Question

Calculate the \(p \mathrm{H}\) and \(\mathrm{pOH}\) of each solution at \(25^{\circ} \mathrm{C}\). a. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.7 \times 10^{-8} \mathrm{M}\) b. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}\) c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=2.2 \times 10^{-6} \mathrm{M}\)

Short answer

a. pH = 7.77, pOH = 6.23; b. pH = 7.00, pOH = 7.00; c. pH = 5.66, pOH = 8.34.

Step-by-step solution

- Calculate pH

pH is the negative base-10 logarithm of the hydrogen ion concentration. Calculate pH using the formula pH = -log([H3O+]). Perform this calculation for each given concentration.

- Calculate pOH

At 25 degrees Celsius, the sum of pH and pOH is 14. Calculate pOH by subtracting the pH from 14 for each solution.

Solution for a

For [H3O+] = 1.7 x 10^-8 M, pH = -log(1.7 x 10^-8) and pOH = 14 - pH.

Solution for b

For [H3O+] = 1.0 x 10^-7 M, pH = -log(1.0 x 10^-7) and pOH = 14 - pH.

Solution for c

For [H3O+] = 2.2 x 10^-6 M, pH = -log(2.2 x 10^-6) and pOH = 14 - pH.

Key concepts

pOH

Understanding the concept of pOH is crucial in mastering acid and base chemistry. pOH is a measure that represents the concentration of hydroxide ions ( OH-) in a solution. It is calculated as the negative logarithm (base 10) of the hydroxide ion concentration. Mathematically, it is expressed as: \[ pOH = -\log[OH^-] \] At a temperature of 25 degrees Celsius, the pH and pOH of a solution will always add up to 14. This relationship allows us to quickly find one value if we know the other. Now, this concept is practically applied in the exercises to determine the pOH once the pH has been calculated. For instance, if a solution has a pH of 7, its pOH would consequently be 7, indicating a neutral solution. Conversely, a high pH means a low pOH, and vice versa, with higher pOH values indicating more basic (or less acidic) solutions.

acid and base chemistry

Acid and base chemistry is a foundational topic in chemistry that explores the properties of acidic and basic substances. An acid is a substance that increases the hydrogen ion ( H+) concentration in a solution, typically by releasing H+ ions. In water, these are often represented as hydronium ions ( H3O+). A base, on the other hand, decreases the H+ concentration, usually by providing hydroxide ions ( OH-) that combine with H+ to form water.

• Acids taste sour and turn blue litmus paper red.
• Bases taste bitter, feel slippery, and turn red litmus paper blue.
• The strength of an acid or base is determined by its ability to donate or accept H+ ions, respectively.

The pH scale quantifies the acidity or basicity of a solution. In the given exercises, we use this knowledge to determine the pH and subsequently the pOH of various solutions with known hydrogen ion concentrations.

hydrogen ion concentration

Hydrogen ion concentration is pivotal in the study of chemical reactions, especially in the context of acids and bases. When an acid dissolves in water, it releases hydrogen ions ( H+), which are often represented as hydronium ions ( H3O+) in aqueous solutions. This concentration of hydrogen ions dictates the acidity of the solution. \[ [H_3O^+] = \text{{concentration of hydronium ions in moles per liter (M)}} \] By knowing the hydrogen ion concentration, as shown in the exercise examples, we can calculate the pH, allowing us to describe the solution as acidic, basic, or neutral. The steps include calculating pH directly from the hydronium ion concentration. Significantly, a low hydrogen ion concentration correlates to a high pH (a basic solution), whereas a high concentration correlates to a low pH (an acidic solution).

logarithmic scale

The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. A logarithmic scale means that each number on the scale represents a tenfold change in hydrogen ion concentration. This scale ranges from 0 to 14, with 7 as the midpoint, which is considered neutral. \[ \text{{For pH: }} pH = -\log[H_3O^+] \]

• pH values less than 7 indicate acidity (more hydrogen ions).
• pH values greater than 7 indicate basicity (fewer hydrogen ions).
• A pH of 7 is neutral (pure water).

In the provided exercises, we apply the concept of this logarithmic nature to convert the given hydrogen ion concentrations into a more understandable pH value. Because of the logarithmic scale, a solution with a hydronium ion concentration of 1.0 x 10^-7 M has a pH of 7, which is neutral, while one with a concentration of 1.0 x 10^-6 M would have a more acidic pH of 6.