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Chapter 16: Problem 20

Define \(\mathrm{pH}\). Why do chemists normally choose to discuss the acidity of a solution in terms of \(\mathrm{pH}\) rather than hydronium ion concentration \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] ?\)

Short Answer

Expert verified
\(\mathrm{pH}\) is a logarithmic measure of hydrogen ion concentration, used for convenience and simplicity in comparing acidity.

Step by step solution

01

Understanding pH

The term \(\mathrm{pH}\) stands for 'potential of hydrogen' and indicates the acidity or basicity of a solution. It is a logarithmic scale used to specify the hydrogen ion concentration. The formula is \(\mathrm{pH} = -\log_{10}[\mathrm{H}_3\mathrm{O}^+]\).
02

The pH Scale

The \(\mathrm{pH}\) scale typically ranges from 0 to 14. A \(\mathrm{pH}\) less than 7 indicates an acidic solution, a \(\mathrm{pH}\) of 7 is neutral, and a \(\mathrm{pH}\) greater than 7 indicates a basic solution.
03

Logarithmic Interpretation

The logarithmic nature of the \(\mathrm{pH}\) scale means that a change of one unit in \(\mathrm{pH}\) represents a tenfold change in hydronium ion concentration \([\mathrm{H}_3\mathrm{O}^+]\). This makes it easier to compare the acidity levels of different solutions.
04

Simplicity and Convenience

Using \(\mathrm{pH}\) simplifies discussions about acidity because it avoids dealing with very small numbers. Hydronium ion concentrations can range from \(10^{-1}\) to \(10^{-14}\), so using \(\mathrm{pH}\) provides a more convenient scale.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acidity
Acidity refers to the level of acid present in a solution. It is derived from the Latin word 'acidus,' meaning sour. You may notice that sour foods like lemons and vinegar have a distinct sharp taste caused by acids. Acids release hydrogen ions (\( ext{H}^+\)) in a solution.
These ions contribute to the acidity of the solution. When we say a solution is acidic, it means there are more hydrogen ions present compared to hydroxide ions (\( ext{OH}^-\)).
  • Acidity is important in several chemical reactions and biological processes.
  • It plays a role in the taste and preservation of food and beverages.
  • It affects the environment, influencing soil pH and water acidity.
Understanding acidity helps in analyzing the behavior of solutions in different conditions, essential for fields like chemistry, biology, and environmental science.
Hydronium Ion Concentration
The hydronium ion concentration, denoted as \([ ext{H}_3 ext{O}^+]\), measures how many hydronium ions are present in a solution.
Hydronium ions form when water molecules accept a proton (\( ext{H}^+\)) from an acid. This concentration is a direct indicator of acidity, as more hydronium ions mean a more acidic solution.
  • High hydronium concentration: indicates stronger acidity.
  • Low hydronium concentration: suggests the solution is less acidic or more basic.
Chemists often use pH instead of directly using hydronium ion concentration because these concentrations can be tiny numbers, like \(10^{-1}\) to \(10^{-14}\), making calculations cumbersome.
Expressing acidity as pH is easier for understanding and communicating.
Logarithmic Scale
The concept of a logarithmic scale is central to how pH is measured. Logarithmic scales are nonlinear scales used to handle wide-ranging numerical values. Unlike a linear scale, where each step is equal, each step on a logarithmic scale represents a tenfold change in value.
For example:
  • A change from pH 2 to pH 3 means the concentration of hydronium ions decreases tenfold.
  • A shift from pH 3 to pH 5 means a hundredfold reduction in hydronium ion concentration.
This scale is particularly useful in chemistry because it allows us to easily express and understand the vast range of acidity found in solutions using more manageable numbers. By converting the minute differences into a broader scale, it simplifies many scientific analyses and comparisons.
Acidic and Basic Solutions
Solutions can be classified as acidic, neutral, or basic, depending on their pH value. A pH less than 7 is considered acidic, with more hydronium ions than hydroxide ions. Lemon juice, with a pH around 2, is a common example.
  • Acidic solutions: pH < 7.
  • Neutral solutions: pH = 7 (like pure water).
  • Basic solutions: pH > 7, fewer hydronium ions.
Basic solutions, also known as alkaline solutions, have more hydroxide ions compared to hydronium ions. Baking soda in water, which has a pH of about 9, is a frequently used example.
Being able to distinguish between these types of solutions helps in predicting their behavior in chemical reactions and their effects in various applications, including medicinal, culinary, and industrial usages.

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Most popular questions from this chapter

What are the concentrations of \(\mathrm{HSO}_{4}^{-}, \mathrm{SO}_{4}^{2-}\), and \(\mathrm{H}_{3} \mathrm{O}^{+}\) in a \(0.20 \mathrm{M} \mathrm{KHSO}_{4}\) solution? (Hint: \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is a strong acid; \(K_{\mathrm{a}}\) for \(\mathrm{HSO}_{4}^{-}=1.3 \times 10^{-2}\).)

When the concentration of a strong acid is not substantially higher than \(1.0 \times 10^{-7} M\), the ionization of water must be taken into account in the calculation of the solution's \(\mathrm{pH}\). (a) Derive an expression for the \(\mathrm{pH}\) of a strong acid solution, including the contribution to \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) from \(\mathrm{H}_{2} \mathrm{O}\). (b) Calculate the pH of a \(1.0 \times 10^{-7} M \mathrm{HCl}\) solution.

Tooth enamel is largely hydroxyapatite \(\left[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}\right]\). When it dissolves in water (a process called demineralization), it dissociates as follows: $$ \mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH} \longrightarrow 5 \mathrm{Ca}^{2+}+3 \mathrm{PO}_{4}^{3-}+\mathrm{OH}^{-} $$ The reverse process, called remineralization, is the body's natural defense against tooth decay. Acids produced from food remove the \(\mathrm{OH}^{-}\) ions and thereby weaken the enamel layer. Most toothpastes contain a fluoride compound such as \(\mathrm{NaF}\) or \(\mathrm{SnF}_{2}\). What is the function of these compounds in preventing tooth decay?

A \(0.400 M\) formic acid (HCOOH) solution freezes at \(-0.758^{\circ} \mathrm{C}\). Calculate the \(K_{a}\) of the acid at that temperature. (Hint: Assume that molarity is equal to molality. Carry out your calculations to three significant figures and round off to two for \(K_{\mathrm{a}}\).)

Calculate the \(K_{\mathrm{a}}\) of a weak acid if a \(0.19-M\) aqueous solution of the acid has a \(\mathrm{pH}\) of 4.52 at \(25^{\circ} \mathrm{C}\).
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