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Chapter 13: Problem 49

Under what conditions is the ion-product constant of water, \(K_{\mathrm{w}}\), a constant?

Short Answer

Expert verified
The ion-product constant of water, \(K_{\mathrm{w}}\), remains constant at a given temperature, for pure water or natural water that is neither acidic nor basic. It changes with the change in temperature.

Step by step solution

01

Concept Understanding

The ion-product constant of water is a measure of the product of the concentrations of the ions in water, specifically the hydronium ion (\(H_{3}O^+\)) and the hydroxide ion (\(OH^-\)). It is defined by the expression \(K_{\mathrm{w}}= [H_{3}O^+][OH^-]\). It's important to note that concentrations are usually given in terms of molarity (\(M\) or \(mol/L\)).
02

Identifying conditions in which \(K_{\mathrm{w}}\) remains constant

The ion-product constant of water, \(K_{\mathrm{w}}\), remains constant, at a given temperature, when the water is either pure or when the solution is a natural water i.e., it is neither acidic nor basic.
03

Explaining effects of temperature on \(K_{\mathrm{w}}\)

The value of \(K_{\mathrm{w}}\) will vary with temperature in spite of the concentration of \(H_{3}O^+\) and \(OH^-\) ions. This implies that the pH of water also changes with the temperature even though there are no additions of acids or bases.

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Key Concepts

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

Hydronium Ion Concentration
Hydronium ions, represented as \( H_3O^+ \), play a crucial role in the chemistry of water. They are formed when water molecules naturally dissociate. When water
  • dissociates, it forms both hydronium ions (\( H_3O^+ \)) and hydroxide ions (\( OH^- \)).
  • The concentration of hydronium ions is an essential component in calculating the ion-product constant of water, \( K_{\mathrm{w}} \).
To calculate this, we use the formula \( K_{\mathrm{w}} = [H_3O^+][OH^-] \). At 25掳C, \( K_{\mathrm{w}} \) is typically \( 1.0 \times 10^{-14} \), showing how the concentrations of hydronium and hydroxide ions relate to each other.
In pure water, the concentrations of \( H_3O^+ \) and \( OH^- \) are equal, representing a neutral pH of 7. However, if the hydronium ion concentration increases, it indicates a more acidic solution, reflected in a lower pH.
Temperature Effects on Water
Temperature has a unique effect on water and its properties. The ion-product constant of water, \( K_{\mathrm{w}} \), essentially changes with fluctuating temperatures. This means:
  • As the temperature increases, \( K_{\mathrm{w}} \) typically increases, indicating more dissociation of water molecules.
  • Conversely, a decrease in temperature results in a smaller \( K_{\mathrm{w}} \), meaning fewer hydronium and hydroxide ions are present.
This variation underlies the reason why pH values may change with temperature. Despite maintaining neutrality in pure water at room temperature, deviations arise with temperature shifts.
pH Variation with Temperature
pH is a measure of the hydrogen ion concentration in a solution, and temperature can have a notable effect on it. At room temperature, pure water has a neutral pH of 7. However, as the temperature changes:
  • Higher temperatures result in an increase in \( K_{\mathrm{w}} \), which in turn reduces the pH, making water slightly more acidic.
  • Lower temperatures decrease \( K_{\mathrm{w}} \), leading to a higher pH, reflecting a more basic solution.
It's crucial to understand that while the pH scale typically goes from 0 to 14 under standard conditions, these boundaries might shift slightly with temperature changes. This underscores the importance for chemists to take temperature into account when analyzing pH and the effects of hydronium ion concentration in various conditions.

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Most popular questions from this chapter

What happens to the concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}\)and \(\mathrm{OH}^{-}\) when acid is added to water? When a base is added to water?

What are the advantages of using \(\mathrm{pH}\) paper to measure \(\mathrm{pH}\) ?

What can we say about the \(\mathrm{pH}\) of a solution that is red when the indicator thymol blue is added? When the solution is yellow? When the solution is blue?

What is the \(\mathrm{pH}\) of solutions having the following \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentrations? Identify each as acidic, basic, or neutral. (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-3} \mathrm{M}\) (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-13} \mathrm{M}\) (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.4 \times 10^{-10} \mathrm{M}\)

Would you expect the pH of a \(0.010 \mathrm{MNH}_{3}\) solution to be higher or lower than \(12.0\) ?
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