Problem 32 - Chemistry The Science in Context

Question

Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of the solutions with the following hydrogen ion or hydroxide ion concentrations. Indicate which solutions are acidic, basic, or neutral. a. \(\left[\mathrm{OH}^{-}\right]=8.2 \times 10^{-11} \mathrm{M}\) b. \(\left[\mathrm{OH}^{-}\right]=7.7 \times 10^{-6} \mathrm{M}\) c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.2 \times 10^{-4} \mathrm{M}\) d. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}\)

Step-by-Step Solution

Answer

Question: Calculate the pH and pOH values for each given concentration and determine whether the solution is acidic, basic, or neutral. a. [OH^-] = 8.2 * 10^-11 M b. [OH^-] = 7.7 * 10^-6 M c. [H3O^+] = 3.2 * 10^-4 M d. [H3O^+] = 1.0 * 10^-7 M

Step 1: Find the pH and pOH for each given concentration

To begin with, we can use the formula to find the pH and pOH values of the solutions. We will use the following formulas: pH = -log([H3O+]) pOH = -log([OH-]) and the relationship between pH and pOH: pH + pOH = 14 For the following given concentrations, we will calculate the pH and pOH values: a. [OH^-] = 8.2 * 10^-11 M b. [OH^-] = 7.7 * 10^-6 M c. [H3O^+] = 3.2 * 10^-4 M d. [H3O^+] = 1.0 * 10^-7 M

Step 2: Apply the pH and pOH formulas for each concentration and determine the solution's acidity/neutrality/basicity

Now we will apply the formulas for pH and pOH for each concentration given and determine whether the solution is acidic, basic, or neutral. For reference, if the pH < 7, the solution is acidic; if the pH > 7, the solution is basic; and if the pH = 7, the solution is neutral. a. Since [OH^-] is given, first find the pOH: pOH = -log(8.2 * 10^-11) = 10.086 Now, find the pH value: pH = 14 - pOH = 14 - 10.086 = 3.914 Since pH < 7, the a solution is acidic. b. Similarly for b, find the pOH: pOH = -log(7.7 * 10^-6) = 5.114 Now, find the pH value: pH = 14 - pOH = 14 - 5.114 = 8.886 Since pH > 7, the b solution is basic. c. For c, we have [H3O^+] given, so find the pH directly: pH = -log(3.2 * 10^-4) = 3.495 Next, find the pOH value: pOH = 14 - pH = 14 - 3.495 = 10.505 Since pH < 7, the c solution is acidic. d. Again, for d, we have [H3O^+] given, so find the pH directly: pH = -log(1.0 * 10^-7) = 7 Next, find the pOH value: pOH = 14 - pH = 14 - 7 = 7 Since pH = 7, the d solution is neutral.

Step 3: Summary of results

For each given concentration, we have calculated the pH and pOH values and determined whether the solution is acidic, basic, or neutral: a. acidic solution (pH = 3.914, pOH = 10.086) b. basic solution (pH = 8.886, pOH = 5.114) c. acidic solution (pH = 3.495, pOH = 10.505) d. neutral solution (pH = 7, pOH = 7)

Key Concepts

Acidic and Basic Solutions

Understanding the nature of acidic and basic solutions is fundamental in chemistry. An acidic solution has an excess of hydrogen ions \(\mathrm{H}_3\mathrm{O}^{+}\), and a basic solution, also known as alkaline, has an excess of hydroxide ions \(\mathrm{OH}^{-}\). The defining characteristic of an acidic solution is a pH value less than 7, while a basic solution has a pH value greater than 7. A solution with a pH of exactly 7 is considered neutral, which means it is neither acidic nor basic.

For example, solution 'a' calculated to have a pH of 3.914, which is less than 7, is classified as acidic. On the other hand, solution 'b' with a pH of 8.886 is basic because its pH is above 7. These designations help scientists and students understand the chemical behavior of various substances in different environments.

Hydrogen Ion Concentration

The hydrogen ion concentration in a solution, represented as \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\), is a critical component in the characterization of the solution's acidity. To measure the concentration of hydrogen ions, we use the pH scale, which is the negative logarithm of the hydrogen ion concentration: \(\mathrm{pH} = -\log(\left[\mathrm{H}_3\mathrm{O}^{+}\right])\).

For instance, solution 'c' with a given concentration of hydrogen ions \(3.2 \times 10^{-4} \mathrm{M}\) yields a pH of 3.495 after applying the formula. This low pH indicates a high concentration of hydrogen ions, making the solution acidic. It is essential to understand this inverse relationship: as hydrogen ion concentration increases, pH decreases, indicating increased acidity.

Hydroxide Ion Concentration

Conversely, the hydroxide ion concentration, noted as \(\left[\mathrm{OH}^{-}\right]\), is used to express the basicity of a solution. Here, the calculation of pOH is similar to that of pH but for hydroxide ions: \(\mathrm{pOH} = -\log(\left[\mathrm{OH}^{-}\right])\). The pH and pOH values are related through the equation \(\mathrm{pH} + \mathrm{pOH} = 14\), reflecting the balance of hydrogen and hydroxide ions in pure water.

Take solution 'b' - with a hydroxide ion concentration of \(7.7 \times 10^{-6} \mathrm{M}\), we find a pOH of 5.114. By using the relationship between pH and pOH, we obtain a pH greater than 7, indicating that solution 'b' is basic. The lower the pOH, the higher the hydroxide ion concentration, and hence, the more basic the solution.

pH Scale

The pH scale is a dimensionless unit, typically ranging from 0 to 14, used to quantify the acidity or basicity of solutions. A pH below 7 signifies an acidic solution, pH equal to 7 signifies a neutral solution, and a pH above 7 signifies a basic solution. This scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value. This logarithmic nature explains why even small changes in pH can represent significant changes in hydrogen ion concentration.

Using the pH calculations from solution 'd' as an illustration, which has a pH of exactly 7, we recognize it as neutral. On the pH scale, this equates to a hydrogen ion concentration of \(1.0 \times 10^{-7} \mathrm{M}\), which is the concentration of hydrogen ions in pure water at 25°C. The pH scale is central to chemical analysis and plays a crucial role in fields ranging from medicine to environmental science.