Question

Calculate the \(\mathrm{pH}\) corresponding to each of the hydrogen ion concentrations given below, and indicate whether each solution is acidic or basic. a. \(\left[\mathrm{H}^{+}\right]=4.97 \times 10^{-7} \mathrm{M}\) b. \(\left[\mathrm{H}^{+}\right]=1.01 \times 10^{-12} \mathrm{M}\) c. \(\left[\mathrm{H}^{+}\right]=2.49 \times 10^{-4} \mathrm{M}\) d. \(\left[\mathrm{H}^{+}\right]=1.00 \times 10^{-7} \mathrm{M}\)

Short answer

a. The pH of the solution is approximately 6.30, making it acidic. b. The pH of the solution is approximately 11.995, making it basic. c. The pH of the solution is approximately 3.604, making it acidic. d. The pH of the solution is approximately 7.000, making it neutral.

Step-by-step solution

a. Calculate pH and classify the solution

Given \(\left[\mathrm{H}^{+}\right]=4.97 \times 10^{-7} \mathrm{M}\), apply the pH formula: \(\mathrm{pH}=-\log \left( 4.97 \times 10^{-7}\right)\) Compute the pH value: \(\mathrm{pH}\approx 6.30\) Since \(\mathrm{pH}<7\), the solution is acidic.

b. Calculate pH and classify the solution

Given \(\left[\mathrm{H}^{+}\right]=1.01 \times 10^{-12} \mathrm{M}\), apply the pH formula: \(\mathrm{pH}=-\log \left(1.01 \times 10^{-12}\right)\) Compute the pH value: \(\mathrm{pH}\approx 11.995\) Since \(\mathrm{pH}>7\), the solution is basic.

c. Calculate pH and classify the solution

Given \(\left[\mathrm{H}^{+}\right]=2.49 \times 10^{-4} \mathrm{M}\), apply the pH formula: \(\mathrm{pH}=-\log \left(2.49 \times 10^{-4}\right)\) Compute the pH value: \(\mathrm{pH}\approx 3.604\) Since \(\mathrm{pH}<7\), the solution is acidic.

d. Calculate pH and classify the solution

Given \(\left[\mathrm{H}^{+}\right]=1.00 \times 10^{-7} \mathrm{M}\), apply the pH formula: \(\mathrm{pH}=-\log \left(1.00 \times 10^{-7}\right)\) Compute the pH value: \(\mathrm{pH}\approx 7.000\) Since \(\mathrm{pH}=7\), the solution is neutral.

Key concepts

pH scale

Understanding the pH scale is essential when studying chemistry, as it is a measure of how acidic or basic a solution is. The scale ranges from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are basic (or alkaline).

Water, which is neutral, has a pH close to 7. Each whole pH value below 7 is ten times more acidic than the next higher value. For example, a solution with a pH of 6 is ten times more acidic than one with a pH of 7. Similarly, each whole pH value above 7 is ten times more basic than the one below it.

This logarithmic scale means that small changes in pH represent significant changes in acidity or basicity, which is important to consider when conducting experiments that involve pH.

Acids and bases

Acids and bases are two fundamental categories of chemicals that have unique properties due to the presence of hydrogen ions \(\mathrm{H^+}\) and hydroxide ions \(\mathrm{OH^-}\), respectively. Acids are substances that can donate \(\mathrm{H^+}\) ions to other substances, while bases accept \(\mathrm{H^+}\) ions.

An acid's strength is measured by how completely it dissociates in water, releasing \(\mathrm{H^+}\) ions. Strong acids, such as hydrochloric acid, almost completely dissociate, while weak acids dissociate to a lesser extent. Bases, on the other hand, can also be strong or weak based on their ability to accept \(\mathrm{H^+}\) ions. For example, sodium hydroxide is a strong base that readily accepts \(\mathrm{H^+}\) ions and dissociates almost completely in solution.

Hydrogen ion concentration

The concept of hydrogen ion concentration is at the heart of pH calculations. It indicates the amount of hydrogen ions per liter of solution, expressed in moles per liter (M). In chemistry, \(\left[\mathrm{H^+}\right]\) symbolizes this concentration.

The concentration of \(\mathrm{H^+}\) is inversely related to the pH: a high \(\mathrm{H^+}\) concentration results in a low pH (acidic), whereas a low \(\mathrm{H^+}\) concentration yields a high pH (basic). It's a critical parameter in assessing a solution's acidity or basicity, helping us to understand chemical reactions, calculate equilibrium states, and maintain proper conditions in biological and environmental systems.

Logarithmic calculations

The pH of a solution is calculated using logarithmic calculations based on the negative logarithm to base 10 of the hydrogen ion concentration: \(\text{pH} = -\log \left[\mathrm{H^+}\right]\). This logarithmic relationship means pH is not a linear scale, but a measure of orders of magnitude.

In practical terms, to calculate the pH, you take the logarithm of the inverse of the hydrogen ion concentration. Because of the negative sign, as the concentration of \(\mathrm{H^+}\) ions increases, the pH decreases, reflecting increased acidity. The opposite is true for decreasing concentrations of \(\mathrm{H^+}\) ions. Due to logarithms, even small changes in \(\mathrm{H^+}\) concentration can lead to significant shifts in pH. Understanding this principle is crucial for accurately determining the acidity or basicity of a solution.