Posted by K on Friday, November 30, 2007 at 1:36am.
& 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.
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.
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!!!!!
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