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Write an equation relating \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in solu tion at \(25^{\circ} \mathrm{C}\).

Short Answer

Expert verified
\(\left[\mathrm{H}^{+}\right] \times \left[\mathrm{OH}^{-}\right] = 1.0 \times 10^{-14} \) at 25°C.

Step by step solution

01

Understanding the Concept of Water Ionization

At 25°C, pure water undergoes a self-ionization process, in which water molecules ionize slightly to form hydrogen ions \( \left[\mathrm{H}^{+}\right] \) and hydroxide ions \( \left[\mathrm{OH}^{-}\right] \). The equilibrium constant for this process is called the ionic product of water, denoted as \(K_w\).
02

Recall the Value of the Ionic Product of Water

At 25°C, the value of \(K_w\) for water is \(1.0 \times 10^{-14} \). This value represents the product of the concentrations of hydrogen ions and hydroxide ions in the water.
03

Write the Ionic Product Equation

The relationship between \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) at equilibrium is given by the equation: \[ \left[\mathrm{H}^{+}\right] \times \left[\mathrm{OH}^{-}\right] = 1.0 \times 10^{-14} \] This is known as the ionic product of water equation, specific to conditions at 25°C.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Water Ionization
Water ionization, a fascinating yet subtle process, occurs naturally even in pure water. At 25°C, water molecules self-ionize, meaning they split into hydrogen ions (\[\mathrm{H}^{+}\]) and hydroxide ions (\[\mathrm{OH}^{-}\]). This process is crucial for understanding the properties of solutions. Every water molecule has a chance to ionize, although this is relatively rare. This self-ionization sets the stage for much of our chemistry in aqueous solutions.
Whenever water ionizes, it forms one hydrogen ion and one hydroxide ion from a water molecule. This balanced ionization ensures the neutrality of pure water. It’s important to note that this is an equilibrium process. The concentrations of (\[\mathrm{H}^{+}\]) and (\[\mathrm{OH}^{-}\]) remain constant under stable conditions.
Equilibrium Constant
The equilibrium constant in acid-base chemistry, particularly for water, is called the ionic product of water. Symbolized as (\[K_w\]),this constant gives the relationship between hydrogen ion and hydroxide ion concentrations in water at equilibrium. For water at 25°C, (\[K_w\])is valued at (\[1.0 \times 10^{-14}\]).This means even a small change in (\[\mathrm{H}^{+}\]) concentration results in a significant impact on (\[\mathrm{OH}^{-}\]) concentration and vice versa.
At equilibrium, the product of the concentrations of both ion types equals (\[K_w\]).This is a fundamental principle known as dynamic equilibrium. It’s crucial for calculating the pH of a solution, predicting the behavior of acids and bases in water.
Hydrogen Ions
Hydrogen ions (\[\mathrm{H}^{+}\])play a vital role in determining the acidity of a solution. Their concentration directly impacts the pH value, which is a measure of how acidic or basic a solution is. In pure water at 25°C, the concentration of hydrogen ions is (\[10^{-7}\])M, maintaining a neutral pH of 7.
When an acid dissolves in water, it increases the (\[\mathrm{H}^{+}\])concentration. This results in a lower pH, indicating increased acidity. Conversely, a decrease in hydrogen ions signifies a basic or alkaline environment. Understanding (\[\mathrm{H}^{+}\])is essential for grasping acid-base reactions and buffer solutions.
Hydroxide Ions
Hydroxide ions (\[\mathrm{OH}^{-}\])are equally important in chemical reactions involving water. They determine the basicity or alkalinity of a solution. A pure water solution possesses a hydroxide ion concentration also equal to (\[10^{-7}\])M in equilibrium at 25°C. This reflects a balance with hydrogen ions.
Adding a base to the solution increases the (\[\mathrm{OH}^{-}\])concentration, which raises the pH, signifying a more basic solution. Hydroxide ions are pivotal in explaining how alkaline solutions neutralize acids. The balance between (\[\mathrm{H}^{+}\])and (\[\mathrm{OH}^{-}\])is vital for maintaining pH levels in various chemical and biological systems.

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