/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 How is \(\mathrm{pH}\) defined?... [FREE SOLUTION] | 91影视

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How is \(\mathrm{pH}\) defined?

Short Answer

Expert verified
pH is defined as the negative logarithm of hydrogen ion concentration in a solution.

Step by step solution

01

Understanding pH

The term pH stands for 'potential of hydrogen' and is a scale used to specify the acidity or basicity of an aqueous solution. It is a logarithmic measure of the hydrogen ion concentration.
02

pH Formula

The pH of a solution is mathematically defined as the negative base 10 logarithm of the activity of hydrogen ions (H鈦) in moles per litre. The formula is: \( \mathrm{pH} = -\log_{10}[H^+] \).
03

Interpretation of pH Scale

The pH scale ranges from 0 to 14. A pH of 7 is considered neutral, meaning the concentration of hydrogen ions is equal to the concentration of hydroxide ions. A pH below 7 indicates an acidic solution (higher concentration of hydrogen ions), while a pH above 7 indicates a basic solution (lower concentration of hydrogen ions).

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Key Concepts

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

Hydrogen Ion Concentration
When we talk about hydrogen ion concentration, we're essentially discussing how many hydrogen ions, or H鈦 ions, are present in a solution. Think of it as counting the heads in a room 鈥 the more heads, the fuller the room. In the context of a solution, more H鈦 ions mean the solution is more acidic. Understanding this concentration is vital because it directly affects the pH value of a solution.
The concentration is measured in moles per liter. This is a standard way of expressing the amount of a substance in a liquid. A substance with higher hydrogen ion concentration is more acidic. This basic understanding helps us make sense of how solutions behave. For example:
  • High concentration of H鈦 = More acidic
  • Low concentration of H鈦 = Less acidic or more basic
Understanding hydrogen ion concentration helps in predicting how acidic or basic a solution will be, giving us control over the chemical behavior in various applications, from industrial to everyday household products.
pH Formula
The pH formula is a neat mathematical way to express the acidity or basicity of a solution through numbers. The formula is:\[ \text{pH} = -\log_{10}[H^+] \]Let's break this down. The pH formula involves taking the negative logarithm, base 10, of the hydrogen ion concentration, which is expressed as \[H^+\]\, in moles per liter.
This calculation helps us transform a possibly tiny number (like 0.0001 moles/liter) into a manageable one (like 4). Thanks to this formula, instead of discussing complicated concentrations, we simply talk about a number within the 0-14 range. Remember:
  • Higher [H鈦篯 leads to a lower pH value (meaning acidic).
  • Lower [H鈦篯 leads to a higher pH value (meaning basic).
The formula is practical and handy. It allows us to easily compare different solutions by just looking at their pH value, making the science of acidity and basicity far more approachable.
Acidity and Basicity Scale
The pH scale is a brilliant tool that helps us understand how acidic or basic (alkaline) a solution is. Ranging from 0 to 14, this scale gives us a visual representation of solution properties. Here's a quick guide:
  • pH 0-6: Acidic, with 0 being the most acidic.
  • pH 7: Neutral, like pure water 鈥 balanced between H鈦 and OH鈦 ions.
  • pH 8-14: Basic (also known as alkaline), with 14 being the most basic.
This scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration. So, a solution with a pH of 3 is ten times more acidic than one with a pH of 4.
Scientists and everyday users alike rely on this scale to understand and work with different solutions, from soil and water testing to cooking and medicine. The pH scale's simplicity and utility make it an essential concept in science and everyday life.

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Most popular questions from this chapter

What happens when a weak acid such as \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) is dissolved in water?

What are the molarity and the normality of a solution made by dissolving \(25 \mathrm{~g}\) of citric acid (triprotic, \(\left.\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \mathrm{H}_{3}\right)\) in enough water to make \(800 \mathrm{~mL}\) of solution?

What are the \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\) concentrations of solutions that have the following \(\mathrm{pH}\) values? (a) \(\mathrm{pH} 4\) (b) \(\mathrm{pH} 11\) (c) \(\mathrm{pH} 0\) (d) \(\mathrm{pH} 1.38\) (e) \(\mathrm{pH} 7.96\)

Label the Br酶nsted-Lowry acids and bases in the following equations, and tell which substances are conjugate acid-base pairs. $$ \begin{array}{l} \text { (a) } \mathrm{CO}_{3}^{2-}(a q)+\mathrm{HCl}(a q) \longrightarrow \mathrm{HCO}_{3}^{-}(a q)+\mathrm{Cl}^{-}(a q) \\ \text { (b) } \mathrm{H}_{3} \mathrm{PO}_{4}(a q)+\mathrm{NH}_{3}(a q) \longrightarrow \\ & \mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)+\mathrm{NH}_{4}^{+}(a q) \\ \text { (c) } \mathrm{NH}_{4}^{+}(a q)+\mathrm{CN}^{-}(a q) \rightleftarrows \mathrm{NH}_{3}(a q)+\mathrm{HCN}(a q) \\ \text { (d) } \mathrm{HBr}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Br}^{-}(a q) \end{array} $$ (e) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)+\mathrm{N}_{2} \mathrm{H}_{4}(a q) \rightleftarrows\) $$ \mathrm{HPO}_{4}^{2-}(a q)+\mathrm{N}_{2} \mathrm{H}_{5}^{+}(a q) $$

How is \(K_{\mathrm{w}}\) defined, and what is its numerical value at \(25^{\circ} \mathrm{C}(298 \mathrm{~K}) ?\)

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