Problem 14 - Chemistry: Principles and Reactions

Question

Find the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of solutions with the following \(\left[\mathrm{H}^{+}\right]\). Classify each as acidic or basic. (a) \(1.0 \mathrm{M}\) (b) \(1.7 \times 10^{-4} \mathrm{M}\) (c) \(6.8 \times 10^{-8} \mathrm{M}\) (d) \(9.3 \times 10^{-11} M\)

Step-by-Step Solution

Answer

Question: Given the concentrations of hydronium ions in the following solutions, calculate their pH, pOH, and classify them as acidic or basic. (a) \(\left[\mathrm{H}^{+}\right] = 1.0 \mathrm{M}\) (b) \(\left[\mathrm{H}^{+}\right] = 1.7 \times 10^{-4} \mathrm{M}\) (c) \(\left[\mathrm{H}^{+}\right] = 6.8 \times 10^{-8} \mathrm{M}\) (d) \(\left[\mathrm{H}^{+}\right] = 9.3 \times 10^{-11} \mathrm{M}\) Answer: (a) pH = 0, pOH = 14, acidic (b) pH ≈ 3.77, pOH ≈ 10.23, acidic (c) pH ≈ 7.17, pOH ≈ 6.83, basic (d) pH ≈ 10.03, pOH ≈ 3.97, basic

Step 1: Calculate the pH of the solution

To determine the pH, we use the formula \(\mathrm{pH}= -\log(\left[\mathrm{H}^{+}\right])\). Therefore, \(\mathrm{pH} = -\log(1.0) = 0\).

Step 2: Calculate the pOH of the solution

To find the pOH, we use the relationship \(\mathrm{pH}+\mathrm{pOH}=14\). Since the pH is \(0\), the pOH is \(14-0=14\).

Step 3: Determine whether the solution is acidic or basic

Since the pH is less than \(7\), this solution is acidic. (b) \(\left[\mathrm{H}^{+}\right] = 1.7 \times 10^{-4} \mathrm{M}\):

Step 1: Calculate the pH of the solution

Using the formula \(\mathrm{pH} = -\log(\left[\mathrm{H}^{+}\right])\), we find: \(\mathrm{pH} = -\log(1.7 \times 10^{-4}) \approx 3.77\).

Step 2: Calculate the pOH of the solution

Following the relationship \(\mathrm{pH}+\mathrm{pOH}=14\), the pOH is \(14-3.77 \approx 10.23\).

Step 3: Determine whether the solution is acidic or basic

With a pH of approximately \(3.77\), this solution is acidic. (c) \(\left[\mathrm{H}^{+}\right] = 6.8 \times 10^{-8} \mathrm{M}\):

Step 1: Calculate the pH of the solution

Applying the formula \(\mathrm{pH}=-\log(\left[\mathrm{H}^{+}\right])\), we get: \(\mathrm{pH} = -\log(6.8 \times 10^{-8}) \approx 7.17\).

Step 2: Calculate the pOH of the solution

Given the relationship \(\mathrm{pH}+\mathrm{pOH}=14\), the pOH is \(14-7.17 \approx 6.83\).

Step 3: Determine whether the solution is acidic or basic

As the pH of the solution is approximately \(7.17\), it is basic. (d) \(\left[\mathrm{H}^{+}\right] = 9.3 \times 10^{-11} \mathrm{M}\):

Step 1: Calculate the pH of the solution

We use the formula \(\mathrm{pH}=-\log(\left[\mathrm{H}^{+}\right])\). Thus, \(\mathrm{pH} = -\log(9.3\times 10^{-11}) \approx 10.03\).

Step 2: Calculate the pOH of the solution

Based on the relationship \(\mathrm{pH}+\mathrm{pOH}=14\), the pOH is \(14-10.03 \approx 3.97\).

Step 3: Determine whether the solution is acidic or basic

With a pH of approximately \(10.03\), this solution is basic.

Key Concepts

Acidic and Basic Solutions

Acidic and basic solutions differ dramatically in their properties due to the concentration of hydrogen ions (\(H^+\) ions) they contain. When we say a solution is acidic, it means that it has a higher concentration of hydrogen ions compared to pure water.

Basic solutions, on the other hand, have a lower concentration of hydrogen ions but a higher concentration of hydroxide ions (\(OH^-\) ions). The properties of these solutions such as taste, reactivity with metals and carbonates, and ability to conduct electricity, shift correspondingly. For instance, acidic solutions often have a sour taste and can corrode metals, while basic solutions may feel slippery and are less likely to react with metals.

To enhance understanding in exercises, always correlate the numerical pH values to these practical characteristics of acidic and basic solutions.

Hydrogen Ion Concentration

The hydrogen ion concentration, denoted by \(\left[\mathrm{H}^{+}\right]\), is a critical factor in determining the acidity or basicity of a solution. In pure water at 25°C, the concentration of hydrogen ions is \(1.0 \times 10^{-7} M\), establishing the neutral midpoint on the pH scale. Solutions with higher hydrogen ion concentrations than this are acidic, while those with lower concentrations are basic.

Understanding this concept can be simplified by using the analogy of a scale where increasing hydrogen ion concentration tips the balance towards the acidic side, and a decrease does the opposite. By using this visualization, it becomes easier for students to grasp the effect of hydrogen ion concentration on the overall character of the solution.

pH Scale

The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution. The pH value is a more practical representation of \(\left[\mathrm{H}^{+}\right]\) because it condenses the wide range of hydrogen ion concentrations into a manageable scale.

To make the pH scale more relatable, consider comparing it to a popularity meter for a social media post; a lower number represents fewer likes (more acidic), while a higher number means more likes (more basic). Just like the excitement of tallying likes, understanding pH can be made engaging by associating it with everyday experiences.

pOH Scale

Complementary to the pH scale is the pOH scale, which represents the concentration of hydroxide ions (\(OH^-\)) in a solution. It's calculated using the formula \(\mathrm{pOH}= -\log(\left[\mathrm{OH}^{-}\right])\). The pOH scale also runs from 0 to 14, where a lower value indicates a more basic solution, and a higher value indicates a more acidic solution.

It might be helpful to think of the pOH scale as a mirror image of the pH scale, where each reflects the property not shown by the other. Whenever students calculate pH, they should remember that pOH can also be found, as they sum up to 14 in aqueous solutions at 25°C. Making this connection reinforces the reciprocal relationship between acidity and basicity in solutions.