Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 136

Argon crystallizes in the face-centered cubic arrangement at \(40 \mathrm{~K}\). Given that the atomic radius of argon is \(191 \mathrm{pm}\), calculate the density of solid argon.

Short Answer

Expert verified
The density of solid argon can be calculated through the given steps taking into account the face-centered cubic arrangement it crystallizes into and its atomic radius. Following these steps will provide the correct density in the units of \(kg/m^3\).

Step by step solution

01

Face-Centered Cubic Arrangement Characteristics

In a face-centered cubic (fcc) arrangement, each unit cell contains 4 atoms. Since argon crystallizes as fcc, this 4 atoms per unit cell information will be used.
02

Calculation of the Volume of an Argon Atom

The volume of an atom can be calculated based on its atomic radius using the formula for the volume of a sphere which is \( V = \frac{4}{3}\pi r^3\). Given that the atomic radius of argon is \(191 \mathrm{pm}\), convert it to \(1.91 \times 10^{-10} m\) and substitute it into the formula to get the volume.
03

Calculation of the Volume Occupied by One Unit Cell

In a fcc structure, the length of the edge (a) of the unit cell can be calculated as \(a = 4r/\sqrt[]{2}\). Therefore, the volume of the unit cell is given by \(a^3\) which is \(\left(\frac{4r}{\sqrt[]{2}}\right)^3\). Substituting the radius to get the actual volume is the next step.
04

Calculation of the Density of Solid Argon

Density is calculated as mass divided by volume. In calculating the mass, the atomic weight of argon \(39.95 u\) needs to be converted into kg, which can be done using the conversion factor \(1 u = 1.660539x10^{-27} kg\). The volume is the volume of the unit cell as calculated in the previous step. Plug in the values into the density formula to get the density of solid argon.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Freeze-dried coffee is prepared by freezing brewed coffee and then removing the ice component with a vacuum pump. Describe the phase changes taking place during these processes.

Wet clothes dry more quickly on a hot, dry day than on a hot, humid day. Explain.

A face-centered cubic cell contains \(8 \mathrm{X}\) atoms at the corners of the cell and 6 Y atoms at the faces. What is the empirical formula of the solid?

Use water and mercury as examples to explain adhesion and cohesion.

A solid is soft and has a low melting point (below \(100^{\circ} \mathrm{C}\) ). The solid, its melt, and an aqueous solution containing the substance are all nonconductors of electricity. Classify the solid.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Kinetics

Read Explanation

Physical Chemistry

Read Explanation

Chemistry Branches

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.

Sign-up for free