Question

Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following pH values. a. \(\mathrm{pH}=2.75\) b. \(\mathrm{pH}=12.8\) c. \(\mathrm{pH}=4.33\) d. \(\mathrm{pH}=9.61\)

Short answer

The hydrogen ion concentrations for each solution are: a. pH 2.75: \(1.78 \times 10^{-3} \, M\) b. pH 12.8: \(1.58 \times 10^{-13} \, M\) c. pH 4.33: \(4.69 \times 10^{-5} \, M\) d. pH 9.61: \(2.46 \times 10^{-10} \, M\)

Step-by-step solution

Using the formula \([\mathrm{H^{+}}] = 10^{(-\mathrm{pH})}\), plug in the pH value given: \[ [\mathrm{H^{+}}] = 10^{(-2.75)}\] \[ [\mathrm{H^{+}}] = 1.78 \times 10^{-3} \, M\] #Step 2: Calculate the hydrogen ion concentration for pH=12.8#

Using the formula \([\mathrm{H^{+}}] = 10^{(-\mathrm{pH})}\), plug in the pH value given: \[ [\mathrm{H^{+}}] = 10^{(-12.8)}\] \[ [\mathrm{H^{+}}] = 1.58 \times 10^{-13} \, M\] #Step 3: Calculate the hydrogen ion concentration for pH=4.33#

Using the formula \([\mathrm{H^{+}}] = 10^{(-\mathrm{pH})}\), plug in the pH value given: \[ [\mathrm{H^{+}}] = 10^{(-4.33)}\] \[ [\mathrm{H^{+}}] = 4.69 \times 10^{-5} \, M\] #Step 4: Calculate the hydrogen ion concentration for pH=9.61#

Using the formula \([\mathrm{H^{+}}] = 10^{(-\mathrm{pH})}\), plug in the pH value given: \[ [\mathrm{H^{+}}] = 10^{(-9.61)}\] \[ [\mathrm{H^{+}}] = 2.46 \times 10^{-10} \, M\] The hydrogen ion concentrations for each solution are as follows: a. pH 2.75: \(1.78 \times 10^{-3} \, M\) b. pH 12.8: \(1.58 \times 10^{-13} \, M\) c. pH 4.33: \(4.69 \times 10^{-5} \, M\) d. pH 9.61: \(2.46 \times 10^{-10} \, M\)

Key concepts

Understanding Hydrogen Ion Concentration

Hydrogen ion concentration is a measure of the number of hydrogen ions (H\(^+\)) present in a solution. The concentration is typically expressed in moles per liter (M). This measurement is crucial in determining the acidity or basicity of a solution. The more hydrogen ions present, the more acidic the solution is.

The formula used to calculate hydrogen ion concentration from a pH value is \[ [\text{H}^+] = 10^{-\text{pH}} \].This equation reveals the inverse logarithmic relationship between pH and hydrogen ion concentration. It shows us that a small change in pH corresponds to a significant change in hydrogen ion concentration.

For instance, if the pH decreases by 1 unit, the hydrogen ion concentration increases by ten times. This concept emphasizes the importance of precision when working with pH values.

Basics of Acid-Base Chemistry

Acid-base chemistry is all about understanding how acids and bases behave in water. An acid is a substance that donates hydrogen ions (H\(^+\)) to a solution, while a base is a substance that can accept hydrogen ions or produce hydroxide ions (OH\(^-\)).

The pH scale, which ranges from 0 to 14, is a tool used to determine whether a solution is acidic or basic. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are basic or alkaline. A pH of exactly 7 indicates a neutral solution, such as pure water.

Understanding the behavior of acids and bases, and their impact on the pH and hydrogen ion concentration, is essential in many scientific and industrial processes, including chemistry, biology, medicine, and environmental science.

Solution Concentration Essentials

Solution concentration refers to the amount of solute present in a given volume of solvent. In acid-base chemistry, the concentration of hydrogen ions in a solution is a key concept that determines the pH.

Concentration is commonly expressed in molarity (M), which represents moles of solute per liter of solution. Molarity provides a clear and standardized way to convey just how concentrated or dilute a solution is. For acids, higher molarity means a larger number of hydrogen ions and thus, a more acidic solution.

When calculating hydrogen ion concentrations, simply knowing the pH isn't enough. You must understand how concentration impacts the solution's overall behavior and characteristics. This knowledge helps in predicting reactions and the overall reactivity of a solution.

The pH Scale and Its Significance

The pH scale is a numeric scale used to specify the acidity or basicity of an aqueous solution. It is an exponential scale, meaning each whole number change in pH represents a tenfold difference in hydrogen ion concentration.

The scale ranges from 0 to 14. A pH of 0 indicates a very high concentration of hydrogen ions, making it extremely acidic. Conversely, a pH of 14 means the solution has very few hydrogen ions, being highly basic.

Understanding the pH scale is critical, especially when trying to control or utilize the chemical properties of a solution. It plays a pivotal role in chemistry, biology, and environmental science, helping to determine the suitable environment for reactions, living organisms, and ecosystems.

• A pH below 7 means the solution is acidic.
• A pH of 7 is neutral.
• A pH above 7 indicates a basic solution.

The pH scale provides a simple yet powerful way to communicate the chemical nature of a solution.