Question

What is the \(\mathrm{pH}\) of solutions having the following \(\mathrm{OH}^{-}\) concentrations? Identify each as acidic, basic, or neutral. (a) \(\left[\mathrm{OH}^{-}\right]=6.4 \times 10^{-4} M\) (b) \(\left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M}\) (c) \(\left[\mathrm{OH}^{-}\right]=2.7 \times 10^{-10} M\)

Short answer

(a) The solution with \(\left[\mathrm{OH}^{-}\right]=6.4 \times 10^{-4} M\) is basic with \(\mathrm{pH}>7\). (b) The solution with \(\left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M}\) is strongly basic with an expected \(\mathrm{pH}\) far greater than \(7\), and (c) The solution with \(\left[\mathrm{OH}^{-}\right]=2.7 \times 10^{-10} M\) is acidic with \(\mathrm{pH}<7\).

Step-by-step solution

Computing pOH

First, calculate the \(\mathrm{pOH}\) for each solution based on the given \(\mathrm{OH}^{-}\) concentration. This is done by taking the negative logarithm of the \(\mathrm{OH}^{-}\) concentration.

Calculate pH

Now calculate the \(\mathrm{pH}\) by subtracting the obtained \(\mathrm{pOH}\) from \(14\).

Identify the solution character

From the calculated \(\mathrm{pH}\) value, determine whether the solutions are acidic, basic, or neutral by comparing the \(\mathrm{pH}\) value with \(7\) as explained above.

Key concepts

pOH Calculation

To understand how to calculate the pOH of a solution, you need to know the concentration of hydroxide ions \[ \left( \mathrm{OH}^{-} \right) \]. pOH is determined using the formula: \[\text{pOH} = -\log \left( \left[ \mathrm{OH}^{-} \right] \right) \] This formula finds the negative logarithm (base 10) of the hydroxide ion concentration.

The pOH scale helps gauge the basicity of a solution. A lower pOH indicates a more basic solution, while a higher pOH means it's less basic. It’s an important step towards determining the pH of a solution.

For example, if a solution has an \( \left[ \mathrm{OH}^{-} \right] \) of \(6.4 \times 10^{-4} \ M \), the pOH is calculated as follows:

• \( \text{pOH} = -\log \left( 6.4 \times 10^{-4} \right) \)
• Using a calculator, you find the pOH is approximately \(3.19\).

Understanding the pOH is key to further calculations in pH and identifying the nature of the solution.

Acidic Basic Neutral Solutions

Solutions are classified based on their pH value into three main categories: acidic, basic, and neutral.

- **Acidic Solutions**: These have a pH value less than 7. They're rich in hydrogen ions \( \left( \mathrm{H}^{+} \right) \) and taste sour (like vinegar).- **Basic Solutions**: These solutions have a pH value greater than 7. They contain more hydroxide ions \( \left( \mathrm{OH}^{-} \right) \) and often feel slippery (like soapy water).- **Neutral Solutions**: These have a pH of exactly 7, indicating a balance between hydrogen and hydroxide ions. Pure water is a classic example.

The pH scale typically runs from 0 to 14, where a pH close to 0 is highly acidic and a pH close to 14 is highly basic. Knowing how to classify solutions based on their pH is crucial for applications like nutrient management in agriculture and formulating safe household cleaning products.

Hydroxide Concentration

Hydroxide concentration \( \left( \left[ \mathrm{OH}^{-} \right] \right) \) plays a pivotal role in defining the nature of a solution as acidic, basic, or neutral. It's directly used to calculate pOH and eventually pH.

To determine the hydroxide concentration of a solution, you usually need information about how the solution is prepared or its pH. Inversely, given the hydroxide concentration, one can deduce important characteristics about the solution.

Here's a step-by-step to understand its importance:

• Measure or know \( \left[ \mathrm{OH}^{-} \right] \), the molar concentration of hydroxide ions.
• Use this concentration to find the pOH with the formula \( \text{pOH} = -\log \left( \left[ \mathrm{OH}^{-} \right] \right) \).
• Next, calculate the pH by subtracting the pOH from 14: \( \text{pH} = 14 - \text{pOH} \).
• This pH value will tell you if the solution is acidic, basic, or neutral.

Understanding and calculating hydroxide concentration helps in multiple fields such as chemistry labs, environmental science, and even personal care product formulation.