Problem 60 - Chemistry An Atoms First Approach

Question

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

Step-by-Step Solution

Answer

The concentration of the aqueous HBr solution with a given pH of 4.25 can be found using the formula \([H^+] = 10^{-pH}\). By substituting the pH value into the formula, we find that the concentration of the HBr solution is approximately \(5.623 \times 10^{-5} \,M\).

Step 1: Understanding the pH formula

The pH of a solution is calculated using the formula: pH \( = -\log_{10} [H^+] \) Here, pH is the measure of the acidity of a solution, and \([H^+]\) represents the concentration of \(H^+\) ions in the solution. Since the given solution is HBr (a strong acid), it will dissociate completely into \(H^+\) and \(Br^-\) ions: HBr \( \rightarrow H^+ + Br^- \) The concentration of \(H^+\) ions will be equal to the concentration of HBr.

Step 2: Solve for the concentration of \(H^+\) ions

We are given the pH value of 4.25 and we need to find the concentration of \(H^+\) ions in the solution. We can use the pH formula and solve for the \([H^+]\) concentration: \( 4.25 = -\log_{10} [H^+] \)

Step 3: Rearranging the pH formula

To find \([H^+]\), we need to rearrange the pH formula: \([H^+] = 10^{-pH} \)

Step 4: Substituting the given pH value in the formula

Now substitute the given pH value (4.25) into the formula to find the \([H^+]\) concentration: \[ [H^+] = 10^{-4.25} \]

Step 5: Calculating the concentration of \(H^+\) ions

Using a calculator, find the concentration of \(H^+\) ions: \([H^+] \approx 5.623 \times 10^{-5} \,M \)

Step 6: Finding the concentration of HBr

Since the concentration of \(H^+\) ions is equal to the concentration of HBr in the solution (because HBr is a strong acid and dissociates completely), the concentration of the HBr solution is: \[ [HBr] = [H^+] = 5.623 \times 10^{-5} \,M \] So the concentration of the HBr solution is approximately \(5.623 \times 10^{-5} \,M\).

Key Concepts

pH calculation

The concept of pH is vital in understanding the acidity or basicity of a solution. pH is a logarithmic scale that measures the concentration of hydrogen ions (\([H^+]\)) in a solution. The formula to calculate pH is:\[pH = -\log_{10} [H^+]\]This equation indicates that a lower pH value corresponds to a higher concentration of \([H^+]\) ions, meaning the solution is more acidic. Conversely, a higher pH value indicates a lower \([H^+]\) concentration, making the solution more basic. When solving for \([H^+]\) given a specific pH value, rearrange the equation to:\[[H^+] = 10^{-\mathrm{pH}}\]This rearrangement helps you find the concentration of hydrogen ions when the pH is known. If the pH is 4.25, the concentration of \([H^+]\) ions can be calculated using this formula. Understanding pH calculations is essential in various fields, such as chemistry, biology, and environmental science.

strong acids

Strong acids are a category of acids that completely dissociate in water, releasing all of their hydrogen ions (\(H^+\)) into the solution. This complete dissociation is the key characteristic that defines a strong acid, and it results in a high concentration of \(H^+\) ions compared to weak acids that partially dissociate.Some common examples of strong acids include:

• Hydrochloric acid (\(HCl\))
• Hydrobromic acid (\(HBr\))
• Sulfuric acid (\(H_2SO_4\))
• Nitric acid (\(HNO_3\))

For a strong acid like HBr, the concentration of \(H^+\) ions produced in the solution will be the same as the concentration of the acid itself. This is because the dissociation equation, \(HBr \rightarrow H^+ + Br^-\), results in the stoichiometric release of hydrogen ions.Knowing the properties of strong acids is important in predicting their behavior in chemical reactions, their impact on the environment, and their role in various industrial processes.

chemical dissociation

Chemical dissociation refers to the process where molecules break apart into smaller constituents, such as ions. In the case of acids, dissociation typically involves the breaking of the bond between hydrogen and another element, resulting in the release of hydrogen ions (\(H^+\)).For example, an acid like hydrobromic acid (\(HBr\)) dissociates in water:\[HBr \rightarrow H^+ + Br^-\]In this dissociation reaction, HBr splits into hydrogen ions (\(H^+\)) and bromide ions (\(Br^-\)). The extent of dissociation depends on whether the acid is strong or weak:

• **Strong acids** dissociate completely, meaning 100% of the acid molecules split into ions.
• **Weak acids** dissociate partially, meaning only a fraction of the acid molecules split to produce ions.

Understanding chemical dissociation is crucial for predicting the behavior of substances in a solution, determining the strength of an acid, and calculating concentrations of ions present in a variety of chemical contexts.