Question

Give the \(\mathrm{pH}\) that corresponds to each of the following solutions and classify them as acidic, basic, or neutral: a. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=0.01\) b. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=10^{-9}\) c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=10^{-7}\) d. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=10^{-5}\)

Short answer

a. pH = 2 (acidic), b. pH = 9 (basic), c. pH = 7 (neutral), d. pH = 5 (acidic)

Step-by-step solution

Identify the pH Formula

The pH of a solution is calculated using the formula \( pH = -\log [H_{3}O^{+}] \), where\([H_{3}O^{+}]\)is the concentration of hydronium ions in moles per liter.

Calculate pH for Solution a

For solution a with \( [H_{3}O^{+}] = 0.01 M \), use the formula: \( pH = -\log(0.01) \) to get \( pH = 2 \) which is acidic.

Calculate pH for Solution b

For solution b with \( [H_{3}O^{+}] = 10^{-9} M \), use the formula: \( pH = -\log(10^{-9}) \) to get \( pH = 9 \) which is basic.

Calculate pH for Solution c

For solution c with \( [H_{3}O^{+}] = 10^{-7} M \), use the formula: \( pH = -\log(10^{-7}) \) to get \( pH = 7 \) which is neutral.

Calculate pH for Solution d

For solution d with \( [H_{3}O^{+}] = 10^{-5} M \), use the formula: \( pH = -\log(10^{-5}) \) to get \( pH = 5 \) which is acidic.

Key concepts

Acidic and Basic Solutions

Understanding the nature of acidic and basic solutions is crucial for many areas of science, including chemistry, biology, and environmental science. An acidic solution has a higher concentration of hydronium ions, represented by \(\mathrm{H}_3\mathrm{O}^+\), than a basic solution. Conversely, a basic or alkaline solution contains more hydroxide ions \(\mathrm{OH}^-\) than hydronium ions.

The pH scale is a measure of how acidic or basic a solution is. If a solution has a pH less than 7, it is considered acidic, and if it has a pH greater than 7, it's classified as basic. A pH of exactly 7 is neutral, which is the pH of pure water at room temperature. The exercise mentioned above presents a clear example of how to distinguish between these types of solutions. For instance, a solution with a hydronium concentration of \(0.01 M\) has a pH of 2, which is acidic, whereas a solution with a hydronium concentration of \(10^{-9} M\) has a pH of 9, indicating it is basic.

It's important to realize that the pH scale is logarithmic, which means each whole number on the scale represents a tenfold increase or decrease in acidity. For example, a solution with a pH of 3 is ten times more acidic than a solution with a pH of 4.

Hydronium Ion Concentration

The concentration of hydronium ions in a solution is a key factor in determining the solution's acidity. This concentration is typically measured in moles per liter (M), and it directly influences the pH level of the solution.

The hydronium ion, \(\mathrm{H}_3\mathrm{O}^+\), is formed when an acid dissolves in water and donates a proton (\(H^+\)) to a water molecule. This process is exemplified in the dissociation of hydrochloric acid: \(\mathrm{HCl} + \mathrm{H}_2\mathrm{O} → \mathrm{H}_3\mathrm{O}^+ + \mathrm{Cl}^-\).

In the exercise solutions, different concentrations of hydronium ions lead to different pH values. For instance, a hydronium ion concentration of \(10^{-5} M\) results in a pH of 5, which is acidic. This demonstrates that as the concentration of hydronium ions decreases, the solution becomes less acidic and moves closer towards neutrality or basicity. Conversely, increasing \(\mathrm{H}_3\mathrm{O}^+\) concentration results in a lower pH, indicating a more acidic solution.

pH Scale

The pH scale is a numerical way of expressing the acidity or basicity of a solution. It typically ranges from 0 to 14, with 7 being neutral. As mentioned earlier, solutions with a pH lower than 7 are acidic, and those with a pH higher than 7 are basic or alkaline.

The pH is calculated by taking the negative logarithm (base 10) of the hydronium ion concentration. The formula \( pH = -\log [H_{3}O^{+}] \) shows that a small change in the concentration of hydronium ions can result in a significant shift in pH. This concept can be a bit challenging for students to grasp, but it's essential for understanding a wide range of chemical reactions, bioprocesses, and environmental phenomena.

It's also notable that the pH scale is an inverse measure of hydronium ion concentration; a high concentration yields a low pH, and a low concentration yields a high pH. This property of the pH scale is clearly demonstrated in the given exercise, which shows the calculation of pH for different concentrations of hydronium ions—highlighting the logarithmic relationship between the hydronium ion concentration and pH value.

Remember, accurate pH calculation is fundamental in areas like medicine, where the body's pH must be maintained within a narrow range, and in environmental science, where pH affects ecosystem health.