/*! 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 62 Find \(\left[\mathrm{H}_{3} \mat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 62

Find \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) in a solution of \(\mathrm{pH} 4\).

Short Answer

Expert verified
The concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in a solution with \(\mathrm{pH}\) 4 is \(10^{-4}\) M.

Step by step solution

01

Understanding pH and \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration

The \(\mathrm{pH}\) of a solution is defined as the negative logarithm (base 10) of the molar concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the solution. So the formula that connects \(\mathrm{pH}\) and \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions concentration (\(\mathrm{H+}\)) is: \[\mathrm{pH} = - \log [\mathrm{H+}]\]
02

Inverting operation

In order to find the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions for given a \(\mathrm{pH}\) value the inversion operation is done using the same formula. After rearranging the formula the \[\mathrm{H+} = 10^{-\mathrm{pH}}\]
03

Substitute pH value in the formula

Now we can substitute the \(\mathrm{pH}\) value of 4 into the equation to get the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration. So, we have \[\mathrm{H+} = 10^{-4}\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Hydronium Ion Concentration
The hydronium ion, represented as \([\mathrm{H}_{3}\mathrm{O}^{+}]\), is a crucial component in understanding the acidity of a solution. When an acid dissolves in water, it increases the concentration of hydronium ions. This concentration can be specified in molarity, which is moles per liter. In terms of calculation, knowing the pH of a solution allows us to determine the hydronium ion concentration using the formula: \\[\mathrm{H+} = 10^{-\mathrm{pH}}\].Essentially, the hydronium ion concentration indicates how acidic or basic a solution is. Here is a quick summary to help:
  • Higher hydronium ion concentration means a more acidic solution.
  • Lower hydronium ion concentration indicates a less acidic, or more basic, solution.
  • Neutral solutions, like pure water, have a hydronium ion concentration of \(10^{-7}\) M.
Exploring Logarithmic Functions
Logarithmic functions are mathematical operations that help us solve exponential equations by expressing a number as a power of another number. In pH calculations, a common logarithm (base 10) is used. This makes them highly useful in chemical equations where we deal with exponential growth or decay, as seen in the acidity levels and hydronium ion concentrations.The fundamental relationship between pH and hydronium ion concentration is \\[\mathrm{pH} = - \log\left[\mathrm{H}_{3}\mathrm{O}^{+}]\right]\].Understanding how to manipulate these logs allows chemists to tackle problems involving acidic or basic substances more efficiently. Here are some points to remember:
  • Logarithms transform multiplications into additions, simplifying calculations.
  • The pH is an inverse logarithmic function of hydronium ion concentration.
  • A unit change in pH reflects a tenfold change in hydronium ion concentration.
Basics of Acid-Base Chemistry
Acid-base chemistry revolves around the concepts of acids, bases, and their interactions in solutions. Acids are substances that donate protons (\(\mathrm{H}^+\)), while bases accept them. When dissolved in water, acids increase the hydronium concentration, making the solution acidic, whereas bases decrease it.The pH scale, ranging from 0 to 14, provides a measure of the acidity or basicity of a solution:
  • A pH less than 7 indicates an acidic solution.
  • A pH of 7 is neutral.
  • A pH greater than 7 signifies a basic (alkaline) solution.
These principles not only help classify substances but also guide reactions and predict outcomes in various chemical processes. Understanding acid-base concepts is fundamental for students as they delve deeper into chemistry topics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is the conjugate acid of the base ammonia, \(\mathrm{NH}_{3}\) ?

Explain the relationship between the self-ionization of water and \(K_{w}\) .

If the pH of a solution is \(4.3,\) what is the hydroxide ion concentration?

What two buret readings need to be recorded in order to determine the volume of solution dispensed by the buret?

A solution of acetic acid had the following solute concentrations: \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]=\) \(0.035 \mathrm{M},\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.4 \times 10^{-4} \mathrm{M},\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]=7.4 \times 10^{-4} \mathrm{M} .\) Calculate the \(K_{a}\) of acetic acid based on these data.
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Kinetics

Read Explanation

Making Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.