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Chapter 8: Problem 1

Why doesn't water dissociate to produce \(10^{-7} \mathrm{M} \mathrm{H}^{+}\)and \(10^{-7} \mathrm{M}\) \(\mathrm{OH}^{-}\)when some \(\mathrm{HBr}\) is added?

Short Answer

Expert verified
Water dissociates less because the added HBr increases \([\text{H}^+]\) beyond \(10^{-7}\, \text{M}\), shifting equilibrium and reducing water's ionization.

Step by step solution

01

Understanding Water's Self-Ionization

Pure water at 25掳C has a self-ionization equilibrium given by the reaction: \[ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- \]The equilibrium constant for water, known as the ion-product constant \( K_w \), is expressed as: \[ K_w = [\text{H}^+][\text{OH}^-] = 10^{-14} \] In pure water, since \([\text{H}^+] = [\text{OH}^-]\), both concentrations are \(10^{-7}\, \text{M}\).
02

Adding HBr to Water

HBr is a strong acid, meaning it dissociates completely in water. When HBr is added to water, it increases the \([\text{H}^+]\) concentration significantly beyond \(10^{-7}\, \text{M}\).
03

Impact on Water's Ionization Equilibrium

With the addition of HBr, the increased \([\text{H}^+]\) shifts the equilibrium between water's self-ionization. According to Le Chatelier's principle, adding more \(\text{H}^+\) shifts the equilibrium towards the left, decreasing the ionization of water and therefore, further decreasing \([\text{OH}^-]\) as \([\text{H}^+]\) is compensated.
04

Establishing a New Equilibrium

In the presence of a strong acid like HBr, the \( K_w \) remains constant at \(10^{-14}\), but the individual concentrations of \([\text{H}^+]\) and \([\text{OH}^-]\) will no longer be equal to \(10^{-7}\, \text{M}\). The concentration of \([\text{OH}^-]\) will be reduced due to the larger \([\text{H}^+]\) from HBr.

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Key Concepts

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

Self-Ionization of Water
Water has a unique ability to undergo self-ionization. At 25掳C, water molecules will occasionally split into two ions: a hydrogen ion \(\text{H}^+\) and a hydroxide ion \(\text{OH}^-\). This process can be represented by the chemical equation: \[ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- \] It's important to remember that in pure water, the concentrations of these ions are equal at \(10^{-7} \, \text{M}\).
  • At equilibrium, the concentration of \(\text{H}^+\) equals the concentration of \(\text{OH}^-\).
  • This balanced state is highly sensitive to changes in the environment.
Any significant alteration can shift the equilibrium, which is crucial to understanding chemical reactions in solutions.
Strong Acids
Strong acids, like hydrobromic acid \(\text{HBr}\), are characterized by their complete dissociation in water. This means that when \(\text{HBr}\) is added to water, it breaks up entirely into \(\text{H}^+\) ions and \(\text{Br}^-\) ions.
  • The presence of these freely available \(\text{H}^+\) ions increases the overall hydrogen ion concentration rapidly.
  • This disrupts the natural balance of self-ionization in water, making the usual ion concentrations deviate.
By overpowering the naturally occurring \(\text{H}^+\) and \(\text{OH}^-\), strong acids result in a new dynamic balance that necessitates chemical adjustment based on the Le Chatelier's principle.
Le Chatelier's Principle
Le Chatelier's Principle is a fundamental concept in chemistry used to predict the behavior of a system when subjected to changes in concentration, temperature, or pressure. In terms of water's self-ionization equilibrium, when additional \(\text{H}^+\) ions are added through an acid like \(\text{HBr}\), the equilibrium shifts.
  • This principle implies a system at equilibrium will adjust to minimize the effect of the change.
  • In this scenario, it means the reaction shifts to the left, forming more \(\text{H}_2\text{O}\) and reducing \(\text{OH}^-\) concentration.
This action helps maintain the constant product of the ion concentrations, despite the new imbalance caused by the strong acid.
Ion-Product Constant
The ion-product constant, denoted as \(K_w\), is crucial for understanding the behavior of water at equilibrium, \([\text{H}^+][\text{OH}^-] = 10^{-14}\) at 25掳C. This constant remains unchanged, even when the system is disturbed by added acids or bases.
  • Despite the changes in individual ion concentrations, the product, \(K_w\), always equates to \(10^{-14}\).
  • For example, an increase in \(\text{H}^+\) means a reciprocal decrease in \(\text{OH}^-\) to restore the balance.
Hence, while \(\text{H}^+\) may dominate due to a strong acid addition, \(\text{OH}^-\) will decrease to ensure that the ion-product constant does not change.

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