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Chapter 15: Problem 25

The value of the ion-product constant for water, \(K_{w}\), increases with temperature. What will be the effect of lowering the temperature on the \(\mathrm{pH}\) of pure water?

Short Answer

Expert verified
Lowering the temperature increases the pH of pure water.

Step by step solution

01

Understanding the Ion-Product Constant for Water

The ion-product constant for water, denoted as \(K_w\), is the product of the concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) in water. At 25掳C, \(K_w = 1.0 \times 10^{-14}\), but this value increases with temperature. It is important to understand that as \(K_w\) changes, so do the concentrations of \([H^+]\) and \([OH^-]\), affecting the pH.
02

Effect of Temperature on Kw and pH

When the temperature is lowered, \(K_w\) decreases because it is endothermic in nature. A decrease in \(K_w\) means that the product of \([H^+]\) and \([OH^-]\) is less, leading to a decrease in the concentrations of these ions in water. This affects the neutrality condition of the pH scale.
03

Determining the pH of Pure Water at Lower Temperatures

For pure water, the concentrations of \([H^+]\) and \([OH^-]\) are equal, hence \([H^+] = [OH^-]\). When \(K_w\) decreases, both \([H^+]\) and \([OH^-]\) concentrations are lower, thus less than \(1.0 \times 10^{-7}\) M, corresponding to neutral pH at 25掳C. Calculating the new pH using \( pH = -\log[H^+] \), since \([H^+]\) is lower, the pH will be slightly higher than 7.

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Key Concepts

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

Ion-Product Constant
The ion-product constant of water, often represented as \(K_w\), is a vital concept in understanding the chemistry of water. It is defined as the product of hydrogen ion concentration \([H^+]\) and hydroxide ion concentration \([OH^-]\): \(K_w = [H^+][OH^-]\). This value reflects the extent to which water molecules dissociate into these ions. At 25掳C, \(K_w\) is typically \(1.0 \times 10^{-14}\). However, it's important to note that \(K_w\) is not a fixed value and changes with temperature.
  • At lower temperatures, \(K_w\) decreases, indicating fewer ions in solution.
  • At higher temperatures, \(K_w\) increases, meaning more ions are present.
The concept of \(K_w\) helps in predicting the behavior of water under different temperature conditions, which is crucial for calculating pH accurately.
Temperature Effect on pH
Temperature can have a significant effect on the pH of water because it alters the \(K_w\). Since \(K_w\) decreases with decreasing temperature, the availability of hydrogen and hydroxide ions also decreases. This means fewer \([H^+]\) and \([OH^-]\) are present in the water.

These changes affect the condition of neutrality. At standard room temperature (25掳C), a pH of 7 is considered neutral. This neutrality is due to equal concentrations of \([H^+]\) and \([OH^-]\). However, when temperature drops, because both ion concentrations decrease simultaneously and equally, the amount of \([H^+]\) becomes less than \(1.0 \times 10^{-7}\) M, the pH value rises above 7, indicating a shift in neutrality.
Kw and Temperature
The relationship between \(K_w\) and temperature is crucial for understanding how water's ionic properties fluctuate. As a thermodynamic property, \(K_w\) responds to temperature changes due to its endothermic nature.
  • If the temperature increases, \(K_w\) increases, resulting in more ion dissociation, which causes more acidic behavior (lower pH).
  • Conversely, lowering the temperature causes \(K_w\) to decrease, leading to fewer ions and a more basic pH (pH>7).
This behavior highlights the sensitivity of water's chemistry to temperature changes and how it influences everything from biochemical reactions to everyday water usages. Understanding this concept is fundamental to grasp the dynamics of pH variations in environmental and laboratory settings.

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Most popular questions from this chapter

Complete each of the following equations. Then write the Lewis formulas of the reactants and products and identify each reactant as a Lewis acid or a Lewis base. a. \(\mathrm{GaBr}_{3}+\mathrm{Br}^{-} \longrightarrow\) b. \(\mathrm{BF}_{3}+\mathrm{F}^{-} \longrightarrow\)

You make a solution by dissolving \(0.0010\) mol of \(\mathrm{HCl}\) in enough water to make \(1.0 \mathrm{~L}\) of solution. a. Write the chemical equation for the reaction of \(\mathrm{HCl}(a q)\) and water. b. Without performing calculations, give a rough estimate of the \(\mathrm{pH}\) of the \(\mathrm{HCl}\) solution. Justify your answer. c. Calculate the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration and the \(\mathrm{pH}\) of the solution. d. Is there any concentration of the base \(\mathrm{OH}^{-}\) present in this solution of \(\mathrm{HCl}(a q) ?\) If so, where did it come from? e. If you increase the OH \(^{-}\) concentration of the solution by adding \(\mathrm{NaOH}\), does the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration change? If you think it does, explain why this change occurs and whether the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration increases or decreases. f. If you were to measure the \(\mathrm{pH}\) of 10 drops of the original HCl solution, would you expect it to be different from the pH of the entire sample? Explain. g. Explain how two different volumes of your original \(\mathrm{HCl}\) solution can have the same \(\mathrm{pH}\) yet contain different moles of \(\mathrm{H}_{3} \mathrm{O}^{+}\) h. If \(1.0 \mathrm{~L}\) of pure water were added to the \(\mathrm{HCl}\) solution, would this have any impact on the \(\mathrm{pH}\) ? Explain.

Morphine is a narcotic that is used to relieve pain. A solution of morphine has a pH of \(9.61\) at \(25^{\circ} \mathrm{C}\). What is the hydroxide-ion concentration?

Write a reaction for each of the following in which the species acts as a Br酶nsted base. The equilibrium should favor the product side. a. \(\mathrm{H}_{2} \mathrm{O}\) b. \(\mathrm{HCO}_{3}^{-}\) c. \(\mathrm{NH}_{3}\) d. \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\)

An antiseptic solution at \(25^{\circ} \mathrm{C}\) has a hydroxide-ion concentration of \(8.4 \times 10^{-5} M\). Is the solution acidic, neutral, or basic?
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