it will increase the concentration of hydrogen ions, making the solution acidic. The pH scale ranges from 0 to 14, with 0 being the most acidic. Therefore, the lowest possible pH of an acidic solution is 0.

Step 3: Statement c

A strong acid solution will have a lower pH than a weak acid solution. This statement is true. Strong acids ionize completely in water, whereas weak acids only partially ionize. This means that strong acids produce a higher concentration of hydrogen ions in solution, resulting in a lower pH value than weak acids at equivalent concentrations.

Step 4: Statement d

A 0.0010 M Ba(OH)₂ solution has a pOH that is twice the pOH value of a 0.0010 M KOH solution. This statement is false. To analyze this statement, we must consider the dissociation of each base in solution: \(Ba(OH)_2 → Ba^{2+} + 2OH^-\) This reaction shows that one mole of \(Ba(OH)_2\) produces 2 moles of \(OH^-\) ions, so the concentration of \(OH^-\) ions would be 2 times the concentration of \(Ba(OH)_2 (0.0020 \mathrm{M}\). \(KOH → K^+ + OH^-\) This reaction shows that one mole of KOH produces one mole of \(OH^-\) ions, so the concentration of \(OH^-\) ions would be the same as the concentration of KOH (0.0010 M). Now let's calculate the pOH of each solution: pOH = -log10[OH⁻] pOH of \(Ba(OH)_2\) solution = -log10(0.0020) ≈ 2.70 pOH of KOH solution = -log10(0.0010) ≈ 3.00 As we can see, the pOH of the \(Ba(OH)_2\) solution is not twice the pOH value of the KOH solution. Corrected statement: A 0.0010 M \(Ba(OH)_2\) solution has a lower pOH value than a 0.0010 M KOH solution.

Key Concepts

Acid-Base Chemistry

Understanding acid-base chemistry is essential for scientists and students alike, as it is a fundamental aspect of chemistry involved in various phenomena, from industrial processes to biological systems. Acids are substances that can donate a proton (H+) in a chemical reaction, and bases are substances that can accept a proton. This interaction is well captured by the Bronsted-Lowry acid-base theory. Another way to view acids and bases is through the Lewis theory, where acids are electron pair acceptors, and bases are donors.

There are two main types of acids and bases: strong and weak. The strength of an acid or a base dictates how completely it ionizes in water. A strong acid or base ionizes completely, releasing a greater number of hydrogen ions (H+) or hydroxide ions (OH-) in water, respectively. This complete ionization affects the conductivity, reactivity, and pH of a solution.

pH Scale

The pH scale is a measure of how acidic or basic a solution is on a scale ranging from 0 to 14. Pure water has a pH of 7, which is considered neutral, meaning it is neither acidic nor basic. Substances with a pH lower than 7 are acidic, while those with a pH higher than 7 are basic (alkaline). The pH scale is logarithmic, indicating that each unit change represents a tenfold change in the concentration of hydrogen ions (H+).

The pH of a solution is calculated using the formula \( pH = -\log_{10}[H^+] \) where \( [H^+] \) is the concentration of hydrogen ions. Consequently, a small change in [H+] can lead to a large change in pH, making the pH scale a sensitive indicator of acidity or basicity.

Strong and Weak Acids

Strong acids, such as hydrochloric acid (HCl), sulfuric acid (H2SO4), and nitric acid (HNO3), dissociate completely in water, which means they donate all their available hydrogen ions to the solution. This characteristic allows strong acids to produce high concentrations of hydrogen ions, resulting in a lower pH. In contrast, weak acids, like acetic acid (CH3COOH) or citric acid (C6H8O7), partially dissociate in water and establish an equilibrium between the undissociated acid and the ions. Thus, they produce fewer hydrogen ions, leading to a higher pH than that of strong acids at the same concentration.

Understanding the difference between strong and weak acids is crucial for predicting the acidity of a solution and for various practical applications, such as buffer solutions in biochemical systems and the manufacturing of different kinds of acids for industrial use.

Hydroxide Ion Concentration

Hydroxide ion concentration is a key factor when dealing with basic solutions. The pOH is a measure of the concentration of hydroxide ions in a solution and is related to pH through the relationship \( pH + pOH = 14 \) in aqueous solutions at 25°C. The pOH can be calculated using the formula \( pOH = -\log_{10}[OH^-] \) where \( [OH^-] \) is the concentration of hydroxide ions.

In the context of the exercise, understanding that a base like barium hydroxide (\(Ba(OH)_2\)) dissociates to produce two moles of hydroxide ions for every mole of dissolved substance clarifies why a 0.0010 M \(Ba(OH)_2\) solution has a lower pOH (and correspondingly higher pH) than a 0.0010 M KOH solution, which dissociates to produce one mole of OH- per mole of KOH. Therefore, the hydroxide ion concentration is an important aspect of basic solutions that directly influences the pOH and pH.