Problem 75 - Chemistry Matter and Change

Question

What is the relationship between the pOH and the OH- ion concentration of a solution?

Step-by-Step Solution

Answer

The relationship between pOH and the hydroxide ion (OH-) concentration of a solution is given by the equation \(pOH = -log(OH^- \text{concentration})\), which can be rewritten as \(OH^- \text{concentration} = 10^{-pOH}\). This relationship indicates that a higher pOH corresponds to a lower OH- concentration (less basic solution), while a lower pOH corresponds to a higher OH- concentration (more basic solution).

Step 1: Definition of pOH

pOH is the negative base-10 logarithm of the hydroxide ion (OH-) concentration in a solution. It is a measure of the basicity of a solution and is mathematically defined as: pOH = -log(OH- concentration)

Step 2: Relationship between pOH and OH- ion concentration

To find the relationship between pOH and the OH- ion concentration, we can rewrite the expression in terms of the OH- concentration: OH- concentration = 10^(-pOH) This is the relationship between the pOH and the OH- ion concentration of a solution. The higher the pOH, the lower the hydroxide ion concentration and the less basic the solution. Conversely, the lower the pOH, the higher the hydroxide ion concentration and the more basic the solution.

Key Concepts

pOH Definition

Understanding the concept of pOH is crucial for students delving into the chemistry of acids and bases. Simply put, pOH is a scale used to quantify the basicity of a solution. It is related to the more commonly known pH scale, which measures acidity. The pOH value is the negative base-10 logarithm of the concentration of hydroxide ions (\text{OH}^-) present in a solution.

The formula to calculate pOH is:
\[ pOH = -\text{log}([\text{OH}^-]) \]
This formula makes it evident that as the concentration of hydroxide ions increases, the pOH value decreases, indicating a more basic solution. It's the logarithmic nature of this scale that allows us to manage the wide range of hydroxide ion concentrations found in different solutions, from very diluted to highly concentrated.

pOH and Basicity

The concept of basicity is intimately tied to the pOH of a solution. Basicity refers to the capacity of a compound to accept protons or donate electron pairs, which in aqueous solutions, is represented by the presence of hydroxide ions. A basic or alkaline solution has a higher concentration of these ions.

Basic Solutions and pOH

As a rule of thumb, a solution with a pOH less than 7 is considered basic, a pOH of 7 is neutral (pure water), and a pOH greater than 7 is acidic. This might be slightly counterintuitive at first, as we usually associate lower numbers with acids. However, remember that the pOH scale runs in the opposite direction to the pH scale. The two scales are connected through the relationship:\[ pOH + pH = 14 \]
For basic solutions, therefore, a low pOH corresponds to a high pH. The lower the pOH, the stronger the base, meaning a greater ability for the solution to accept protons or donate a pair of electrons.

Hydroxide Ion Concentration Calculation

Calculating the concentration of hydroxide ions in a solution requires an understanding of the inverse logarithmic relationship described by the pOH. When we know the pOH of a solution, we can determine how many hydroxide ions are present.

The relationship is established through the formula:
\[ [\text{OH}^-] = 10^{-pOH} \]
This expression allows us to reverse the pOH calculation. If, for instance, we have a solution with a pOH of 3, using the above formula, we can calculate the hydroxide ion concentration:
\[ [\text{OH}^-] = 10^{-3} = 0.001 \text{ M} \]
The result is the molarity (M), which is the number of moles of hydroxide ions per liter of solution. By applying this formula, students can decipher the link between the pOH and the actual number of hydroxide ions in a solution, allowing for a deeper understanding of a solution's basicity.