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Chapter 16: Problem 28

(a) Write a chemical equation that illustrates the autoionization of water. (b) Write the expression for the ion-product constant for water, \(K_{w}\) (c) If a solution is described as basic, which of the following is true: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right]\), (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right]\), or (iii) \(\left[\mathrm{H}^{+}\right]<[\mathrm{OH}]\) ?

Short Answer

Expert verified
(a) The autoionization of water is represented by the equation: \[2 H_{2}O \rightleftharpoons H_{3}O^{+} + OH^{-}\] (b) The ion-product constant for water is expressed as: \[K_w = [H^{+}] [OH^{-}]\] (c) For a basic solution, the true statement is (iii) \(\left[\mathrm{H}^{+}\right]<[\mathrm{OH}]\).

Step by step solution

01

Part (a): Autoionization of Water

The autoionization of water is represented as the equilibrium reaction between water molecules, where two water molecules form a hydronium ion (H鈧僌鈦� or H鈦� in simpler notation) and a hydroxide ion (OH鈦�). The equation is: \[2 H_{2}O \rightleftharpoons H_{3}O^{+} + OH^{-}\]
02

Part (b): Ion-Product Constant for Water Expression and \(K_w\)

For any chemical equilibrium reaction, we can set up an equilibrium constant (K). In the case of water, we have an ion-product constant, \(K_w\), which is the equilibrium constant for the autoionization of water. The expression for \(K_w\) can be described as: \[K_w = [H^{+}] [OH^{-}]\] It is essential to remember that the concentrations of these ions are in moles per liter (mol/L). At 25掳C, the ion-product constant for water is \(K_w = 1.0 \times 10^{-14}\).
03

Part (c): Determining the True Statement for a Basic Solution

A solution is considered basic or alkaline if it has a greater concentration of hydroxide ions (OH鈦�) than hydronium ions (H鈧僌鈦� or H鈦� for simplicity). Let's analyze the given options: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right]\) - This statement is representative of an acidic solution, where the concentration of H鈦� is greater than OH鈦�. (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right]\) - This statement is representative of a neutral solution, where the concentrations of H鈦� and OH鈦� are equal. (iii) \(\left[\mathrm{H}^{+}\right]<[\mathrm{OH}]\) - This statement is representative of a basic solution, where the concentration of OH鈦� is greater than H鈦�. For a basic solution, statement (iii) \(\left[\mathrm{H}^{+}\right]<[\mathrm{OH}]\) is true.

