CHEM****

Initial info:

The atoms of crystalline solid pack together into a three-dimensional array of many small repeating units called unit cells. The simplest of the unit cells are those that have cubic symmetry, with atoms positioned at the corners of a cube. Atoms can also be found in the sides (faces) of the cube, or centered within the body of the cube. It is important to realize that a unit cell is surrounded by other unit cells in every direction. Therefore, face and corner atoms are shared with neighboring unit cells. The fraction varies with the type of atom as shown in the following table.

Type of atom / Fraction in unit cell
corner 1/8
face 1/2
body 1

The size of a unit cell in any given solid can be calculated by using its density. This and the reverse calculation are common test questions in general chemistry courses.

**I am having problems with the following 2 questions:

1. Gallium crystallizes in a primitive cubic unit cell. The length of an edge of this cube is 362pm. What is the radius of a gallium atom?

Express your answer numerically in picometers.

"radius = _____pm"

&

2. The face-centered gold crystal has an edge length of 407pm. Based on the unit cell, calculate the density of gold.

Express your answer numerically in grams per cubic centimeter.

density = ______g/cm^3

For Further Reading

CHEM - DrBob222, Thursday, November 29, 2007 at 10:49am

For a primitive unit cell, a = 2r where a is the length of the edge of the cell and r is the radius.

For the fcc gold atom, density = mass/volume.
volume calculation:
Volume = (edge)3. Don't forget to change the pm to cm if you want density in g/cc.

mass calculation:
There are 4 atoms per unit cell along the face of one cube.
mass = (4atoms)(atomic mass Au)/6.02 x 10^23 atoms mol-1

Then density = mass/volume

Does this mean for #1 then, when you say a=2r...
you just go: a*2=r therefore: 362*2 = r .... radius = 724pm's??

  1. 👍
  2. 👎
  3. 👁
  1. & for #2 (with the gold/Au):

    Volume = (407pm)^3??? = 67,419,143 (or: 6.74 * 10^7)??
    then does 6.74*10^-7pm's translate to: 6.74*10^+10 cm's??

    Then go something like:
    (4 atoms)(196.967g/mol Au)/6.02*10^23 atoms mol-1
    = 1.30875*10^-21 g??

    Then density = mass/volume:

    d = 1.30875*10^-21 g / 6.74*10^+10 cm's

    *****d = 1.9418*10^-32 g/cm^3????!!!***

    PLEASE let me know if I have totally worked these two problems wrong!!! I am pretty sure I am not correct.

    1. 👍
    2. 👎
  2. I am having problems with the following 2 questions:

    1. Gallium crystallizes in a primitive cubic unit cell. The length of an edge of this cube is 362pm. What is the radius of a gallium atom?

    Express your answer numerically in picometers.

    "radius = _____pm"

    &

    2. The face-centered gold crystal has an edge length of 407pm. Based on the unit cell, calculate the density of gold.

    Express your answer numerically in grams per cubic centimeter.

    density = ______g/cm^3

    For Further Reading

    CHEM - DrBob222, Thursday, November 29, 2007 at 10:49am

    For a primitive unit cell, a = 2r where a is the length of the edge of the cell and r is the radius.

    For the fcc gold atom, density = mass/volume.
    volume calculation:
    Volume = (edge)3. Don't forget to change the pm to cm if you want density in g/cc.

    mass calculation:
    There are 4 atoms per unit cell along the face of one cube.
    mass = (4atoms)(atomic mass Au)/6.02 x 10^23 atoms mol-1

    Then density = mass/volume

    Does this mean for #1 then, when you say a=2r...
    you just go: a*2=r therefore: 362*2 = r .... radius = 724pm's??

    No. a=2r. Why did you change it to a*2 = r? a*2=diameter but a=edge length=2*radius You take the edge length (a) and divide it by 2 to obtain the radius. So 362 pm/2 = ?? pm radius.

    CHEM**** - K, Friday, November 30, 2007 at 1:53am
    & for #2 (with the gold/Au):

    Volume = (407pm)^3??? = 67,419,143 (or: 6.74 * 10^7)??
    then does 6.74*10^-7pm's translate to: 6.74*10^+10 cm's??

    No. Cubing the edge to obtain volume, using picometers, is ok BUT it makes the conversion from cubic picometers to cubic centimeters a little harder. I would convert 407 pm to cm FIRST, then cube.
    407 pm x (10^-10 cm/pm) = 4.07 x 10^-8 cm. Then volume = (4.07 x 10^-8 cm)3 = 6.74 x 10^-23 cc. Check my arithmetic.


