Question

Arrange the following \(0.1 M\) aqueous solutions in order of increasing pH (lowest to highest). \(\begin{array}{lllll}\mathrm{KOH}, & \mathrm{KF}_{3} & \mathrm{KCl}, & \mathrm{ZnCl}_{2}, & \mathrm{HCl}\end{array}\)

Short answer

Question: Arrange the following solutions in order of increasing pH: KOH, KF₃, KCl, ZnCl₂, and HCl. Answer: HCl, ZnCl₂, KCl, KF₃, and KOH.

Step-by-step solution

Identify if the solution is acidic, basic or neutral

We'll start by identifying whether each compound, when dissolved in water, will form an acidic, basic, or neutral solution. - KOH: This is a strong base and will form a basic solution - KF\(_{3}\): This is a salt. When dissolved in water, it will form K\(^{+}\) ions and F\(_{3}^-\) ions. Since F\(_{3}^-\) comes from a weak acid (HF\(_{3}\)), its conjugate base F\(_{3}^-\) will cause the solution to be basic. - KCl: This is a salt. When dissolved in water, it will form K\(^{+}\) ions and Cl\(^-\) ions. Cl\(^-\) is the conjugate base of the strong acid HCl, and K\(^{+}\) comes from the strong base KOH, so the solution will be neutral. - ZnCl\(_{2}\): This is a salt. When dissolved in water, it will form Zn\(^{2+}\) ions and Cl\(^-\) ions. Zn\(^{2+}\) comes from Zn(OH)\(_{2}\), which is a weak base, so the solution will be acidic. - HCl: This is a strong acid and will form an acidic solution

Arrange solutions based on pH value

We can now rank the solutions according to their pH. Remember that a pH of 7 indicates a neutral solution, a pH below 7 indicates an acidic solution, and a pH above 7 indicates a basic solution. 1. HCl (strong acid, low pH) 2. ZnCl\(_{2}\) (acidic solution, pH below 7 but higher than HCl) 3. KCl (neutral solution, pH = 7) 4. KF\(_{3}\) (basic solution, pH above 7 but lower than KOH) 5. KOH (strong base, high pH) So, the final order, from lowest to the highest pH, is: HCl, ZnCl\(_{2}\), KCl, KF\(_{3}\), and KOH.

Key concepts

Acidic and Basic Solutions

Understanding the nature of acidic and basic solutions is key to grasping the principles of pH. Acids are substances that increase the concentration of hydrogen ions (\( H^+ \) or more accurately hydronium ions \(H_3O^+\))) in a solution. In contrast, bases reduce the concentration of hydrogen ions, typically by increasing the concentration of hydroxide ions (\( OH^- \) in a solution. For instance, when you dissolve hydrochloric acid (HCl) in water, it ionizes completely to produce a high concentration of hydronium ions, creating an acidic solution with a low pH value.

Bases, like potassium hydroxide (KOH), dissociate in water to yield potassium ions (\(K^+\))) and hydroxide ions (\(OH^-\))), thereby creating a basic solution with a higher pH value. While strong acids and bases ionize completely, weak acids and bases only partially dissociate in water. This partial dissociation leads to solutions that are less acidic or basic compared to their strong counterparts. For example, the salt KF\(_3\), made from the weak acid HF\(_3\), results in a basic solution, but not as strongly basic as the KOH solution, due to the incomplete dissociation of the weak acid.

pH Scale

The pH scale is a numerical scale ranging from 0 to 14 used to specify the acidity or basicity of an aqueous solution. It is a logarithmic scale based on the concentration of hydronium ions in the solution: the lower the pH, the higher the acidity, and the higher the pH, the greater the basicity. A pH of 7 is considered neutral, representing a balance between hydronium and hydroxide ions.

The pH scale is critical for categorizing substances as acidic, neutral, or basic. In relation to our exercise, a strong acid like HCl has a very low pH, close to 0, while a strong base like KOH has a pH close to 14. Salts such as KCl form neutral solutions with a pH of approximately 7, as they derive from strong acids and strong bases, which cancel out each other's effects. The pH scale helps us understand that each step on the scale represents a tenfold change in ion concentration, illustrating the significant difference between each pH unit.

Conjugate Acids and Bases

Analyzing the behavior of conjugate acids and bases furthers our comprehension of acidity, basicity, and pH. When an acid donates a proton (\(H^+\))) to a base, it forms what's known as a conjugate base. Conversely, when a base accepts a proton, it forms a conjugate acid. This understanding helps us predict the behavior of substances in solution.

In our exercise, KF\(_3\) is a salt formed from the conjugate base of a weak acid. The presence of the conjugate base F\(_3^-\) in solution makes the solution basic, as it has a tendency to capture protons. Because it stems from a weak acid, it doesn't capture protons as effectively as the hydroxide ion (OH^-), resulting in a less basic solution compared to KOH. The conjugate acid-base pairs illustrate a relative strength; the stronger the acid, the weaker its conjugate base, and vice versa. For instance, Cl^- is the conjugate base of the strong acid HCl, and thus Cl^- is a weak base that does not affect the pH of the KCl solution, rendering it neutral.