Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 110

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 at \( 40 K \) is defined as the mass of one cell divided by the volume of one cell from steps 5 and 3, respectively.

Step by step solution

01

Number of atoms in an FCC cell

In a face-centered cubic (FCC) unit cell, there are 8 corners with 1/8 of each atom within the cell and 6 face-centered atoms with 1/2 of each atom within the cell. Therefore, the effective number of atoms in an FCC cell is \(1(8 \times 1/8) + 3(6 \times 1/2) = 4\).
02

Calculate edge length of the cell

The atomic radius \(r\) is half the face diagonal in the FCC unit. Therefore, the face diagonal is \(2r\) and is equal to \( \sqrt{2} \) times the edge length \(a\) of the cubic cell. This can be solved for \(a\), and looks like this: \(a = \sqrt{2} \times r = \sqrt{2} \times 191 \times 10^{-12} meters\).
03

Compute the volume of the cell

The volume \(V\) of the cube is \( a^3 \). Substituting the edge length from the previous calculation, the volume of the cell can be calculated.
04

Calculate the molar mass of argon

The molar mass \( M \) of Argon is \(39.948 g/mol\).
05

Compute the mass of one cell

The mass is obtained by multiplying the number of atoms by the molar mass of the atom and dividing by Avogadro’s number \(N_A\) (because it’s the mass of one mole to the number of particles in a mole). The mass of a cell \(m_c\) is \(\frac{4 M}{N_A} = \frac{4 \times 39.948 \times 10^{-3}}{6.022 \times 10^{23}} kg\).
06

Determine the density

Finally, the density \( \rho \) of Argon can be obtained by dividing the mass of one cell by its volume: \( \rho = \frac{m_c}{V} \).

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

State which substance in each of these pairs you would expect to have the higher boiling point and explain why: (a) Ne or \(\mathrm{Xe},\) (b) \(\mathrm{CO}_{2}\) or \(\mathrm{CS}_{2},\) (c) \(\mathrm{CH}_{4}\) or \(\mathrm{Cl}_{2},\) (d) \(\mathrm{F}_{2}\) or \(\mathrm{LiF}\) (e) \(\mathrm{NH}_{3}\) or \(\mathrm{PH}_{3}\)

Outdoor water pipes have to be drained or insulated in winter in a cold climate. Why?

At \(-35^{\circ} \mathrm{C}\), liquid HI has a higher vapor pressure than liquid HF. Explain.

A beaker of water is placed in a closed container. Predict the effect on the vapor pressure of the water when (a) its temperature is lowered, (b) the volume of the container is doubled, (c) more water is added to the beaker.

Metallic iron crystallizes in a cubic lattice. The unit cell edge length is \(287 \mathrm{pm}\). The density of iron is \(7.87 \mathrm{~g} / \mathrm{cm}^{3}\). How many iron atoms are there within a unit cell?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Nuclear Chemistry

Read Explanation

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

Kinetics

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