Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 59

Galena, also called lead glance, is a mineral composed of lead(II) sulfide(PbS). The mineral adopts the rock salt structure. The length of an edge of the PbS unit cell is \(0.593 \mathrm{nm}\) at \(25^{\circ} \mathrm{C}\). Determine the density of \(\mathrm{PbS}\) in \(\mathrm{g} / \mathrm{cm}^{3}\).

Short Answer

Expert verified
The density of PbS at 25°C is approximately 1.911 g/cm³.

Step by step solution

01

Calculate the volume of the unit cell

Our unit cell is a cubic structure with an edge length (a) of 0.593 nm. To find the volume of the unit cell, we cube the edge length. Note that we must convert the edge length to cm for the final density to be in g/cm³. a = 0.593 nm * (1x10^(-7) cm/nm) = 5.93x10^(-8) cm Volume = a^3 = (5.93x10^(-8) cm)^3 = 2.084x10^(-22) cm³
02

Calculate the number of PbS formula units per unit cell

Galena has a rock salt (face-centered cubic) structure, which means there is one Pb and one S atom per unit cell. So, there is one PbS formula unit per unit cell.
03

Calculate the molar mass of PbS

To find the molar mass of PbS, we add the atomic masses of Pb and S together. Molar mass of Pb = 207.2 g/mol Molar mass of S = 32.1 g/mol Molar mass of PbS = 207.2 g/mol + 32.1 g/mol = 239.3 g/mol
04

Use the values to find the density of PbS

The density of PbS can be found using the following equation: Density = (mass of PbS in unit cell) / (volume of unit cell) To find the mass of PbS in one unit cell, we need to convert the mass of one PbS formula unit from moles to grams using the molar mass we found. 1 PbS formula unit * (239.3 g/mol) / Avogadro's number = 3.982x10^(-22) g Now we can calculate the density: Density = (3.982x10^(-22) g) / (2.084x10^(-22) cm³) = 1.911 g/cm³ The density of PbS at 25°C is approximately 1.911 g/cm³.

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

Indicate whether the following statement is true or false: For an addition polymerization, there are no by-products of the reaction (assuming \(100 \%\) yield).

An addition polymerization forms the polymer originally used as Saran" wrap. It has the following structure $\mathrm{t} \mathrm{CCl}_{2}-\mathrm{CH}_{2}+_{n}$. Draw the structure of the monomer.

The rutile and fluorite structures, shown here (anions are colored green), are two of the most common structure types of ionic compounds where the cation to anion ratio is 1: 2 . (a) For \(\mathrm{CaF}_{2}\) and \(\mathrm{ZnF}_{2}\) use ionic radii, \(\mathrm{Ca}^{2+}(r=114 \mathrm{pm})\), $\mathrm{Zn}^{2+}(r=88 \mathrm{pm})\(, and \)\mathrm{F}^{-}(r=119 \mathrm{pm})$, to predict which compound is more likely to crystallize with the fluorite structure and which with the rutile structure. (b) What are the coordination numbers of the cations and anions in each of these structures?

Imagine the primitive cubic lattice. Now imagine grabbing opposite corners and stretching it along the body diagonal while keeping the edge lengths equal. The three angles between the lattice vectors remain equal but are no longer \(90^{\circ}\). What kind of primitive lattice have you made?

The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is \(75 \mathrm{~mol} \%\) silver and $25 \mathrm{~mol} \%$ gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy. (b) If an alloy is formed that is 75 mol\% copper and 25 mol\% gold, what is the karat number of the alloy? What is the color of this alloy?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

Chemistry Branches

Read Explanation

Nuclear Chemistry

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