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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

Describe how you might use a titration to figure out the concentration of potassium hydroxide in a water sample.

When you add water to an acidic solution, describe what happens to the pH of that solution.

Label the substances listed below as acids or bases. In each case, list the ions you would expect to find in solution. a. hydroiodic acid, HI b. formic acid, HCOOH c. rubidium hydroxide, RbOH d. hypochlorous acid, HOCl e. selenous acid, H_{2} \operatorname { S e O } _ { 4 } f. phosphine, PH_ g. perchloric acid, HClO_ \(_{4}\) h. calcium hydroxide, Ca(OH)_

Which of these substances might be useful in neutralizing a lake damaged by acid rain? (A) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) (B) \(\mathrm{CH}_{3} \mathrm{COOH}\) (C) \(\mathrm{CaCl}_{2}\) (D) \(\mathrm{Ca}(\mathrm{OH})_{2}\)

Explain why the pH of a NaCl solution does not change if you dilute the solution.
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