Problem 20 - Chemistry: Principles and Reactions

Question

Solution \(\mathrm{X}\) has \(\mathrm{pH}\) 11.7. Solution \(\mathrm{Y}\) has \(\left[\mathrm{OH}^{-}\right]=4.5 \times 10^{-2}\). Which solution is more basic? Which has the higher \(\mathrm{pOH}\) ?

Step-by-Step Solution

Answer

Answer: Solution Y is more basic, and solution X has a higher pOH value.

Step 1: Determine the pOH of solution X

We have the pH of solution X, which is 11.7. We can use the relationship between pH and pOH to determine the pOH of solution X: pOH = 14 - pH Plugging in the given pH value: pOH (Solution X) = 14 - 11.7 = 2.3

Step 2: Determine the pH of solution Y

We have the concentration of hydroxide ions (OH-) for solution Y. To find the pH, we first need to determine the pOH using the formula: pOH = -log10[OH-] Plugging in the given value of [OH-]: pOH (Solution Y) = -log10(4.5 × 10^-2) ≈ 1.35 Now, we can find the pH of solution Y using the relationship between pH and pOH: pH = 14 - pOH pH (Solution Y) = 14 - 1.35 ≈ 12.65

Step 3: Compare the basicity of the solutions

To determine which solution is more basic, we compare their pOH values. Lower pOH indicates higher basicity. pOH (Solution X) = 2.3 pOH (Solution Y) = 1.35 Since the pOH value for solution Y is lower than that of solution X, solution Y is more basic.

Step 4: Determine which solution has the higher pOH value

We already have the pOH values of both solutions from the previous steps. pOH (Solution X) = 2.3 pOH (Solution Y) = 1.35 Since the pOH value of solution X is higher than that of solution Y, solution X has the higher pOH value.

Key Concepts

pH and pOH relationship

The concepts of pH and pOH are central themes in acid-base chemistry, offering a way to describe the acidity or basicity of a solution. The pH scale measures how acidic or basic a solution is, with 7 considered neutral. On the other hand, pOH is a mirror to the pH, specifically focusing on the concentration of hydroxide ions (OH-). The relationship between pH and pOH is straightforward and inversely related: both always add up to 14 in a balanced solution. This relationship can be expressed with the equation:

\[pH + pOH = 14\]

• If the pH is known, the pOH can be found by subtracting the pH from 14.
• Conversely, if the pOH is given, the pH can be calculated similarly.

A solution with a pH less than 7 is acidic, while a solution with a pH greater than 7 is basic. Likewise, higher pOH values indicate lower basicity. This reciprocal relationship allows chemists to interchangeably study the pH or pOH to understand the chemical nature of a solution.

Hydroxide ion concentration

Hydroxide ion concentration (\[\left[\text{OH}^{-}\right]\]) is a key factor in determining the pOH of a solution, which then helps in identifying the solution's basicity. To calculate the pOH from hydroxide ion concentration, we use the formula:

\[\text{pOH} = -\log_{10} \left(\left[\text{OH}^{-}\right]\right)\]

• The process involves finding the negative logarithm (base 10) of the hydroxide ion concentration.
• The result, the pOH, gives insight into how basic the solution is.

In the exercise we discussed, solution Y's hydroxide ion concentration was given as \(4.5 \times 10^{-2}\), leading to a calculated pOH of approximately 1.35, indicating a highly basic solution. This is because a lower pOH corresponds to a higher concentration of hydroxide ions, and thus a higher degree of basicity.

Basicity comparison

Comparing the basicity of solutions involves analyzing either their pH or pOH values, as these indicate their position on the acid-base spectrum. For the solutions (\[\text{X and Y}\]in this instance), basicity comparison is straightforward:

• Lower pOH values reflect higher basicity because they mean greater hydroxide ion concentration.
• Conversely, higher pOH values denote a lesser degree of basicity.

In the given task, solution X has a pH of 11.7, resulting in a pOH of 2.3. Meanwhile, solution Y, with an \(\left[\text{OH}^{-}\right]\) of \(4.5 \times 10^{-2}\), results in a pOH of 1.35. Because solution Y has a lower pOH than solution X, it is deemed more basic.

This method of using pOH values simplifies the comparison between the basicity of multiple solutions, especially when dealing with varying forms of data, such as pH versus hydroxide ion concentration. Understanding these concepts allows for efficient analysis of chemical environments and their basic nature.