Question

Why is the pH of water at \(25^{\circ} \mathrm{C}\) equal to \(7.00 ?\)

Short answer

The pH of water at \(25^{\circ} \mathrm{C}\) is equal to 7.00 because the concentration of hydrogen ions (H+) in pure water is \(1.0 \times 10^{-7} \mathrm{mol/L}\), calculated from the ion product constant for water (Kw) at that temperature. Since pH is defined as the negative logarithm base 10 of the hydrogen ion concentration, the pH of water at \(25^{\circ} \mathrm{C}\) is: pH = -log10(\(1.0 \times 10^{-7}\)) = 7.00.

Step-by-step solution

Understanding pH

The pH is a scale used to specify the acidity or basicity of an aqueous solution. It is defined as the negative logarithm base 10 of the hydrogen ion (H+) concentration: pH = -log10[H+] Here [H+] represents the concentration of hydrogen ions in moles per liter (mol/L).

Water dissociation

Water can dissociate into hydrogen ions (H+) and hydroxide ions (OH-) in the following equilibrium reaction: H2O (l) ⇌ H+ (aq) + OH- (aq) At 25°C, the equilibrium constant for this reaction, known as the ion product constant for water (Kw), is equal to 1.0 x 10^-14. The mathematical representation of Kw is: Kw = [H+] [OH-] Since water is a neutral substance, the concentration of hydrogen ions (H+) equals the concentration of hydroxide ions (OH-) in pure water: [H+] = [OH-]

Determining the concentration of hydrogen ions

To determine the concentration of hydrogen ions in water at 25°C, we need to use the above equations. As [H+] = [OH-], we can rewrite the Kw equation as follows: Kw = [H+]^2 Now we can solve for [H+]: [H+]^2 = 1.0 x 10^-14 [H+] = √(1.0 x 10^-14) [H+] = 1.0 x 10^-7 mol/L

Calculating pH of water at 25°C

Now that we have the concentration of hydrogen ions, we can calculate the pH of water at 25°C using the pH formula: pH = -log10(1.0 x 10^-7) pH = 7.00 Therefore, the pH of water at 25°C is equal to 7.00.

Key concepts

Water Dissociation

When exploring the fascinating world of chemistry, one vital concept is the dissociation of water. This phenomenon occurs when water molecules (H2O) separate into ions – hydrogen ions (H+) and hydroxide ions (OH-). The process can be described by a simple yet fundamental chemical equilibrium:

H2O (l) ⇌ H+ (aq) + OH- (aq)

This reversible reaction is fundamental to understand because it sets the stage for numerous reactions in aqueous solutions. Additionally, the balance between H+ and OH- ions is critical for maintaining the pH level of solutions, making it a key player in understanding acidity and basicity.

Hydrogen Ion Concentration

The concentration of hydrogen ions, often represented as [H+], is crucial in determining the acidity of a solution. It's measured in moles per liter (mol/L), giving us a quantifiable way to assess how acidic or basic a solution is. Knowing the [H+] allows scientists and educators like us to anticipate the behavior of substances in different environments—whether it's in a classroom experiment, industrial process, or natural water bodies. A higher concentration of hydrogen ions corresponds to a lower pH, indicating increased acidity, while a lower [H+] indicates a higher pH and a more basic solution.

pH Scale

Embarking on the journey to understand the pH scale is like unlocking a secret code to the world of acidity and basicity. The pH scale ranges from 0 to 14, serving as a concise metric to relay the hydrogen ion concentration in solutions.

The formula pH = -log10[H+] transforms the concept of hydrogen ion concentration into a more digestible format. A pH below 7 signifies an acidic solution, pH 7 is neutral (like pure water at 25°C), and above 7 indicates a basic or alkaline environment. This scale is not just an academic exercise—it is integral in fields like medicine, agriculture, and environmental science, influencing decision-making based on the acidity or basicity of a substance.

Ion Product Constant

Dive a little deeper, and you hit upon the ion product constant for water, represented by Kw. This constant is the product of the concentrations of hydrogen ions [H+] and hydroxide ions [OH-], given by the formula:

Kw = [H+] [OH-]

At a temperature of 25°C, Kw is always 1.0 x 10^-14. It's a pivotal constant that stands as the backbone for calculations related to the pH of solutions. The beauty of Kw lies in its consistency; despite the inner workings of the solution, Kw remains steadfast at a given temperature, a constant guide on our quest to understand chemical reactions in water.

Acidity and Basicity

Grasping the concept of acidity and basicity is essential for understanding the chemistry of everyday substances. Acidity is associated with a high concentration of hydrogen ions, which translates into a lower pH value. On the other end, basicity corresponds with a low concentration of hydrogen ions and a higher concentration of hydroxide ions, leading to a higher pH value.

Beyond just theory, the acidity or basicity of solutions affects biological systems, industrial processes, and environmental health. Therefore, being able to assess and adjust these properties is a critical skill in many scientific and practical applications, from fine-tuning the pH of pool water to ensuring the correct soil conditions for agriculture.