
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN: 9781259696527
Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Question

Transcribed Image Text:**Question:**
A metal has a body-centered cubic lattice with a unit cell edge length of 2.866 Å (1 Å = 10^-10 m). The density of the metal is 7.87 g/cm³. What is the mass of an atom of this metal in grams? (1 m = 10^12 pm).
**Explanation:**
This question involves calculating the mass of an atom in a metal with a body-centered cubic (BCC) structure.
### Key Concepts:
- **Body-Centered Cubic (BCC) Lattice:** In a BCC lattice, each unit cell contains two atoms. One atom is at the center of the cube, and the corners of the cube each contribute 1/8th of an atom to the unit cell.
- **Unit Cell Edge Length:** The length of the cube's edge is given as 2.866 Å.
- **Density:** The density of the metal is 7.87 g/cm³.
- **Atomic Mass Calculation:** To find the mass of an atom, use the formula for density and the fact that density = mass/volume.
### Steps to Solve:
1. **Convert Edge Length:** Convert edge length from Ångströms to centimeters.
\(2.866 \, \text{Å} = 2.866 \times 10^{-8} \, \text{cm}\)
2. **Calculate Volume of Unit Cell:**
Volume = edge length\(^3 = (2.866 \times 10^{-8} \, \text{cm})^3\)
3. **Use Density Formula:**
Density = Mass / Volume
\(7.87 \, \text{g/cm}^3 = \text{Mass} / \text{Volume of unit cell}\)
Solve for Mass of the unit cell.
4. **Calculate Mass of Single Atom:**
Since there are two atoms per unit cell in a BCC lattice, divide the mass of the unit cell by 2 to find the mass of a single atom.
This process will yield the mass of an individual atom in grams.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps

Knowledge Booster
Similar questions
- A solution is made using 250.0 mL of ethanol (density 0.7892 g/mL) and 673.1 mL of water (density 1.000 g/mL). What is the mass percent of the ethanol?arrow_forwardAn intrepid daredevil has a plan to fly to Mars and go skydiving in the Martian atmosphere! They want you to determine if this skydive will be safe by determining the terminal velocity that they will reach on their dive. Our daredevil really wants to go on this trip so they have done some measurements for you! The mass of the person is 75 kg, their projected area (chest-first) is 0.70 m² and their drag coefficient in this orientation is 1.05. The air density of Mars is 0.015 kg/m³ and the gravity on Mars is 38% of Earth's gravity. What is the terminal velocity (in miles per hour) of the person in their skydive descent to Mars' surface? (4 pts)arrow_forward
Recommended textbooks for you
- Introduction to Chemical Engineering Thermodynami...Chemical EngineeringISBN:9781259696527Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark SwihartPublisher:McGraw-Hill EducationElementary Principles of Chemical Processes, Bind...Chemical EngineeringISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEYElements of Chemical Reaction Engineering (5th Ed...Chemical EngineeringISBN:9780133887518Author:H. Scott FoglerPublisher:Prentice Hall
- Industrial Plastics: Theory and ApplicationsChemical EngineeringISBN:9781285061238Author:Lokensgard, ErikPublisher:Delmar Cengage LearningUnit Operations of Chemical EngineeringChemical EngineeringISBN:9780072848236Author:Warren McCabe, Julian C. Smith, Peter HarriottPublisher:McGraw-Hill Companies, The

Introduction to Chemical Engineering Thermodynami...
Chemical Engineering
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:McGraw-Hill Education

Elementary Principles of Chemical Processes, Bind...
Chemical Engineering
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY

Elements of Chemical Reaction Engineering (5th Ed...
Chemical Engineering
ISBN:9780133887518
Author:H. Scott Fogler
Publisher:Prentice Hall


Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:9781285061238
Author:Lokensgard, Erik
Publisher:Delmar Cengage Learning

Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:9780072848236
Author:Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:McGraw-Hill Companies, The