/*! 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 4 Glass of Water Calculate the num... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 22: Problem 4

Glass of Water Calculate the number of coulombs of positive charge in \(250 \mathrm{~cm}^{3}\) of (neutral) water (about a glassful).

Short Answer

Expert verified
The charge is approximately 1.34 脳 10鈦� C.

Step by step solution

01

Understand the problem

We need to calculate the number of coulombs of positive charge in 250 cm鲁 of water. Since the water is neutral, we can use the properties of water molecules and their composition to derive the answer.
02

Determine the number of water molecules

First, calculate the number of moles of water in 250 cm鲁 (or 250 grams, since the density of water is 1 g/cm鲁). The molar mass of water (H鈧侽) is about 18 g/mol.\[ \text{Number of moles} = \frac{250 \text{ g}}{18 \text{ g/mol}} \]
03

Calculate the moles

Find the number of moles from the above expression:\[ \text{Number of moles} = \frac{250}{18} \text{ mol} 鈮� 13.89 \text{ mol} \]
04

Find the number of water molecules

Use Avogadro's number (\text{N_A} = 6.022 脳 10虏鲁 molecules/mol) to find the total number of water molecules in 13.89 mol:\[ \text{Number of molecules} = 13.89 \text{ mol} 脳 6.022 脳 10^{23} \text{ molecules/mol} \]
05

Calculate the number of molecules

Calculate the total number of water molecules:\[ \text{Number of molecules} 鈮� 8.36 脳 10^{24} \text{ molecules} \]
06

Determine the number of protons per water molecule

Each water molecule (H鈧侽) has 2 hydrogen atoms (with one proton each) and 1 oxygen atom (with 8 protons), totaling:\[ 2 \text{ (H)} + 8 \text{ (O)} = 10 \text{ protons per molecule} \]
07

Calculate the total number of protons

Multiply the number of water molecules by the number of protons per molecule:\[ \text{Total protons} = 8.36 脳 10^{24} \text{ molecules} 脳 10 \text{ protons/molecule} = 8.36 脳 10^{25} \text{ protons} \]
08

Find the charge per proton

Knowing the charge of one proton is approximately 1.602 脳 10^{-19} C, calculate the total charge:\[ \text{Total charge} = 8.36 脳 10^{25} \text{ protons} 脳 1.602 脳 10^{-19} \text{ C/proton} \]
09

Calculate the total charge

Finally, calculate the total charge in coulombs:\[ \text{Total charge} 鈮� 1.34 脳 10^{7} \text{ C} \]

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.

