Problem 13 - Chemistry: Principles and Reactions

Question

Find the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of solutions with the following \(\left[\mathrm{H}^{+}\right]\). Classify each as acidic or basic. (a) \(6.0 \mathrm{M}\) (b) \(0.33 \mathrm{M}\) (c) \(4.6 \times 10^{-8} M\) (d) \(7.2 \times 10^{-14} M\)

Step-by-Step Solution

Answer

Question: Calculate the pH and pOH of each solution, and classify them as acidic, neutral, or basic. (a) A solution with a 6.0M hydrogen ion concentration (b) A solution with a 0.33M hydrogen ion concentration (c) A solution with a \(4.6 \times 10^{-8} M\) hydrogen ion concentration (d) A solution with a \(7.2 \times 10^{-14} M\) hydrogen ion concentration Answer: (a) pH ≈ -0.78, pOH ≈ 14.78, acidic (b) pH ≈ 0.48, pOH ≈ 13.52, acidic (c) pH ≈ 7.34, pOH ≈ 6.66, basic (d) pH ≈ 13.14, pOH ≈ 0.86, basic

Step 1: (a) Calculate the pH and pOH of the solution with a 6.0M hydrogen ion concentration and classify it as acidic or basic

First, use the formula for pH: pH = -log[H+] = -log(6.0) ≈ -0.78 Next, use the formula for pOH: pOH = 14 - pH = 14 - (-0.78) ≈ 14.78 Finally, classify it based on the pH value: Since pH < 7, the solution is acidic.

Step 2: (b) Calculate the pH and pOH of the solution with a 0.33M hydrogen ion concentration and classify it as acidic or basic

First, use the formula for pH: pH = -log[H+] = -log(0.33) ≈ 0.48 Next, use the formula for pOH: pOH = 14 - pH = 14 - 0.48 ≈ 13.52 Finally, classify it based on the pH value: Since pH < 7, the solution is acidic.

Step 3: (c) Calculate the pH and pOH of the solution with a \(4.6 \times 10^{-8} M\) hydrogen ion concentration and classify it as acidic or basic

First, use the formula for pH: pH = -log[H+] = -log(\(4.6 \times 10^{-8}\)) ≈ 7.34 Next, use the formula for pOH: pOH = 14 - pH = 14 - 7.34 ≈ 6.66 Finally, classify it based on the pH value: Since pH > 7, the solution is basic.

Step 4: (d) Calculate the pH and pOH of the solution with a \(7.2 \times 10^{-14} M\) hydrogen ion concentration and classify it as acidic or basic

First, use the formula for pH: pH = -log[H+] = -log(\(7.2 \times 10^{-14}\)) ≈ 13.14 Next, use the formula for pOH: pOH = 14 - pH = 14 - 13.14 ≈ 0.86 Finally, classify it based on the pH value: Since pH > 7, the solution is basic.

Key Concepts

Acidic and Basic Solutions

Understanding whether a solution is acidic or basic is fundamental in chemistry and is determined by the solution's hydrogen ion concentration, \( [H^+] \). An acidic solution has a higher concentration of hydrogen ions, which results in a pH less than 7. Conversely, a basic (or alkaline) solution has a lower hydrogen ion concentration and a pH greater than 7.

When a solution has a pH of exactly 7, it’s considered neutral, meaning it is neither acidic nor basic. Everyday substances can display a wide range of pH values; lemon juice and vinegar, for example, are acidic, whereas baking soda and soap tend to be basic. Correct classification of a solution's acidity or basicity is crucial in many applications, from biological processes to industrial chemistry.

Hydrogen Ion Concentration

The concentration of hydrogen ions in a solution, represented by \( [H^+] \), dictates its acidity and can be measured in moles per liter (M). The higher the concentration of hydrogen ions, the more acidic the solution is, and vice versa.

In aqueous solutions, \( [H^+] \)'s influence on chemical reactions and properties is significant. For example, highly acidic solutions can be corrosive, while basic solutions might be slippery to the touch. Precisely measuring \( [H^+] \) is critical in many fields, including environmental science, medicine, and food science, to control processes and maintain safety standards.

pH Scale

The pH scale is a logarithmic scale that measures how acidic or basic a solution is. The scale ranges from 0 to 14, with 7 being neutral. pH values lower than 7 are acidic, and those above 7 are basic.

The pH scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value. For instance, a solution with a pH of 3 is ten times more acidic than one with a pH of 4. Similarly, each whole pH value above 7 is ten times more basic than the next lower value. Understanding this scale helps in making precise adjustments to solutions, which is essential in processes such as neutralization reactions and buffer preparations.

Logarithmic Calculations

Logarithmic calculations are vital for computing pH values from hydrogen ion concentrations and vice versa. The pH of a solution is calculated using the formula \(\text{pH} = -\log([H^+])\), where \(\log\) refers to the base-10 logarithm, and \( [H^+] \) is the molar concentration of hydrogen ions.

The logarithmic nature of the pH scale means that each change of one pH unit represents a tenfold change in hydrogen ion concentration. As a result, working with logarithms is necessary for understanding the precise relationship between pH and hydrogen ion concentration. This type of calculation is not only used in pH but also in many other areas of science and engineering where exponential relationships are observed.