Question

Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following pH or pOH values. a. \(\mathrm{pOH}=4.99\) b. \(\mathrm{pH}=7.74\) c. \(\mathrm{pOH}=10.74\) d. \(\mathrm{pH}=2.25\)

Short answer

a. \([H⁺] \approx 2.00 \times 10^{-9}\, M\) b. \([H⁺] \approx 1.82 \times 10^{-8}\, M\) c. \([H⁺] \approx 1.74 \times 10^{-4}\, M\) d. \([H⁺] \approx 5.62 \times 10^{-3}\, M\)

Step-by-step solution

Calculate OH⁻ concentration from pOH value

We are given the pOH value, which we can use to find the OH⁻ concentration. Using the pOH equation, we can rearrange to solve for [OH⁻]: \[[OH⁻] = 10^{-pOH}\] Plugging in the given pOH value, we get: \[[OH⁻] = 10^{-4.99}\]

Calculate H⁺ concentration using the ion product constant of water

Now we use the ion product constant of water to find the H⁺ concentration: \[[H⁺] = \frac{K_w}{[OH⁻]}\] Plugging in the known values, we get: \[[H⁺] = \frac{1.0 \times 10^{-14}}{10^{-4.99}}\] ##b. pH = 7.74##

Calculate H⁺ concentration from pH value

We are given the pH value. Using the pH equation, we can rearrange to solve for [H⁺]: \[[H⁺] = 10^{-pH}\] Plugging in the given pH value, we get: \[[H⁺] = 10^{-7.74}\] ##c. pOH = 10.74##

Calculate OH⁻ concentration from pOH value

As in part a, we can find the OH⁻ concentration using the given pOH value: \[[OH⁻] = 10^{-10.74}\]

Calculate H⁺ concentration using the ion product constant of water

Again, using the ion product constant of water, we find the H⁺ concentration: \[[H⁺] = \frac{1.0 \times 10^{-14}}{10^{-10.74}}\] ##d. pH = 2.25##

Calculate H⁺ concentration from pH value

We are given the pH value. Using the pH equation, we can rearrange to solve for [H⁺]: \[[H⁺] = 10^{-2.25}\] Now, we compute the hydrogen ion concentrations for each case: a. \[[H⁺] \approx 2.00 \times 10^{-9}\, M\] b. \[[H⁺] \approx 1.82 \times 10^{-8}\, M\] c. \[[H⁺] \approx 1.74 \times 10^{-4}\, M\] d. \[[H⁺] \approx 5.62 \times 10^{-3}\, M\]

Key concepts

Hydrogen Ion Concentration

Understanding the hydrogen ion concentration in a solution is a fundamental aspect of acid-base chemistry. The concentration of hydrogen ions \( [H^+] \) is typically measured in moles per liter (M) and is closely related to the pH of the solution. A low hydrogen ion concentration indicates a basic solution, while a high concentration signifies an acidic solution.

The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration. Mathematically, it is expressed as \( pH = -\log[H^+] \). When provided with the pH value, one can calculate the hydrogen ion concentration using the inverse of the logarithmic function: \( [H^+] = 10^{-pH} \). This calculation allows for the quantitative comparison of acidity or basicity between different solutions.

Hydroxide Ion Concentration

The hydroxide ion concentration \( [OH^-] \) is also key in determining the properties of a solution. It represents the amount of hydroxide ions in a solution and helps in assessing the basicity. The measurement is similar to hydrogen ion concentration and is denoted in moles per liter.

The pOH is a scale used to express the hydroxide ion concentration, defined as \( pOH = -\log[OH^-] \). The calculation of the hydroxide ion concentration from the pOH is done by the formula: \( [OH^-] = 10^{-pOH} \). Knowing the value of either \( [OH^-] \) or pOH can provide insight into the overall pH balance of the solution, as pH and pOH are inversely related.

Ion Product Constant of Water

The ion product constant of water, known as Kw, is a critical figure in acid-base chemistry. It represents the product of the hydrogen ion and hydroxide ion concentrations in pure water at a specific temperature, a value which, at 25°C, is \( 1.0 \times 10^{-14} \). The expression for \( K_w \) is \( K_w = [H^+][OH^-] \).

In a neutral solution at 25°C, both \( [H^+] \) and \( [OH^-] \) are equal to \( 1.0 \times 10^{-7} M \). If the concentration of either ion is known, the other can be calculated using \( K_w \) and the formula \( [H^+] = \frac{K_w}{[OH^-]} \) or vice versa. This equation is essential when solving problems involving either acidic or basic solutions, as shown in the exercise.

Acid-Base Chemistry

Acid-base chemistry revolves around the study of acids and bases and their reactions in solution. This field uses the concepts of pH, pOH, and ion concentration to classify solutions as acidic, basic, or neutral.

Acids are substances that increase the hydrogen ion concentration when dissolved in water, while bases reduce it. The strength of an acid or a base is often measured by its ability to dissociate in water, which directly influences the ion concentrations.

• Strong acids and bases dissociate completely, yielding higher concentrations of \( [H^+] \) or \( [OH^-] \) respectively.
• Weak acids and bases dissociate partially, resulting in lower ion concentrations.

In the exercise provided, students calculate hydrogen ion concentrations to determine the acidity or basicity of solutions, seeing firsthand how these fundamental principles are applied in solving practical chemistry problems.