Question

Calculate the concentration of an aqueous HBr solution that has \(\mathrm{pH}=4.25 . \mathrm{HBr}\) is a strong acid.

Short answer

The concentration of the aqueous HBr solution is approximately \(5.62 \times 10^{-5} \ \text{M}\).

Step-by-step solution

Understand the relationship between pH and H+ concentration.

The pH of a solution is defined as: \[pH = -\log_{10}[H^+]\] where [H⁺] is the concentration of hydrogen ions in the solution. Since we are given the pH, we can solve for [H⁺].

Calculate the concentration of H⁺ ions.

To find the concentration of H⁺ ions, we rearrange the formula from step 1 and plug in the given pH value (4.25): \[[H^+] = 10^{-pH} = 10^{-4.25}\] Calculate the concentration of H⁺ ions: \[[H^+] = 10^{-4.25} \approx 5.62 \times 10^{-5} \ \text{M}\]

Determine the concentration of HBr.

Since HBr is a strong acid and ionizes completely, the concentration of HBr in the solution is equal to the concentration of H⁺ ions. Therefore, the concentration of the aqueous HBr solution is approximately \(5.62 \times 10^{-5} \ \text{M}\).

Key concepts

Understanding Strong Acids

Strong acids, such as HBr, play an important role in chemical reactions due to their ability to completely dissociate into their respective ions in water. When we say an acid is "strong," it means that when the acid is dissolved in water, it fully splits into its constituent ions. For HBr (hydrobromic acid), this means it separates into hydrogen ions (H⁺) and bromide ions (Br⁻) completely.
This complete ionization is key to understanding strong acids:

• 100% of the acid molecules dissociate into ions.
• This leads to a high concentration of hydrogen ions, directly affecting the pH of the solution.
• The behavior of strong acids contrasts with weak acids, which only partially dissociate in solution.

Recognizing whether an acid is strong or weak is crucial in pH calculations since strong acids directly influence the hydrogen ion concentration in a predictable way.

Hydrogen Ion Concentration and pH

The concentration of hydrogen ions \([H^+]\) in a solution determines its acidity and is inversely related to the pH value. Understanding this relationship is key to calculating both pH and the concentration of ions:The formula \(pH = -\log_{10}[H^+]\) illuminates this relationship:

• Lower pH values mean higher concentrations of hydrogen ions and stronger acidity.
• The pH scale is logarithmic, so each whole pH value change represents a tenfold difference in ion concentration.

To find the concentration of hydrogen ions when pH is known, the equation is rearranged as \([H^+] = 10^{-pH}\). This method allows you to find the exact concentration of ions from a given pH, which is particularly useful when dealing with solutions of strong acids, where the pH directly represents the hydrogen ion concentration.

Introduction to Chemical Equilibrium in Acid Solutions

Chemical equilibrium refers to the state where the reactants and products formed in a chemical reaction are balanced in concentration over time. For acid-base reactions, particularly with strong acids, this concept differs slightly: In solutions of strong acids like HBr, the idea of equilibrium simplifies because the reaction driving the dissociation of the acid into ions almost entirely loads the products' side:

• All or nearly all acid molecules are converted to ions (e.g., H⁺ and Br⁻).
• The equilibrium constant for strong acids implies nearly complete conversion, often not needing explicit mention.

In a practical sense, when dealing with strong acids, calculations about concentration happen more straightforwardly since the dissociation constant is assumed to be 1, reflecting that practically all of the acid present is contributing to the [H⁺] in solution. This understanding can simplify our approach to many practical problems involving strong acids and acidity assessment.