Question

What is the concentration of \(\mathrm{H}^{+}\) in \(0.00065 \mathrm{M} \mathrm{HNO}_{3} ?\) What is the \(\mathrm{pH}\) of this solution? What is the \(\mathrm{OH}^{-}\) concentration in this solution?

Short answer

The concentration of H+ is 0.00065 M. The pH of the solution is calculated using the formula pH = -log(0.00065), which is approximately 3.19. The OH- concentration can be found with [OH-] = 1.0 x 10^-14 / [H+], which gives approximately 1.54 x 10^-11 M.

Step-by-step solution

Determining the Concentration of H+ Ions

Since HNO3 is a strong acid, it dissociates completely in water. Therefore, the concentration of H+ ions in the solution is equal to the concentration of the HNO3 solution. In this case, the concentration of H+ ions is 0.00065 M.

Calculating the pH

The pH of a solution is given by the negative logarithm (base 10) of the H+ ion concentration. Use the formula pH = -log[H+].

Finding the OH- Concentration

To find the OH- concentration in the solution, use the ion product of water at 25 degrees Celsius, which is 1.0 x 10^-14. The relationship between H+ and OH- concentrations is given by [H+][OH-] = 1.0 x 10^-14. Solve for [OH-] using the previously found [H+].

Key concepts

Understanding Strong Acid Dissociation

When we talk about strong acids, like hydrochloric acid (HCl) or nitric acid (HNO3), what distinguishes them is their ability to fully dissociate in water. This means that when you add a strong acid to water, every molecule of the acid separates into its constituent ions completely. For HNO3, this dissociation can be represented as follows: HNO3 → H+ + NO3-. Because the dissociation is complete, the concentration of H+ ions in the solution is directly equal to the initial concentration of the strong acid. This straightforward relationship simplifies calculations and is essential for understanding the behavior of strong acids in various chemical contexts, such as in titrations or when evaluating their corrosive properties.

Dissociation and Reaction Completeness

Unlike weak acids that only partially dissociate, the strong acid's complete dissociation ensures that the reaction goes to completion. As a result, strong acids are also strong electrolytes, conducting electricity well due to their high ion concentrations in solutions.

Calculating H+ Ion Concentration

The concentration of H+ ions in a solution is a direct reflection of its acidity. When dealing with strong acids, calculating the concentration of H+ ions is straightforward. Since we know strong acids fully dissociate, the concentration of the acid before dissociation is the same as the concentration of the H+ ions after dissociation. So if you have a 0.00065 M solution of HNO3, you also have a 0.00065 M concentration of H+ ions. This concept is vital when we want to calculate pH, which is a measure of the acidity of a solution and is directly based on the concentration of H+ ions.

Importance in Acid-Base Reactions

Knowing the concentration of H+ ions is also important for understanding the extent and direction of acid-base reactions. The concentration determines how an acid will react with bases, and it is also a key factor in buffer solutions that resist changes in pH.

Determining OH- Ion Concentration

In an aqueous solution, OH- ion concentration is a measure of basicity, the counterpart to acidity. For every acid dissociation that releases H+ ions, there is an inverse relationship to OH- ion concentration in water. The product of H+ ion concentration and OH- ion concentration is a constant at a given temperature, known as the ion product of water, and is equal to 1.0 x 10^-14 at 25°C. If we have the concentration of H+ ions from a strong acid like HNO3, we can find the OH- ion concentration by rearranging the ion product equation: [OH-] = 1.0 x 10^-14 / [H+].

Acid-Base Neutralization

This concept is not only fundamental for understanding neutralization reactions where acids and bases react to form water and a salt, but also for determining the pH of solutions since pH and pOH are interconnected. By knowing the concentration of either H+ or OH- ions, one can easily find the other and assess the entire acid-base equilibrium of a solution.

The Ion Product of Water

The ion product of water is a constant value that quantifies the relationship between the concentrations of H+ ions and OH- ions in pure water. At 25 degrees Celsius, this value is always 1.0 x 10^-14. It is the product of the concentrations of H+ and OH- ions, which are equal in pure water, hence each is 1.0 x 10^-7 M. When an acid or a base is dissolved in water, it disturbs this balance, but the product of the two ionic concentrations remains constant. This principle helps to calculate the concentration of one ion if the other is known, and it is crucial in understanding how changes in one part of the system affect the other.

Significance in pH and pOH

The ion product of water is the basis for the pH scale, which is logarithmic. It also helps define pOH, and together they must always add up to 14 in any aqueous solution at 25°C. This relationship provides a comprehensive picture of the solution's chemistry and allows for the calculation of the concentration of one ion based on the other. It's an essential concept in all of chemistry, especially in the study of acid-base reactions.