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Chapter 13: Problem 60

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

Short Answer

Expert verified
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 by step solution

01

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.
02

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: \( 4.25 = -\log_{10} [H^+] \)
03

Rearranging the pH formula

To find \([H^+]\), we need to rearrange the pH formula: \([H^+] = 10^{-pH} \)
04

Substituting the given pH value in the formula

Now substitute the given pH value (4.25) into the formula to find the \([H^+]\) concentration: \[ [H^+] = 10^{-4.25} \]
05

Calculating the concentration of \(H^+\) ions

Using a calculator, find the concentration of \(H^+\) ions: \([H^+] \approx 5.623 \times 10^{-5} \,M \)
06

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 \(5.623 \times 10^{-5} \,M\).

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