Calculating Hydroxide Ion Concentration From POH A Chemistry Guide

In chemistry, understanding the acidity and basicity of solutions is crucial. The pOH is a measure of the hydroxide ion concentration ($[OH^{-}]$) in a solution, analogous to pH for hydrogen ions. This article aims to explain how to calculate the hydroxide ion concentration from a given pOH value, using the formula $[OH^{-}]=10^{-pOH}$. We will delve into the concepts of pOH, hydroxide ion concentration, and the relationship between them, providing a clear and concise explanation for students and chemistry enthusiasts. Understanding these concepts is fundamental in various chemical applications, including titrations, buffer solutions, and reaction kinetics. By mastering the calculation of hydroxide ion concentration from pOH, one can gain deeper insights into the behavior of solutions and their interactions in chemical processes.

Understanding pOH

The pOH of a solution is a measure of its alkalinity or basicity. It is defined as the negative logarithm (base 10) of the hydroxide ion concentration ($[OH^{-}]$) in a solution. Mathematically, it's expressed as:

$pOH = -log_{10}[OH^{-}]$

The pOH scale ranges from 0 to 14, similar to the pH scale. However, the interpretation is reversed: a lower pOH indicates a higher concentration of hydroxide ions and thus a more basic solution, while a higher pOH indicates a lower concentration of hydroxide ions and a more acidic solution. A pOH of 7 signifies a neutral solution at 25°C, where the concentrations of hydroxide and hydrogen ions are equal. To fully grasp the concept of pOH, it's essential to understand its relationship with pH. The sum of pH and pOH in any aqueous solution at 25°C is always 14. This relationship is derived from the ion product of water ($K_w$), which is $1.0 imes 10^{-14}$ at 25°C. The equation representing this relationship is:

$pH + pOH = 14$

This equation is incredibly useful because it allows us to easily calculate either pH or pOH if the other value is known. For instance, if a solution has a pH of 4, its pOH can be calculated as $14 - 4 = 10$. This interconnection between pH and pOH underscores the complementary nature of acidity and basicity in aqueous solutions. The pOH scale, therefore, provides a convenient way to quantify the basicity of a solution, especially in scenarios where hydroxide ion concentrations are more relevant than hydrogen ion concentrations. Furthermore, the pOH concept is vital in various chemical and biological contexts, such as understanding enzyme activity, which is often pH-dependent, and in industrial processes that require precise control of solution alkalinity. By understanding pOH, chemists and other scientists can effectively manage and manipulate chemical reactions and systems to achieve desired outcomes.

Hydroxide Ion Concentration $[OH^{-}]$

The hydroxide ion concentration, denoted as $[OH^{-}]$, represents the amount of hydroxide ions present in a solution, typically measured in moles per liter (M). Hydroxide ions are negatively charged ions formed when a hydroxide compound, such as a base, dissolves in water. They play a crucial role in determining the basicity or alkalinity of a solution. A higher concentration of hydroxide ions indicates a more basic solution, while a lower concentration indicates a more acidic solution. In pure water, a small fraction of water molecules dissociate into hydrogen ions ($H^{+}$) and hydroxide ions ($OH^{-}$), establishing an equilibrium. At 25°C, the concentration of both hydrogen and hydroxide ions in pure water is approximately $1.0 imes 10^{-7}$ M. This equilibrium is described by the ion product of water ($K_w$):

