Question

Calculate \(\left[\mathrm{OH}^{-}\right]\) for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: (a) \(\left[\mathrm{H}^{+}\right]=0.0505 \mathrm{M} ;\) (b) \(\left[\mathrm{H}^{+}\right]=2.5 \times 10^{-10} \mathrm{M} ;(\mathrm{c})\) a solution in which \(\left[\mathrm{H}^{+}\right]\) is 1000 times greater than \(\left[\mathrm{OH}^{-}\right] .\)

Short answer

(a) For [H⁺] = 0.0505 M, [OH⁻] = 1.98 × 10⁻¹³ M and the solution is acidic. (b) For [H⁺] = 2.5 × 10⁻¹⁰ M, [OH⁻] = 4.0 × 10⁻⁵ M and the solution is basic. (c) In a solution where [H⁺] is 1000 times greater than [OH⁻], [OH⁻] = 3.16 × 10⁻⁷ M and the solution is acidic.

Step-by-step solution

Calculate [OH⁻] for part (a)

Given [H⁺] = 0.0505 M, and we know the ion product of water (Kw) is \(1.0 \times 10^{-14}\). Using the Kw equation, we find [OH⁻]: \[1.0 \times 10^{-14} = (0.0505)([OH^-]) \] \[[OH^-] = \frac{1.0 \times 10^{-14}}{0.0505} = 1.98 \times 10^{-13} M\]

Determine the nature of solution (a)

Since [OH⁻] < [H⁺], the solution is acidic. #Part (b)#

Calculate [OH⁻] for part (b)

Given [H⁺] = 2.5 × 10⁻¹⁰ M Using the Kw equation, we find [OH⁻]: \[1.0 \times 10^{-14} = (2.5 \times 10^{-10})([OH^-]) \] \[[OH^-] = \frac{1.0 \times 10^{-14}}{2.5 \times 10^{-10}} = 4.0 \times 10^{-5} M\]

Determine the nature of solution (b)

Since [OH⁻] > [H⁺], the solution is basic. #Part (c)#

Setting up an equation to solve for [OH⁻] in part (c)

Let [H⁺] be x, then the given condition is: [H⁺] = 1000 × [OH⁻]. So, x = 1000 × [OH⁻], and we know Kw = [H⁺][OH⁻].

Calculate [OH⁻] for part (c)

Using the given condition and Kw equation: \[1.0 \times 10^{-14} = (1000[OH^-])([OH^-])\] \[[OH^-]^2 = \frac{1 \times 10^{-14}}{1000}\] \[[OH^-] = \sqrt{\frac{1 \times 10^{-14}}{1000}} = 3.16 \times 10^{-7}\]

Determine the nature of solution (c)

Since [OH⁻] < [H⁺], the solution is acidic.

Key concepts

Ion Product of Water (Kw)

Water is a unique substance, known for its ability to ionize slightly into hydrogen ions ([H^+]) and hydroxide ions ([OH^-]). This process is described by the ion product constant of water, commonly represented as Kw. The Kw value at 25°C is a constant, always equal to 1.0 imes 10^{-14}. This constant relationship allows us to understand that the product of the hydrogen ion concentration and the hydroxide ion concentration will always equal Kw.

This relationship can be expressed as:\[[H^+][OH^-] = Kw = 1.0 imes 10^{-14}\]Whether a solution is acidic, basic, or neutral can be determined by comparing these concentrations. For example, if you know the concentration of [H^+] in a solution, you can determine [OH^-] by rearranging the Kw formula: \[[OH^-] = \frac{Kw}{[H^+]}\]Understanding Kw is crucial because it allows us to calculate the concentrations of either ion if the other is known.The constant nature of Kw forms the basis for various calculations in acid-base equilibrium, making it an essential part of understanding the aqueous chemistry environment.

pH and pOH Calculations

The acidity or basicity of a solution is often measured using the pH and pOH scales. These scales provide a more intuitive way to understand ion concentrations. The relation between them is rooted in Kw, as well as the logarithmic function to scale the values conveniently.

The pH of a solution is calculated by taking the negative logarithm (base 10) of the hydrogen ion concentration:\[ pH = -\log [H^+]\]For hydroxide ion concentration, pOH is calculated similarly:\[ pOH = -\log [OH^-]\]These two scales are interconnected by the equation:\[ pH + pOH = 14\]This equation arises because Kw equals 1.0 \times 10^{-14}, translating to \log(1.0 \times 10^{-14}) equating to 14.

By knowing pH, you can determine pOH, and vice versa. This reflects the balance of hydrogen and hydroxide ions in a solution, helping to categorize its acidity or basicity efficiently. The scales are convenient for expressing a wide range of ion concentrations in a straightforward, manageable way.

Acidic, Basic, and Neutral Solutions

Characterizing a solution as acidic, basic, or neutral is pivotal in chemistry. These terms describe the balance of hydrogen and hydroxide ions in a solution. We use the terms based on their relative concentrations to [H^+] and [OH^-] .

- **Acidic Solution:** When a solution has more hydrogen ions than hydroxide ions, it is considered acidic. In such cases, the [H^+] concentration is higher than [OH^-] , resulting in a pH value of less than 7. - **Basic Solution (or Alkaline):** A basic solution has fewer hydrogen ions than hydroxide ions, making the [OH^-] concentration exceed that of [H^+] . This scenario gives a pH value greater than 7. - **Neutral Solution:** A neutral solution features equal concentrations of hydrogen and hydroxide ions. Here, the value of both [H^+] and [OH^-] are the same, leading to a pH value exactly at 7.

Understanding these characteristics allows for the practical assessment of the solution's nature in various contexts, such as chemical reactions, biological environments, and industrial processes. This classification also helps in predicting the behavior of substances when they interact, such as whether titration will result in a neutralization reaction.