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Chapter 16: Problem 18

What is the relationship between pH and \(\mathrm{H}^{+}\) concentration

Short Answer

Expert verified
pH is inversely related to \([ ext{H}^+]\); higher pH means lower \([ ext{H}^+]\) and vice versa.

Step by step solution

01

Understanding pH definition

The pH is a measure of the hydrogen ion concentration in a solution. It is defined as the negative logarithm of the hydrogen ion concentration, mathematically represented as \( ext{pH} = - ext{log}_{10}[ ext{H}^+] \). This means pH and hydrogen ion concentration are inversely related on a logarithmic scale.
02

Relating \\([ ext{H}^+]\\) to pH

To understand how \([ ext{H}^+]\) relates to pH, rearrange the pH equation to \( [ ext{H}^+] = 10^{- ext{pH}} \). This equation shows that as pH increases, \([ ext{H}^+]\) decreases exponentially.
03

Logarithmic relationship interpretation

The relationship is logarithmic: a decrease in one unit of pH (e.g., from 7 to 6) means the \([ ext{H}^+]\) is 10 times greater. Conversely, a one-unit increase in pH implies a tenfold decrease in \([ ext{H}^+]\).

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Key Concepts

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

Logarithmic Scale
In the world of chemistry, the pH scale is not just a simple linear measurement; it's a logarithmic scale.
This means that instead of increasing in equal amounts, each step on the pH scale represents a tenfold change in hydrogen ion concentration.
  • If pH decreases by just one unit on this scale, the concentration of hydrogen ions, \([\text{H}^{+}]\), becomes ten times higher.
  • This significant change due to a small pH shift is what sets logarithmic scales apart from linear ones.
Thus, a solution with a pH of 3 is not twice as acidic as one with a pH of 6, but instead, it is 1000 times more acidic. This is crucial for understanding how even minor changes in pH can have large effects on the chemical properties of a solution.
Inverse Relationship
The connection between pH and hydrogen ion concentration is an inverse relationship.
This means that when one goes up, the other comes down. And it doesn't just decrease a little bit, it changes by factors of ten, thanks to the logarithmic nature.
  • As pH increases, indicating a more acidic environment, \([\text{H}^{+}]\) decreases. This is because the environment becomes less acidic.
  • Conversely, if \([\text{H}^{+}]\) increases, making the solution more acidic, the pH value drops.
To see this in action, consider the equation \([\text{H}^{+}] = 10^{-\text{pH}}\), showing the mathematical representation of this inverse link. Thus, understanding this relationship helps predict how changes in hydrogen ion concentration affect pH levels.
Acid-Base Chemistry
Acid-base chemistry revolves around the concepts of pH and hydrogen ion concentration. In this branch of chemistry, understanding how acids and bases influence the environment is crucial.
  • Acids are substances that increase the hydrogen ion concentration in a solution, thus lowering the pH.
  • Bases, on the other hand, reduce the concentration of hydrogen ions, resulting in a higher pH.
The pH scale typically ranges from 0 to 14.
  • A pH less than 7 indicates an acidic solution, with more \([\text{H}^{+}]\) ions.
  • A pH greater than 7 signifies a basic solution, where the concentration of \([\text{H}^{+}]\) is lower.
  • A pH of exactly 7 is neutral, meaning the concentration of \([\text{H}^{+}]\) is balanced.
This fundamental understanding of acid and base properties is essential for studying chemical reactions and environmental changes.

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Most popular questions from this chapter

What is the relationship between \(\mathrm{pH}\) and \(\mathrm{H}^{+}\) concentration?

What are some of the observable properties of acids and bases?

Consider a solution of hydrobromic acid, HBr. a. If you draw a particle view of this acid with 10 \(\mathrm{H}^{+}\) ions, how many Br- ions would you need? Explain your thinking. b. Sketch a particle view of an HBr solution with 10 \(\mathrm{H}^{+}\) ions.

How many mL of 0.1 \(\mathrm{M} \mathrm{NaOH}\) would be required to neutralize 2.0 \(\mathrm{L}\) of 0.050 \(\mathrm{M} \mathrm{HCl}\) ?

What is the \(\mathrm{pH}\) of a 2.5 \(\mathrm{M}\) HCl solution?
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