Question

For the following, mix equal volumes of one solution from Group I with one solution from Group II to achieve the indicated pH. Calculate the pH of each solution. $$\begin{array}{rl}\text{ Group I: }& 0.20M{\mathrm{NH}}_4\mathrm{Cl},0.20\mathrm{MCl},0.20M{\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{NH}}_3\mathrm{Cl}\\ & 0.20M{\left({\mathrm{C}}_2{\mathrm{H}}_5\right)}_3\mathrm{NHCl}\end{array}$$ $$\begin{array}{r}\text{ Group II: }0.20M\mathrm{KOI},0.20\mathrm{M}\mathrm{NaCN},0.20\mathrm{M}\mathrm{KOCl},0.20\\ \mathrm{M}{\mathrm{NaNO}}_2\end{array}$$ a. the solution with the lowest pH b. the solution with the highest pH c. the solution with the pH closest to 7.00

Short answer

a. The lowest pH solution is obtained when mixing 0.20 M NH4Cl and 0.20 M NaNO2, resulting in a pH of approximately 3.71. b. The highest pH solution is obtained when mixing 0.20 M C6H5NH3Cl and 0.20 M KOI, resulting in a pH of approximately 10.48. c. The solution with pH closest to 7.00 is obtained when mixing 0.20 M NH4Cl and 0.20 M KOCl, resulting in a pH of approximately 7.11.

Step-by-step solution

Identify suitable reactions for each group

To determine which combinations of Group I and Group II will produce acidic, neutral, and basic solutions, we need to consider the reactions that occur in each solution. Group I consists of ammonium salts with different cations while Group II consists of salts with basic anions. When any ammonium salt reacts with a basic anion, we get a weak acid and a weak base. By comparing the dissociation constants (Ka) of each reactant, we can determine whether the resulting solution will be acidic, neutral, or basic.

Calculate the Ka and Kb values of each reactant

We can use the Ka values and the Kb values to find the pH of the resulting solutions. For ammonium salts (NH4+), the Kb value can be found using the equation: $K_b=\frac{K_w}{K_a}$ Where Kw is the ion product constant of water, which is equal to 1.0 x 10^(-14), and Ka is the dissociation constant of the corresponding acid: NH4Cl, MCl, C6H5NH3Cl, and (C2H5)3NHCl. We also need to find the Kb value for the anions (Group II). Remember that $K_w=K_a\ast K_b$.

Calculate the pH of each combination

Using the given 0.20 M concentrations and the Ka and Kb values, we can calculate the pH of each solution using the following equation: $pH=p{K}_a+\log \frac{[\text{Base}]}{[\text{Acid}]}$ For each combination, the pH of the resulting solution can be calculated and compared.

Find the lowest pH solution

Now, we want to check the pH for all solutions and identify the one with the lowest pH. To do so, list the pH values in an organized table and identify the lowest pH value.

Find the highest pH solution

Similarly, to find the solution with the highest pH, look for the highest pH value in the table of calculated pH values.

Find the pH closest to 7

Lastly, to find the solution with the pH closest to 7, look for the value nearest to 7 in the table of calculated pH values. After performing these calculations and comparisons, you can answer parts (a), (b), and (c) of the given exercise.

Key concepts

Acid-Base Reactions

In chemistry, acid-base reactions involve the transfer of protons (H⁺ ions) between reactants. An acid is a substance that donates a proton, while a base accepts a proton. When ammonium salts in Group I react with basic anions in Group II, an acid-base reaction occurs. This results in the formation of a weak acid and a weak base.
These reactions are crucial for determining the pH levels of solutions, as the strength and concentration of the acids and bases involved influence the final pH.
To predict whether a reaction will produce an acidic, neutral, or basic solution, it's essential to understand the nature of each reactant and how they interact with each other in solution.

Dissociation Constants

Dissociation constants, represented as Ka for acids and Kb for bases, are numerical values that indicate the extent to which a compound dissociates in water.
A high Ka value means an acid dissociates well, producing more hydrogen ions, thus making the solution more acidic. Conversely, a high Kb value means a base dissociates well, leading to a higher concentration of hydroxide ions and thus more basic solution.
The dissociation constants are pivotal when calculating pH because they determine how strong or weak an acid or base is. The relationship is given by the formula: $$K_w=K_a\times K_b$$Where $K_w$ is the ion product constant of water, valued at 1.0 x 10^-14. By calculating these values for the reactants, one can predict the pH of the solution made by mixing components from Group I and Group II.

Ammonium Salts

Ammonium salts, found in Group I of the exercise, consist of an ammonium ion (NH4⁺) paired with various anions. These salts are important in acid-base chemistry because they readily dissociate in water to release ammonium ions, acting as weak acids.
When dissolved, ammonium salts can donate a proton to water, forming hydronium (H3O⁺) and leaving behind ammonia (NH3), which can slightly increase the acidity of the solution: NH4⁺ + H2O ⇌ NH3 + H3O⁺ This ability to exchange protons makes ammonium salts key players in determining the pH of solutions, especially when paired with different anions from Group II.

Basic Anions

Basic anions, found in Group II of the exercise, are negatively charged ions that act as bases by accepting protons. Common examples include cyanide (CN⁻), hypochlorite (OCl⁻), and others.
When these anions are mixed in solution with ammonium salts, they engage in acid-base reactions, often resulting in slightly alkaline solutions because they accept protons from water to form hydroxide ions (OH⁻): A⁻ + H2O ⇌ HA + OH⁻ Here, the anion (A⁻) gains a proton to become its conjugate acid (HA) while increasing the concentration of OH⁻ in the solution. This interaction is essential for determining the resulting pH of the mixed solutions, especially when balancing with the ammonium ions from Group I.