Problem 40 - Chemistry: An Atoms-Focused Approach

Question

Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of the following solutions: a. \(0.0450 M \mathrm{NaOH}\) b. \(0.160 M \mathrm{Ca}(\mathrm{OH})_{2}\) c. a 1: 1 mixture of \(0.0125 M\) HCl and \(0.0125 M \mathrm{Ca}(\mathrm{OH})_{2}\) d. a 2: 3 mixture of \(0.0125 M \mathrm{HNO}_{3}\) and \(0.0125 M \mathrm{KOH}\)

Step-by-Step Solution

Answer

Question: Based on the provided step-by-step solution, determine the pH and pOH values for each of the following solutions: a) 0.0450 M NaOH, b) 0.160 M Ca(OH)2, c) a 1:1 mixture of 0.0125 M HCl and 0.0125 M Ca(OH)2, and d) a 2:3 mixture of 0.0125 M HNO3 and 0.0125 M KOH.

Step 1: Solution a: Calculate the concentrations of H+ and OH- ions

In 0.0450 M NaOH solution, the NaOH dissociates completely to give 0.0450 M of OH- ions. Since it's a neutral solution, [H+] = \(10^{-14}/[OH^{-}]\), where \(10^{-14}\) is the ion product of water.

Step 2: Solution a: Find pH and pOH

In this case, [OH-] = 0.0450 M, [H+] = \((10^{-14})/(0.0450)\) pH = \(-log[H+]\) and pOH = \(-log[OH-]\).

Step 3: Solution b: Calculate the concentrations of H+ and OH- ions

In 0.160 M Ca(OH)2, due to the presence of 2 OH- ions in the formula, the concentration of OH- ions will be twice as much as the Ca(OH)2 concentration. Hence, [OH-] = 2 * 0.160 M = 0.32 M. Similar to solution a, we can find [H+] and then pH and pOH using the formulas.

Step 4: Solution c: Calculating the concentrations of H+ and OH- ions

In the 1:1 mixture of 0.0125 M HCl and 0.0125 M Ca(OH)2, as Ca(OH)2 has 2 OH- ions, the concentration of OH- ions will be 2 * 0.0125 M = 0.025 M. Since HCl dissociates completely, [H+] = 0.0125 M as well. Comparing the two values, we notice that [OH-] is in greater concentration than [H+]. Therefore, this solution will have an excess of [OH-] following the reaction.

Step 5: Solution c: Find pH and pOH

After the reaction, the solution will have a net concentration of OH- ions, which is the difference between the initial concentrations of OH- and H+. Then, we can find [H+] and calculate pH and pOH using the formulas.

Step 6: Solution d: Calculating the concentrations of H+ and OH- ions

In the 2:3 mixture of 0.0125 M HNO3 and 0.0125 M KOH, HNO3 dissociates completely, releasing 2 * 0.0125 M = 0.025 M of H+ ions. Similarly, KOH dissociates completely, releasing 3 * 0.0125 M = 0.0375 M of OH- ions. Comparing the two values, we notice that [OH-] is in greater concentration than [H+]. Therefore, this solution will have an excess of [OH-] following the reaction.

Step 7: Solution d: Find pH and pOH

After the reaction, the solution will have a net concentration of OH- ions, which is the difference between the initial concentrations of OH- and H+. Then, we can find [H+] and calculate pH and pOH using the formulas.

Key Concepts

Acid-Base Reactions

Acid-base reactions are processes where an acid donates a proton (H⁺) to a base. The neutralization that occurs forms water and a salt. When acids and bases mix, their ions can sometimes neutralize one another, altering the ion concentration of the solution.
For example:

• When NaOH (a strong base) dissolves in water, it separates into Na⁺ and OH⁻ ions.
• Similarly, HCl (a strong acid) dissociates into H⁺ and Cl⁻ ions.

In mixing equimolar amounts of an acid and a base, they neutralize each other, forming water:\[ \text{HCl} + \text{NaOH} \rightarrow \text{H}_2\text{O} + \text{NaCl} \] In some cases, there might be excess H⁺ or OH⁻ ions, which will affect the pH and pOH values of the solution. Recognizing these patterns helps in predicting whether the resulting solution will be acidic, basic, or neutral.

pOH Calculation

The pOH of a solution measures the concentration of hydroxide ions (OH⁻) in the solution. It is calculated using the negative logarithm of the hydroxide ion concentration:\[ \text{pOH} = -\log{[\text{OH}^-]} \] This calculation helps in determining the basicity of a solution. A lower pOH indicates a higher concentration of OH⁻ ions, signifying a more basic solution.

• For example, in a solution of 0.0450 M NaOH, the hydroxide concentration \([\text{OH}^-]\) is 0.0450 M.
• The pOH is therefore calculated as \(-\log{0.0450}\).
• If needed, pH can be found using the relationship \((14 = \text{pH} + \text{pOH})\).

Understanding the pOH calculation allows you to measure how basic a given solution is based on its hydroxide ion concentration.

Dissociation of Compounds

Dissociation refers to the process by which compounds separate into their respective ions when dissolved in water. This is a key concept in understanding acid-base chemistry, as the extent of dissociation affects the solution's pH and pOH.

• Strong acids and bases, such as HCl and NaOH, dissociate completely in water.
• For example, when NaOH dissociates, it forms Na⁺ and OH⁻ ions.

Furthermore, for compounds like \(\text{Ca(OH)}_2\), which dissociate to release two hydroxide ions per formula unit, the concentration of OH⁻ doubles. So a 0.160 M solution of \(\text{Ca(OH)}_2\) has a hydroxide ion concentration of 0.320 M.Dissociation also determines the remaining ion concentration in mixed solutions. For instance, in a neutralization reaction between acid and base, recognizing the extent of dissociation helps in calculating leftover ions.

Ion Concentration

The concentration of ions in a solution is critical for understanding its pH, pOH, and overall reactivity. Ion concentration tells you the amount of a specific ion present within a unit volume of solution, usually expressed in moles per liter (M).

• For pure water at 25°C, the concentration of H⁺ and OH⁻ ions is \(1 \times 10^{-7}\) M.
• The product of these ion concentrations is the ion product of water, \(1 \times 10^{-14}\) at 25°C, providing a logarithmic scale for pH and pOH calculations.

If you know the concentration of one type of ion in a complete dissociation, you can easily find the concentration of another. For example:- In calculating the pH of a solution, if the concentration of OH⁻ is known, you can calculate the concentration of H⁺ using \([\text{H}^+] \times [\text{OH}^-] = 10^{-14}\).Understanding ion concentration is crucial to predicting the acidity or basicity of a solution, especially after various chemical reactions, like neutralizations, that alter these concentrations.