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Chapter 15: Problem 129

An aqueous solution has an \(\mathrm{H}_{3} \mathrm{O}\) ' concentration of \(1.0 \mathrm{M}\). What is the OH concentration? Is this solution acidic or basic? Justify your answer.

Short Answer

Expert verified
The OH⁻ concentration is \(1.0 \times 10^{-14}\) M, and since the H₃O⁺ concentration (1.0 M) is greater than the OH⁻ concentration, the solution is acidic.

Step by step solution

01

Determine the H₃O⁺ concentration

The problem states that the hydronium ion concentration is 1.0 M. So, we have: \[ [\mathrm{H}_{3} \mathrm{O}^{+}] = 1.0\,M \]
02

Calculate the OH⁻ concentration using the ion product of water

The ion product of water, Kw, is given by: \[K_w = [\mathrm{H}_{3} \mathrm{O}^{+}] [\mathrm{OH}^{-}] \] At 25°C, the ion product of water is: \[K_w = 1.0 \times 10^{-14}\] To find the OH⁻ concentration, rearrange the equation: \[[\mathrm{OH}^{-}] = \frac{K_w}{[\mathrm{H}_{3} \mathrm{O}^{+}]}\] Substitute the values of Kw and H₃O⁺ concentration: \[[\mathrm{OH}^{-}] = \frac{1.0 \times 10^{-14}}{1.0\,M}\]
03

Calculate the OH⁻ concentration

Now, divide the value of Kw by the given H₃O⁺ concentration: \[[\mathrm{OH}^{-}] = 1.0 \times 10^{-14}\]
04

Determine if the solution is acidic or basic

To determine if the solution is acidic or basic, compare the H₃O⁺ and OH⁻ concentrations: - If H₃O⁺ > OH⁻, the solution is acidic - If H₃O⁺ < OH⁻, the solution is basic - If H₃O⁺ = OH⁻, the solution is neutral Since [\(\mathrm{H}_{3} \mathrm{O}^{+}\)] = 1.0 M and [\(\mathrm{OH}^{-}\)] = \(1.0 \times 10^{-14}\) M, \[ [\mathrm{H}_{3} \mathrm{O}^{+}] > [\mathrm{OH}^{-}] \] Hence, the given solution is acidic.

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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.)

Write the mathematical expression that allows you to solve for the \(\mathrm{OH}^{-}\) concentration in water when you know only the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration.

The equilibrium constant for the reaction \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{NH}_{3}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q)\) is \(5.6 \times 10^{-10}\) (a) Is a solution of ammonium ion very acidic or only slightly acidic? (b) Is water acting as an acid or a base according to the Bronsted-I owry definition? Explain.

Why is the conjugate base of a weak acid like acetic acid often referred to as a salt of the acid?

Determine the ammonia concentration of an aqueous solution that has a pH of \(11.50\). The equation for the dissociation of \(\mathrm{NH}_{3}\) \(\left(\mathrm{K}_{\mathrm{b}}=1.8 \times 10^{-5}\right)\) is \(\mathrm{NH}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows\) \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{OH}^{-}(a q)\)
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