    Then go something like:
    (4 atoms)(196.967g/mol Au)/6.02*10^23 atoms mol-1
    = 1.30875*10^-21 g??
    The mass is ok (except you can't have that many significant figures. I would use 1.31 x -21 g.).

    Then density = mass/volume:

    d = 1.30875*10^-21 g / 6.74*10^+10 cm's

    *****d = 1.9418*10^-32 g/cm^3????!!!***
    I think this will be ok if you substitute the correct value for volume (in cc) in place of the 6.74 x 10^10 cc. I calculated a density of 19.3 g/cc. You can look up the value of gold. Gold is quite dense but not as dense as 10^10. :-).

    PLEASE let me know if I have totally worked these two problems wrong!!! I am pretty sure I am not correct.

    Let me know if you have additional questions on this.

    1. 👍
    2. 👎
  3. this worked out perfectly!...thank you...that was the last question for the year that I had to finish through that program.
    I really must not have been paying attention with "a*2", as opposed to dividing a/2 to solve for "r". Thank you again, & for having pointed that out & with the conversion of pm's to cm's. That looks much faster & correct!
    Thank you for all of your help, & bobpursley's help this past semester!!! It all has guided me to understand what I am doing, for the most part, sooo tremendously!!!!!

    1. 👍
    2. 👎
  4. rhozuq dtigmnxpa dbxvaqu bytlkspqz yiwncovhj ohjeyv wtcun

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. chemistry

    what is the mass in grams? a) 3.011 x 10^23 atoms F b)1.50 x 10^23 atoms Mg c)4.50 x 10^12 atoms Cl d)8.42 x 10^18 atoms Br e) 25 atoms w f) 1 atom Au can you please explain a and b to me then i'll come back later and see if i did

  2. Sciences

    What is a substance that cannot be separated into simpler substances by physical or mechanical methods such as filtering, boiling, or sifting? A crystalline solid A sublimation A pure substance •• An amorphous solid Correct me

  3. Geometry

    In a Hexagon net for a 3 dimensional solid how many regions would there be? My answer is 8 the 6 sides and the top and bottom

  4. Physics

    A weather balloon is floating at a constant height above Earth when it releases a pack of instruments. If the pack hits the ground with a velocity of -68.5 m/s, how far does the pack fall? a = -9.80 m/s^2 Vf = -68.5 m/s d = ?

  1. Chemistry (The Composition of an Atom)

    In 1808, John Dalton wrote his atomic theory of matter. The following is a list of points from that theory. If it is still considered true today, label it true. If it is not considered true today, label it false. 1)Atoms cannot be

  2. chemistry

    You are analyzing a solid isolated from a reaction and find that its boiling point is over 1000 ∘C. You dissolve the compound in water solution and recrystallize it to produce some solid crystals that you use to determine that

  3. Chem - oxides

    When an element is burnt in excess oxygen, is the oxide formed always: 1. a crystalline solid 2. greater in mass than the element 3. soluble in water 4. white in color alright, i know that most oxides are not soluble in water

  4. General Chemistry

    PLEASE ANSWER VERY SOON I AM STUCK! Crystalline silicon has a cubic structure. The unit cell edge length is 543 pm. The density of the solid is 2.33 g/cm3. Calculate the number of Si atoms in one unit cell.

  1. chemistry

    What is the major difference between the two-dimensional and three- dimensional models of ethane and methane? When might you choose to use a two-dimensional model rather than a three-dimensional model when representing one of the

  2. chemistry help!!! please!!! DrBob222 I need you!!

    How many atoms of carbon are needed to produce 0.45 mol Al? 3C + 2Al2O3 4Al + 3CO2 A. 2.6 × 1026 atoms B. 9.7 × 1024 atoms C. 3.0 × 1022 atoms D. 2.0 × 1023 atoms I'm really very stuck with this question. please help me!!!

  3. physics

    A crystalline solid consists of atoms stacked up in a repeating lattice structure. The atoms of a crystal reside at the corners of cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from

  4. Chemistry

    Anthracene is a yellow, crystalline solid found in coal tar. Complete this structure for anthracene, C14H10, by adding bonds and hydrogen atoms as necessary. What type of hybrid orbitals are utilized by carbon in anthracene? >>sp3

You can view more similar questions or ask a new question.