$K_w = [H^{+}][OH^{-}] = 1.0 imes 10^{-14}$

When a base is added to water, it increases the hydroxide ion concentration, shifting the equilibrium and decreasing the hydrogen ion concentration. Conversely, when an acid is added, it increases the hydrogen ion concentration and decreases the hydroxide ion concentration. The relationship between hydroxide ion concentration and pOH is inversely logarithmic, meaning that a small change in pOH can result in a significant change in $[OH^{-}]$. For example, a solution with a pOH of 3 has a much higher hydroxide ion concentration than a solution with a pOH of 10. Measuring and controlling hydroxide ion concentration is essential in numerous applications. In chemical synthesis, the concentration of hydroxide ions can influence reaction rates and product yields. In environmental science, $[OH^{-}]$ levels in natural water bodies affect aquatic life and water quality. In industrial processes, such as wastewater treatment, adjusting hydroxide ion concentration is crucial for removing pollutants and ensuring compliance with environmental regulations. Additionally, in biological systems, the concentration of hydroxide ions plays a vital role in maintaining the pH balance necessary for enzyme function and cellular processes. Therefore, a thorough understanding of hydroxide ion concentration and its measurement is fundamental in various scientific and industrial fields.

Calculating $[OH^{-}]$ from pOH

The relationship between pOH and hydroxide ion concentration $[OH^{-}]$ is defined by the equation:

$pOH = -log_{10}[OH^{-}]$

To find the hydroxide ion concentration $[OH^{-}]$ when the pOH is known, we need to rearrange this equation. This involves taking the antilog (or inverse logarithm) of both sides. The antilog of a base-10 logarithm is simply 10 raised to the power of the value. Therefore, we can rewrite the equation as:

$[OH^{-}] = 10^{-pOH}$

This equation is the key to calculating hydroxide ion concentration from pOH. It states that the hydroxide ion concentration is equal to 10 raised to the power of the negative pOH value. The process is straightforward: given a pOH value, simply plug it into the equation and calculate the result. For instance, if a solution has a pOH of 4, the hydroxide ion concentration can be calculated as:

$[OH^{-}] = 10^{-4} M = 0.0001 M$

This calculation shows that the solution has a hydroxide ion concentration of 0.0001 moles per liter. The exponential nature of this relationship means that even small changes in pOH can lead to substantial changes in hydroxide ion concentration. For example, a change in pOH from 4 to 3 results in a tenfold increase in hydroxide ion concentration. This sensitivity underscores the importance of precise pOH measurements and accurate calculations. In practical applications, this calculation is used extensively in chemistry labs and industrial settings. For example, in titrations, knowing the pOH allows chemists to determine the concentration of a base in a solution. In environmental monitoring, calculating hydroxide ion concentration helps assess water quality and the impact of pollutants. Furthermore, in biochemistry, understanding the relationship between pOH and $[OH^{-}]$ is crucial for studying enzyme kinetics and the pH dependence of biological reactions. By mastering this calculation, one can effectively quantify and manipulate the basicity of solutions in a wide range of scientific and industrial contexts.

Problem

The pOH of a solution is 10.75. What is the concentration of $[OH^{-}]$ ions in the solution? Use $[OH^{-}]=10^{-pOH}]$.

Solution

Given the formula $[OH^{-}]=10^{-pOH}]$ and the pOH value of 10.75, we can calculate the hydroxide ion concentration as follows:

$[OH^{-}] = 10^{-10.75}$

Using a calculator, we find:

$[OH^{-}] hickapprox 1.778 imes 10^{-11} M$

Answer

Therefore, the concentration of $[OH^{-}]$ ions in the solution is approximately $1.778 imes 10^{-11} M$.

The correct answer is B. $1.778 imes 10^{-11} M$.

In conclusion, understanding the relationship between pOH and hydroxide ion concentration is fundamental in chemistry. The ability to calculate $[OH^{-}]$ from pOH using the formula $[OH^{-}]=10^{-pOH}$ is a crucial skill for students and professionals alike. This article has provided a comprehensive explanation of pOH, hydroxide ion concentration, and the method for calculating $[OH^{-}]$ from pOH. By mastering these concepts, one can effectively analyze and manipulate the acidity and basicity of solutions in various chemical and biological contexts. The problem and solution presented demonstrate a practical application of this knowledge, reinforcing the importance of accurate calculations and a thorough understanding of the underlying principles. Whether in the lab, in industrial settings, or in environmental monitoring, the ability to determine hydroxide ion concentration from pOH is an invaluable tool for chemists and scientists.