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

pOH is related to hydroxide ion concentration by the formula \( \text{pOH} = -\log_{10} [\text{OH}^-] \).

Step 1: Understanding pOH

The pOH measures the hydroxide ion concentration in a solution. It is an analogous concept to pH, which measures the concentration of hydrogen ions (H+). The pOH scale is logarithmic, similar to the pH scale.

Step 2: Mathematical Formula for pOH

The pOH of a solution is calculated using a logarithmic equation: \[ \text{pOH} = -\log_{10} [\text{OH}^-] \] where \([\text{OH}^-]\) is the molarity (concentration) of hydroxide ions in moles per liter.

Step 3: Relating pOH and Hydroxide Ion Concentration

To relate pOH to the OH- concentration, note that if you have a pOH value, you can determine the concentration of hydroxide ions using the inverse logarithmic operation: \[ [\text{OH}^-] = 10^{-\text{pOH}} \] This formula helps you find the concentration of OH- ions if the pOH is known.

Key Concepts

Hydroxide Ion Concentration

Understanding Hydroxide ion concentration refers to the amount of hydroxide ions (OH-) present in a solution. These ions are crucial in determining whether a solution is acidic or basic. A higher concentration of hydroxide ions indicates a more basic (alkaline) solution. This concentration is measured in moles per liter (M), also known as molarity. When you want to understand the nature of a solution, looking at the OH- concentration can give insight into its basicity. For instance:

• In pure water, the concentration of OH- ions is equal to the concentration of H+ ions, making it neutral.
• In basic solutions, the OH- concentration is higher than that of H+ ions.
• In acidic solutions, the OH- concentration is lower.

Knowing the OH- concentration helps when calculating the pOH, which is the primary measurement of a solution's basicity, and is inversely related to the pH.

Logarithmic Scale

Explaining the Nature of pOH's Scale The logarithmic scale is a way to express quantities, like ion concentrations, in a more manageable form. Both the pH and pOH scales use this type of expression. The reasoning behind using a logarithmic scale is to handle the wide range of ion concentrations easily, as the concentrations can vary greatly in magnitude. Mathematically, the pOH of a solution is calculated with the equation:\[\text{pOH} = -\log_{10} [\text{OH}^-]\]

• The logarithm is negative, which means that a high OH- concentration results in a low pOH value.
• A tenfold increase in OH- ion concentration decreases the pOH by 1 unit.

This inverse relationship helps to make calculations simpler and more intuitive. By transforming large numbers via the logarithmic scale, we can easily compare ion concentrations and understand their significance in terms of acidity and basicity.

pH Comparison

Relating pH and pOH Both pH and pOH are vital in understanding the acidity or basicity of solutions, with each one providing different insights into the nature of the solution. The relationship between them is intertwined and simple to understand if based on the principle that the sum of pH and pOH equals 14 at 25°C.Here are some key points:

• pH measures the concentration of hydrogen ions \( [\text{H}^+]\), while pOH measures the concentration of hydroxide ions \( [\text{OH}^-]\).
• When the pH is low, indicating high acidity, the pOH is high, indicating low basicity, and vice versa.
• A neutral solution, like pure water, at 25°C has a pH of 7 and a pOH of 7, making the total 14.

By comparing pH and pOH, you have a dual perspective on the solution's properties. This means one can easily switch between understanding the acidic nature with pH or the basic nature with pOH. The pH/pOH relationship enables a more holistic understanding of a solution's acidity or alkalinity.