Problem 226 - Introductory Chemistry Atoms First

Question

What is the \(\mathrm{OH}^{-}\) concentration of a solution that has a pH of \(9.66\) ? Is this solution acidic or basic?

Step-by-Step Solution

Answer

The OH⁻ concentration of the solution is approximately \(4.57 \times 10^{-5} \, M\), and the solution is basic.

Step 1: Calculate pOH

To find pOH, we'll use the following equation: \(pH + pOH = 14\). We want to find pOH, so let's solve for it: \[pOH = 14 - pH\] Now, plug in the given pH value: \[pOH = 14 - 9.66\]

Step 2: Evaluate pOH

Now, compute the pOH value: \[pOH = 4.34\]

Step 3: Calculate OH⁻ concentration

To find the OH⁻ concentration, we'll use the following equation, where we relate pOH to the concentration of hydroxide ions: \[pOH = -\log_{10}[\mathrm{OH}^{-}]\] We want to find the hydroxide ion concentration, so let's solve for \([\mathrm{OH}^{-}]\): \[[\mathrm{OH}^{-}] = 10^{-pOH}\] Now, substitute the pOH value we found in step 2: \[[\mathrm{OH}^{-}] = 10^{-4.34}\]

Step 4: Evaluate OH⁻ concentration

Now, compute the OH⁻ concentration: \[[\mathrm{OH}^{-}] \approx 4.57 \times 10^{-5} \, M\]

Step 5: Determine if the solution is acidic or basic

Since the given pH value (9.66) is greater than 7, the solution is considered basic. The OH⁻ concentration of the solution is approximately \(4.57 \times 10^{-5} \, M\), and the solution is basic.

Key Concepts

Acidic and Basic Solutions

Understanding whether a solution is acidic or basic is fundamental in chemistry. The pH scale, which ranges from 0 to 14, is used to determine the acidity or basicity of a solution. A pH value:

• less than 7 indicates an acidic solution
• equal to 7 indicates a neutral solution
• greater than 7 indicates a basic (or alkaline) solution

In this exercise, the pH of the solution is given as 9.66. Since this value is greater than 7, the solution is considered basic. This means that there are fewer hydrogen ions (\(\mathrm{H}^{+}\)) compared to hydroxide ions (\(\mathrm{OH}^{-}\)) in the solution. Basic solutions often result from a compound dissolving in water and releasing more hydroxide ions.

Hydroxide Ion Concentration

The concentration of hydroxide ions (\(\mathrm{OH}^{-}\)) in a solution is crucial in determining its basicity. As we explore the relationship between pOH and hydroxide ion concentration, it's important to remember:

• A higher concentration of \(\mathrm{OH}^{-}\) ions means a more basic solution.
• When \(\mathrm{OH}^{-}\) concentration increases, pOH decreases, making the solution more basic.

To find the hydroxide ion concentration from a known pOH, we apply the equation:\[[\mathrm{OH}^{-}] = 10^{-pOH}\]In our example exercise, after calculating a pOH of 4.34, substituting into this equation gives:\[[\mathrm{OH}^{-}] = 10^{-4.34} \approx 4.57 \times 10^{-5} \text{ M}\]This value indicates a low concentration of hydroxide ions typically found in basic solutions.

Logarithmic Calculations in Chemistry

Logarithms are an essential component in chemistry, particularly when dealing with the pH and pOH scales. They allow us to manage the wide range of ion concentrations.

• The pH is the negative logarithm of the hydrogen ion concentration: \(\text{pH} = -\log_{10}[\mathrm{H}^{+}]\)
• Similarly, the pOH is also the negative logarithm, but of the hydroxide ion concentration: \(\text{pOH} = -\log_{10}[\mathrm{OH}^{-}]\)

These logarithmic relationships mean that a one-unit change in pH or pOH represents a tenfold change in ion concentration. For instance, if pOH decreases by 1, the concentration of \(\mathrm{OH}^{-}\) ions increases by 10 times. In the original exercise, calculating:\[\text{pOH} = 14 - \text{pH}\]allowed us to translate the known acidity (pH) to basicity (pOH) before finding \(\mathrm{OH}^{-}\) concentration, illustrating the crucial bond between logarithmic calculations and solution properties in chemistry.