Molar Mass
The molar mass is the mass of one mole of a given substance. For water (H鈧侽), it consists of two hydrogen atoms and one oxygen atom. The atomic masses are approximately 1 g/mol for hydrogen and 16 g/mol for oxygen.
  • For H鈧�, the mass is 2 g/mol.
  • For one O, the mass is 16 g/mol.
Consequently, the molar mass of H鈧侽 is approximately 18 g/mol.
This means one mole of water, which is about 6.022 脳 10虏鲁 molecules (thanks to Avogadro's number), weighs 18 grams. Understanding the molar mass is essential for converting grams of a substance into moles, a crucial step in our calculations.
Avogadro's Number
Avogadro's number is a constant that signifies the number of constituent particles (usually atoms or molecules) in one mole of a substance. Its value is approximately 6.022 脳 10虏鲁 particles per mole.
This means:
  • 1 mole of water = 6.022 脳 10虏鲁 water molecules.
  • 1 mole of hydrogen atoms = 6.022 脳 10虏鲁 hydrogen atoms.
  • Any substance in 1 mole = 6.022 脳 10虏鲁 entities of that substance.
In our problem, knowing Avogadro's number allows us to determine how many water molecules are present when we have a specific number of moles. We used it to find that 13.89 moles of water correspond to 8.36 脳 10虏4 molecules of water.
Protons
Protons are positively charged particles found in the nucleus of an atom. Every element has a unique number of protons, which defines its atomic number. Here are the numbers relevant to our exercise:
  • Hydrogen (H) has 1 proton.
  • Oxygen (O) has 8 protons.
Therefore, each water molecule (H鈧侽) contains:
  • 2 protons from the two hydrogen atoms.
  • 8 protons from the one oxygen atom.
So, each water molecule has a total of 10 protons. By multiplying the total number of water molecules by the number of protons per molecule, we derive the total number of protons in our sample of water.
Coulombs
Coulombs (C) measure electric charge. In our problem, we need to find the total positive charge in a glass of water. Each proton carries a positive charge of approximately 1.602 脳 10鈦宦�9 coulombs.
To find the total charge:
  • First, calculate the number of protons in the water.
  • Second, multiply the number of protons by the charge of one proton.
For our 250 cm鲁 (or 250 grams) of water, the total positive charge is found by multiplying 8.36 脳 10虏5 protons by 1.602 脳 10鈦宦�9 C/proton, which equals approximately 1.34 脳 10鈦� coulombs.
Neutral Water
Neutral water means that it has no overall charge; the positive and negative charges are balanced. In a water molecule (H鈧侽):
  • The hydrogen atoms each contribute a single proton with a positive charge.
  • The oxygen atom, which has 8 protons, also contributes enough electrons to balance these protons' positive charges.
Because water is neutral, the number of positive charges (protons) equals the number of negative charges (electrons). Understanding this balance is important. It's why we only calculate the charge from protons in this exercise, knowing that the electrons' negative charge will cancel out these when considering neutral water completely.

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

Split in Two A charge of \(6.0 \mu \mathrm{C}\) is to be split into two parts that are then separated by \(3.0 \mathrm{~mm}\). What is the maximum possible magnitude of the electrostatic force between those two parts?

Fibrillation A charge flow of \(0.300 \mathrm{C} / \mathrm{s}\) through your chest can send your heart into fibrillation, disrupting the flow of blood (and thus oxygen) to your brain. If that current persists for \(2.00 \mathrm{~min}\), how many conduction electrons pass through your chest?

Salt Crystal What is the magnitude of the electrostatic force between a singly charged sodium ion \(\left(\mathrm{Na}^{+}\right.\), of charge \(\left.+e\right)\) and an adjacent singly charged chlorine ion \(\left(\mathrm{Cl}^{-}\right.\), of charge \(\left.-e\right)\) in a salt crystal if their separation is \(2.82 \times 10^{-10} \mathrm{~m}\) ?

Cesium Chloride In the basic \(\mathrm{CsCl}\) (cesium chloride) crystal structure, \(\mathrm{Cs}^{+}\) ions form the corners of a cube and a \(\mathrm{Cl}^{-}\) ion is at the cube's center . The edge length of the cube is \(0.40 \mathrm{~nm}\). The \(\mathrm{Cs}^{+}\) ions are each deficient by one electron (and thus each has a charge of \(+e\) ), and the \(\mathrm{Cl}^{-}\) ion has one excess electron (and thus has a charge of \(-e\) ). (a) What is the magnitude of the net electrostatic force exerted on the \(\mathrm{Cl}^{-}\) ion by the eight \(\mathrm{Cs}^{+}\) ions at the corners of the cube? (b) If one of the \(\mathrm{Cs}^{+}\) ions is missing, the crystal is said to have a defect; what is the magnitude of the net electrostatic force exerted on the \(\mathrm{Cl}^{-}\) ion by the seven remaining \(\mathrm{Cs}^{+}\) ions?

Hanging Ball of Foil (a) Explain how a metal conductor such as a hanging ball of aluminum foil can be attracted to a charged insulator even though the ball of foil has no net charge so that it is electrically neutral. (b) Can two metal balls with no net charge attract each other? Explain. (c) Can the process of induction cause a neutral conductor to be repelled from a charged insulator? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Rotational Dynamics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Turning Points in Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Space Physics

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.