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Key Concepts

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

Chemical Equilibrium
Chemical equilibrium is a dynamic state where the rate of the forward reaction equals the rate of the reverse reaction. This concept is crucial in reactions like the autoionization of water. When water dissociates into hydroxide ions (OH鈦�) and hydronium ions (H鈧僌鈦�), an equilibrium is established. This means that the formation of ions occurs at the same rate as their recombination into water molecules.
This balanced dynamic is depicted in the reaction: \[ 2 H_{2}O \rightleftharpoons H_{3}O^{+} + OH^{-} \] Understanding chemical equilibrium helps predict the concentrations of reactants and products in a reversible reaction.
  • The equilibrium point does not mean that the reactants and products are equal in concentration but that their concentrations remain constant over time.
  • This balance depends on factors like temperature and pressure.
Ion-Product Constant
The ion-product constant of water, denoted as \( K_w \), is a special equilibrium constant for the self-ionization of water. This constant is calculated from the concentrations of H鈦� and OH鈦� ions in the water. At 25掳C, the value of \( K_w \) is \[ K_w = [H^{+}] [OH^{-}] = 1.0 \times 10^{-14} \] This tiny value shows that water is not very ionized, pointing to the low concentration of these ions under normal conditions.
Determining \( K_w \) is essential for understanding the nature of aqueous solutions. This constant provides a reference point for deciding whether a solution is acidic or basic, by comparing the concentrations of H鈦� and OH鈦�.
  • \( K_w \) helps in calculating pH and pOH values, which are measures of acidity and basicity.
  • Changes in temperature can affect the \( K_w \) value, indicating a shift in the equilibrium between water, H鈦�, and OH鈦� ions.
Basic Solution
A basic solution is one in which the concentration of hydroxide ions (OH鈦�) exceeds that of hydrogen ions (H鈦�). In simpler terms, there are more OH鈦� ions than H鈦� ions in a basic solution. This can be represented by the inequality: \( [\mathrm{H}^{+}]<[\mathrm{OH}^-] \)
This is derived from the neutral condition in pure water where \( [H^{+}] = [OH^{-}] = 1.0 \times 10^{-7} \). A basic solution presents a higher OH鈦� ion concentration than this neutral level.
To identify a basic solution:
  • Check if the pH is greater than 7; this indicates basicity.
  • The solution typically has a soapy feel and can turn red litmus paper blue.
Being able to recognize whether a solution is basic is important for many laboratory processes and chemical reactions.
Acidic Solution
An acidic solution has a higher concentration of hydrogen ions (H鈦�) compared to hydroxide ions (OH鈦�). In the context of the autoionization of water, an acidic solution shifts the equilibrium to produce more H鈦� ions. The inequality representing an acidic solution is:\( [\mathrm{H}^{+}]>[\mathrm{OH}^-] \)
In pure water, the concentrations of H鈦� and OH鈦� are equal, but in an acidic environment, the concentration of H鈦� exceeds \( 1.0 \times 10^{-7} \) mol/L.
To determine if a solution is acidic, consider these points:
  • A pH less than 7 indicates an acidic solution.
  • Acidic solutions often taste sour and can turn blue litmus paper red.
Understanding whether a solution is acidic aids in various chemical applications, from industrial processes to everyday life.

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Most popular questions from this chapter

Write the chemical equation and the \(K_{a}\) expression for the acid dissociation of each of the following acids in aqueous solution. First show the reaction with \(\mathrm{H}^{+}(a q)\) as a product and then with the hydronium ion: (a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\), (b) \(\mathrm{HCO}_{3}^{-}\)

(a) Which of the following is the stronger Br酶nsted-Lowry acid, \(\mathrm{HClO}_{3}\) or \(\mathrm{HClO}_{2}\) ? (b) Which is the stronger BronstedLowry base, \(\mathrm{HS}^{-}\)or \(\mathrm{HSO}_{4}^{-}\)?

Indicate whether each of the following statements is true or false. For each statement that is false, correct the statement to make it true. (a) In general, the acidity of binary acids increases from left to right in a given row of the periodic table. (b) In a series of acids that have the same central atom, acid strength increases with the number of hydrogen atoms bonded to the central atom. (c) Hydrotelluric acid ( \(\left.\mathrm{H}_{2} \mathrm{Te}\right)\) is a stronger acid than \(\mathrm{H}_{2} \mathrm{~S}\) because Te is more electronegative than \(\mathrm{S}\).

\mathrm{~A} 0.100 \mathrm{M}\( solution of bromoacetic acid \)\left(\mathrm{BrCH}_{2} \mathrm{COOH}\right)\( is \)13.2 \%\( ionized. Calculate \)\left[\mathrm{H}^{+}\right],\left[\mathrm{BrCH}_{2} \mathrm{COO}^{-}\right],\left[\mathrm{BrCH}_{2} \mathrm{COOH}\right]\( and \)K_{a}$ for bromoacetic acid.

Indicate whether each of the following statements is true or false. For each statement that is false, correct the statement to make it true. (a) Acid strength in a series of \(\mathrm{H}\) - A molecules increases with increasing size of \(A\). (b) For acids of the same general structure but differing electronegativities of the central atoms, acid strength decreases with increasing electronegativity of the central atom. (c) The strongest acid known is \(\mathrm{HF}\) because fluorine is the most electronegative element. Lewis Acids and Bases (Section 16.11)
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