Problem 30 - Chemistry The Central Science

Question

Calculate \(\left[\mathrm{OH}^{-}\right]\) for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: \((\mathbf{a})\left[\mathrm{H}^{+}\right]=0.0505 M (\mathbf{b})\left[\mathrm{H}^{+}\right]=2.5 \times 10^{-10} M ;(\mathbf{c})\) a solution in which \(\left[\mathrm{H}^{+}\right]\) is 1000 times greater than \(\left[\mathrm{OH}^{-}\right] .\)

Step-by-Step Solution

Answer

The concentrations of OH- ions for each solution are: (a) \([\mathrm{OH}^{-}] = 1.98 \times 10^{-13}\,M\), acidic (b) \([\mathrm{OH}^{-}] = 4.0 \times 10^{-5}\,M\), basic (c) \([\mathrm{OH}^{-}] = 1.0 \times 10^{-8.5}\,M\), acidic

Step 1: Find the concentration of OH- ions for each solution

We will use the ion product of water equation to find the concentration of OH- ions for each solution. \(K_{w} = [\mathrm{H}^{+}] [\mathrm{OH}^{-}]\) For (a), (b), and (c), we will plug in the given value of [\(\mathrm{H}^{+}\)] and solve for [\(\mathrm{OH}^{-}\)].

Step 2: Determine whether the solution is acidic, basic, or neutral

To determine the nature of each solution, we will compare the [\(\mathrm{H}^{+}\)] and [\(\mathrm{OH}^{-}\)] concentrations. If [\(\mathrm{H}^{+}\)] > [\(\mathrm{OH}^{-}\)], the solution is acidic. If [\(\mathrm{H}^{+}\)] < [\(\mathrm{OH}^{-}\)], the solution is basic. If [\(\mathrm{H}^{+}\)] = [\(\mathrm{OH}^{-}\)], the solution is neutral. Let's find the concentrations of OH- ions and the nature of each solution.

Step 3: (a)

Given [\(\mathrm{H}^{+}\)] = 0.0505 M, we can find the [\(\mathrm{OH}^{-}\)] concentration: \(1.0 \times 10^{-14} = (0.0505) [\mathrm{OH}^{-}]\) \([\mathrm{OH}^{-}] = \frac{1.0 \times 10^{-14}}{0.0505} = 1.98 \times 10^{-13}\,M\) Since [\(\mathrm{H}^{+}\)] > [\(\mathrm{OH}^{-}\)], the solution is acidic.

Step 4: (b)

Given [\(\mathrm{H}^{+}\)] = \(2.5 \times 10^{-10}\,M\), we can find the [\(\mathrm{OH}^{-}\)] concentration: \(1.0 \times 10^{-14} = (2.5 \times 10^{-10}) [\mathrm{OH}^{-}]\) \([\mathrm{OH}^{-}] = \frac{1.0 \times 10^{-14}}{2.5 \times 10^{-10}} = 4.0 \times 10^{-5}\,M\) Since [\(\mathrm{H}^{+}\)] < [\(\mathrm{OH}^{-}\)], the solution is basic.

Step 5: (c)

Given that [\(\mathrm{H}^{+}\)] is 1000 times greater than [\(\mathrm{OH}^{-}\)], we can write this relation as: \([\mathrm{H}^{+}] = 1000 [\mathrm{OH}^{-}]\) Using the ion product of water: \(1.0 \times 10^{-14} = (1000 [\mathrm{OH}^{-}]) [\mathrm{OH}^{-}]\) \([\mathrm{OH}^{-}]^2 = \frac{1.0 \times 10^{-14}}{1000} = 1.0 \times 10^{-17}\) \([\mathrm{OH}^{-}] = 1.0 \times 10^{-8.5}\,M\) Since [\(\mathrm{H}^{+}\)] > [\(\mathrm{OH}^{-}\)], the solution is acidic.

Key Concepts

Ion Product of Water

Water dissociates into hydrogen ions offers insight into the **acidic** or **basic** nature of a solution. You can determine the balance of in a solution is a foundational concept in understanding **pH** and **acidity**.

pH Calculations

Calculating pH is a simple way to understand the acidity or basicity of a solution. - When we say something is acidic, it usually has a low Using the formula A value of 7 is neutral, like pure water. Anything **below** indicates acidic, and indicates basic conditions.
So, by calculating pH, we can easily categorize solutions.

Solution Acidity

Understanding solution acidity helps in determining whether substances are acidic, basic, or neutral. Neutral solutions, such as pure water, have balanced To note, even small changes in the balance of the important role of balancing solutions underpin many biological and chemical processes.