Question

A solution has an \(\mathrm{OH}\) concentration of \(10^{-11} \mathrm{M}\). (a) Is this solution basic or acidic? Explain how you know. (b) Without using a calculator, explain how you could quickly determine the \(\mathrm{H}_{3} \mathrm{O}\) concentration of this solution. What is that concentration?

Short answer

(a) The solution is acidic because the given OH- concentration (1x10^(-11) M) is less than the neutral value of 1x10^(-7) M, indicating there are fewer OH- ions than in a neutral solution. (b) To find the H3O+ concentration without a calculator, use the ion product constant for water (Kw = 1x10^(-14)) and the given OH- concentration (1x10^(-11) M): Kw = [H3O+] [OH-] ➔ [H3O+] = (1x10^(-14))/(1x10^(-11)) = 1x10^(3) The H3O+ concentration is 1000 M.

Step-by-step solution

(Step 1: Determine if the solution is acidic or basic from its OH- concentration.)

To determine if the solution is acidic or basic, we will compare the given OH- concentration to the neutral value of 1x10^(-7) M. The given OH- concentration is 1x10^(-11) M. Since this value is less than 1x10^(-7) M, there are fewer OH- ions than in a neutral solution, indicating that the solution is acidic.

(Step 2: Use the ion product constant for water to find the H3O+ concentration.)

To find the H3O+ concentration, we'll use the ion product constant for water (Kw), which is given by: Kw = [H3O+] [OH-] = 1x10^(-14) We know the concentration of OH- ions (1x10^(-11) M), so we can plug this value into the equation and solve for the concentration of H3O+ ions: 1x10^(-14) = [H3O+] (1x10^(-11)) Now we can divide both sides by 1x10^(-11) to find the H3O+ concentration: [H3O+] = (1x10^(-14))/(1x10^(-11))

(Step 3: Simplify and calculate the H3O+ concentration without using a calculator.)

To simplify the expression and calculate the H3O+ concentration without using a calculator, we can use the properties of exponents: [H3O+] = 1x10^(-14 - (-11)) [H3O+] = 1x10^(3) [H3O+] = 1000 M The H3O+ concentration in the given solution is 1000 M.

Key concepts

pH and pOH

Understanding the pH and pOH of a solution is crucial in chemistry as it tells us about the acidity or basicity of that solution. The pH is a measure of the hydronium ion (H3O+) concentration, while pOH measures the hydroxide ion (OH-) concentration. Both are on a logarithmic scale, making it easier to handle the wide range of ion concentrations.
In a neutral solution at 25°C, both pH and pOH are equal to 7. If the pH is less than 7, the solution is acidic; if the pH is greater than 7, the solution is basic. The pOH works inversely — a pOH less than 7 indicates a basic solution, and a pOH greater than 7 indicates an acidic solution. The sum of pH and pOH in a given solution at 25°C always equals 14, which is a helpful tip when needing to quickly calculate one from the other without a calculator. This relationship allows us to understand the balance between hydronium and hydroxide ions in any aqueous solution.

Hydroxide Ion Concentration

Hydroxide ion concentration provides insight into the basicity of a solution. Substances that dissociate in water to release OH- ions increase the solution's hydroxide ion concentration. This concentration is typically expressed in molarity (M), which is moles of ions per liter of solution.

For example, when we say a solution has an OH- concentration of \(10^{-11} \mathrm{M}\), it means there are \(10^{-11}\) moles of hydroxide ions per liter of solution. As compared to the neutral concentration (7 on the pOH scale or \(1 \times 10^{-7} \mathrm{M}\) of OH-), this concentration is lower, suggesting the solution is not basic but rather acidic.

Hydronium Ion Concentration

The hydronium ion concentration is a key indicator of a solution's acidity. Higher concentrations of H3O+ ions make a solution more acidic. These ions originate from substances that release protons (H+) which then bond with water molecules to form H3O+.

In situations like the exercise given, understanding how to quickly approximate the hydronium ion concentration can be particularly useful. For instance, if the hydroxide ion concentration is known, one can infer the hydronium ion concentration using the ion product constant of water, without needing to perform complex calculations or use a calculator.

Ion Product Constant of Water

The ion product constant of water (Kw) is an essential concept in the study of acid-base chemistry. It represents the product of the concentrations of the hydronium and hydroxide ions in pure water. At 25°C, Kw is always \(1 \times 10^{-14} \mathrm{M}^2\), which is derived from the product of the concentrations of H3O+ and OH- ions at this temperature: \([\mathrm{H}_3\mathrm{O}^+]\) times \([\mathrm{OH}^-]\).

Utilizing Kw to find an unknown ion concentration is straightforward if the other is known. This method avoids extensive calculations and is quick, especially when a calculator is not handy. This constant is fundamental to understanding the interdependent nature of hydronium and hydroxide ion concentrations in any aqueous solution.