Problem 14 - Chemistry An Atoms First Approach

Question

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

Step-by-Step Solution

Answer

The pH of water at \(25^{\circ}\)C is equal to 7.00 because at this temperature, water undergoes auto-ionization, resulting in equal concentrations of H+ ions and OH- ions at approximately \(1 \times 10^{-7}\) M. When this concentration is plugged into the pH equation \( pH = -\log_{10}[H^+]\), it results in a pH value of 7, representing a neutral solution.

Step 1: Understanding pH scale and pH of water

The pH scale is a measure of the acidity or alkalinity of a solution. It is defined as the negative logarithm of the hydrogen ion (H+) concentration in a solution. Mathematically, pH is represented as: \( pH = -\log_{10}[H^+] \) Water undergoes a process called auto-ionization, in which a small number of water molecules naturally dissociate into hydrogen ions (H+) and hydroxide ions (OH-). At 25°C, the concentration of H+ ions and OH- ions in pure water is equal, and their concentrations are around \(1 \times 10^{-7}\) M. This can be represented as: \( H_2O \rightleftharpoons H^+ + OH^- \) with \( [H^+] = [OH^-] = 1 \times 10^{-7} M \) Now, we can calculate the pH of water at 25°C.

Step 1: Calculate the pH of water

To find the pH of water, we need to plug the concentration of H+ ions into the pH formula: \( pH = -\log_{10}(1 \times 10^{-7}) \)

Step 2: Simplify and solve for pH

Now, we can use the logarithm properties to simplify this expression: \( pH = -\log_{10}(1 \times 10^{-7}) \) \( pH = -(-7) \) \( pH = 7 \) So, the pH of water at 25°C is 7.00. In conclusion, the pH of water at \(25^{\circ}\)C is equal to 7.00 because at that temperature, the concentration of H+ ions and OH- ions is equal and their concentrations are around \(1 \times 10^{-7}\) M, which gives a pH value of 7 when plugged into the pH equation.

Key Concepts

Auto-ionization of Water

Water is a fascinating substance because it can undergo a process called auto-ionization. This means that some water molecules WASH!spontaneously dissociate into ions. This natural process occurs even when water appears to be pure and still.
The dissociation forms hydrogen ions (H⁺) and hydroxide ions (OH⁻). The auto-ionization reaction can be represented by:

• \( H_2O \rightleftharpoons H^+ + OH^- \)

At 25°C, the concentrations of these ions are equal in pure water, each being roughly \(1 \times 10^{-7}\) M. This balance is crucial because it establishes water as a neutral solution on the pH scale.
The concept of auto-ionization is important because it underlies the pH neutrality of water and explains why water can slightly conduct electricity. Understanding this process is key to exploring further chemical reactions in aqueous solutions.

Hydrogen Ion Concentration

The concentration of hydrogen ions (H⁺) in a solution is a fundamental concept in chemistry. In pure water at 25°C, this concentration is found to be very low, about \(1 \times 10^{-7}\) M.
This value signifies that there is one part in ten million of the water molecules that are dissociated into hydrogen ions.
Hydrogen ion concentration influences the pH value of a solution greatly.

• It's expressed in moles per liter (M), which indicates the number of H⁺ ions present in one liter of water.

For instance, the pH equation relies on knowing this concentration to determine a solution’s acidity or alkalinity.
By understanding the concentration of H⁺ ions, scientists can predict how acidic or basic a solution will be, providing essential insight into chemical reactivity and processes.

pH Calculation

The pH of a solution is a mathematical representation of its acidity or basicity. The pH formula is given by:

• \( pH = -\log_{10}[H^+] \)

This formula uses the logarithm base 10 to express the hydrogen ion concentration as a simpler number, making it easier to handle in calculations and discussions.
For water at 25°C, we know the hydrogen ion concentration is \(1 \times 10^{-7}\) M. Substituting this value into the formula:

• \( pH = -\log_{10}(1 \times 10^{-7}) \)
• \( pH = 7 \)

The logarithm simplifies the process, turning our tiny concentration number into an approachable whole number for measuring.
Hence, pH = 7 means that the water is neutral, representing a perfect balance between acidity and basicity. Learning how to calculate pH helps in analyzing the chemical nature of solutions in everyday and laboratory settings.

Acidity and Alkalinity

Acidity and alkalinity are terms describing a solution's ability to donate or accept hydrogen ions. A solution's pH determines where it stands on the scale of acidity and alkalinity.
A lower pH (below 7) indicates acidity, where there are more hydrogen ions present. Conversely, a higher pH (above 7) points to alkalinity, indicating fewer hydrogen ions and more hydroxide ions.

• Neutral pH is at exactly 7, as seen with pure water.
• Acidic solutions, like lemon juice, have pH values around 2-3.
• Alkaline solutions, such as baking soda in water, feature pH values around 9-10.

Understanding these concepts is crucial for many fields, including chemistry, biology, and environmental science. Knowing whether a solution is acidic or alkaline can impact everything from chemical reactions to biological functions in living organisms.