Question

Calculate the hydronium ion concentration in \(\mathrm{mol} / \mathrm{L}\) for solutions with the following \(\mathrm{pH}\) values: (a) \(2.42,\) (b) \(11.21,\) (c) 6.96 (d) 15.00 .

Short answer

(a) \(3.80 \times 10^{-3}\); (b) \(6.17 \times 10^{-12}\); (c) \(1.10 \times 10^{-7}\); (d) \(1.00 \times 10^{-15}\) mol/L.

Step-by-step solution

Understanding pH and Hydronium Ion Concentration

The pH of a solution is related to its hydronium ion concentration ([H₃O⁺]) by the equation: \( \text{pH} = -\log_{10}([\text{H}_3\text{O}^+]) \).To find the hydronium ion concentration from pH, we use the inverse function:\([\text{H}_3\text{O}^+] = 10^{-\text{pH}} \).This allows us to convert a given pH into the hydronium ion concentration.

Calculate Hydronium Ion Concentration for pH = 2.42

To find the hydronium ion concentration for pH = 2.42, we plug into the formula \([\text{H}_3\text{O}^+] = 10^{-2.42}\).Evaluating this gives:\([\text{H}_3\text{O}^+] = 3.80 \times 10^{-3} \text{ mol/L} \).

Calculate Hydronium Ion Concentration for pH = 11.21

For pH = 11.21, we use the same formula:\([\text{H}_3\text{O}^+] = 10^{-11.21}\).This evaluates to:\([\text{H}_3\text{O}^+] = 6.17 \times 10^{-12} \text{ mol/L} \).

Calculate Hydronium Ion Concentration for pH = 6.96

To find the hydronium ion concentration for pH = 6.96, substitute into the formula:\([\text{H}_3\text{O}^+] = 10^{-6.96}\).This results in:\([\text{H}_3\text{O}^+] = 1.10 \times 10^{-7} \text{ mol/L} \).

Calculate Hydronium Ion Concentration for pH = 15.00

For pH = 15.00, apply the formula:\([\text{H}_3\text{O}^+] = 10^{-15.00}\).The concentration is:\([\text{H}_3\text{O}^+] = 1.00 \times 10^{-15} \text{ mol/L} \).

Key concepts

pH Scale

The pH scale is a measure that describes how acidic or basic a solution is. It ranges from 0 to 14, with 0 being extremely acidic, 7 being neutral, and 14 being extremely basic. Each value on the pH scale corresponds to a tenfold difference in acidity or basicity, due to its logarithmic nature. For example:

• A pH of 2 is 10 times more acidic than a pH of 3.
• Pure water has a neutral pH of 7.
• A pH above 7 indicates a basic solution, while below 7 indicates an acidic solution.

It's crucial to understand that pH is directly related to the concentration of hydronium ions ( [H₃O⁺ ]) in a solution. This relationship is critical in fields like chemistry and biology for maintaining systems at healthy, functional pH levels. When calculating pH, we're essentially counting the number of protons available in a solution. Knowing the pH helps us predict how solutions will behave in chemical reactions.

Logarithmic Functions in Chemistry

In chemistry, logarithmic functions play a significant role, particularly when dealing with pH. The relationship between pH and hydronium ion concentration ([H₃O⁺]) is expressed logarithmically as:\[pH = -\log_{10}([\text{H}_3\text{O}^+])\]This equation shows that pH is the negative logarithm of the hydronium ion concentration. It allows chemists to simplify large ranges of concentration values into more manageable numbers.
To find the hydronium ion concentration from a given pH, the equation is inverted:\[[\text{H}_3\text{O}^+] = 10^{-\text{pH}}\]This formula provides a way to calculate the concentration of hydronium ions when the pH is known. Logarithms make it easier to understand and compute changes in acidity and basicity, which often involve exponentials.
The use of logarithms in chemistry highlights the simplicity brought by mathematical tools when dealing with complex chemical phenomena like reaction rates and equilibria.

Acid-Base Chemistry

Acid-base chemistry focuses on the study of acids, bases, and their reactions. Acids are substances that increase the concentration of hydronium ions ( [H₃O⁺ ]) in a solution, while bases increase the concentration of hydroxide ions ( [OH⁻ ]). These reactions are essential for various chemical processes, such as:

• Neutralizing reactions, where acids and bases react to form water and salts.
• Buffer solutions, which help maintain a stable pH in physiological systems.
• Determining the pH levels crucial for industrial chemistry and biological systems.

Acid-base reactions are pivotal in monitoring environmental conditions, medical diagnostics, and even culinary applications. Understanding these reactions helps in controlling or manipulating pH levels for desired outcomes, such as reducing acidity or maintaining stability in biochemical processes.
The study of acid-base chemistry not only enhances our comprehension of chemical interactions but also empowers us to optimize conditions across various scientific and practical fields.