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Chapter 15: Problem 211

What is the molar hydroxide ion concentration in a solution that is 1000 times more acidic than a solution that has a pH of \(9.20\) ?

Short Answer

Expert verified
The molar hydroxide ion concentration in the given solution is approximately \(1.58 \times 10^{-8}\) M.

Step by step solution

01

Determine the pH of the given solution.

Since the solution is 1000 times more acidic than a solution with a pH of 9.20, we need to express this acidity difference using the pH scale. The pH scale is logarithmic, and a difference of 1 on the pH scale corresponds to a 10-fold difference in acidity. Thus, we are looking for a pH difference of 3 (since 10^3 = 1000). Since the given solution is more acidic, the pH value will be lower than 9.20. So, subtracting 3 from the given pH, we have: pH = 9.20 - 3 = 6.20
02

Find the pOH of the given solution.

To find the pOH of the solution, we use the relationship between pH and pOH: pH + pOH = 14 Now, we can plug in the pH value we have calculated in the previous step to find the pOH: pOH = 14 - 6.20 = 7.80
03

Calculate the molar hydroxide ion concentration.

Finally, we can use the definition of pOH to find the molar OH- ion concentration: \[pOH = -\log_{10}([OH^{-}])\] Now, we can rearrange the equation to solve for [OH-]: \[[OH^{-}] = 10^{-pOH}\] Plug in the pOH value we have calculated in step 2: \[[OH^{-}] = 10^{-7.80}\] \[[OH^{-}] \approx 1.58 \times 10^{-8} \,M\] So, the molar hydroxide ion concentration in the given solution is approximately \(1.58 \times 10^{-8}\) M.

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Most popular questions from this chapter

Hydride ion, \(\mathrm{H}\), is an exceptionally strong base, reacting with water to produce lots of hydroxide ion and \(\mathrm{H}_{2}\) gas. The \(K_{\mathrm{eq}}\) for this reaction is huge. (a) Write the balanced equation for the reaction between hydride and water. (b) Explain why \(\mathrm{H}_{2}\) gas forms. (Hint: Use the Bronsted-Lowry definition of base.)

Can a buffer resist \(\mathrm{pH}\) changes for any added amount of strong acid or base? Explain.

The base- 10 logarithm of 60 is a number: (a) Between \(-2\) and \(-1\) (b) Between \(-1\) and 0 (c) Between 0 and 1 (d) Between 1 and 2 (e) Between 2 and 3

What is the \(\mathrm{pH}\) of these aqueous solutions? (a) \(1.0 \mathrm{M} \mathrm{HCl}\), (b) \(0.1 \mathrm{M} \mathrm{HCl}\), (c) \(0.001 \mathrm{M} \mathrm{HCl}\), (d) \(1.0 \times 10^{-5} \mathrm{M} \mathrm{HCl}\), (e) \(1.10 \times 10^{-7} \mathrm{M} \mathrm{HCl}\)

A buffer works by replacing added strong acid with weak acid. Explain how.
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