All categories

4 years ago

Calculate the fraction of empty space in cubic closest packing to five significant figures.

Chemistry

1 answer:

nata0808 [166]4 years ago

4 0

0.259 52 . The fraction of empty space in a ccp cell is 0.259 52

Cubic closest packing is another name for face centred cubic.

Refer to the attached diagram of an fcc unit cell from hemantmore.

<h2>a) Volume of atoms in unit cell </h2>

a. Number of atoms in unit cell

In an fcc lattice, there are eight atoms at the eight corners of the cube and one at the centre of each face

∴ No. of atoms

= 8 corners x (1/8 atom)/(1 corner) + 6 faces x (½ atom/1 face)

= 1 atom + 3 atoms = 4 atoms

b. Volume of atoms

Let r be the radius of an atom. Then

Volume of 1 atom = (4/3)πr^3

Total volume of atoms = 4 atoms × [(4/3)πr^3]/(1 atom) = (16/3)πr^3

<h2>b) Volume of unit cell </h2>

The length of the diagonal AB is

AB = 4r

Let a be the edge length of the cube.

AB^2 = AC^^2 + BC^2

(4r)^2 = a^2 + a^2

16r^2= 2a^2

a^2 = 8r^2

a = rx8^½

V = a^3 = (rx8^½)^3 = 8r^3x8^½

<h2>c) Fraction of occupied space (packing efficiency, PE) </h2>

PE = Volume of atoms/Volume of cell = [(16/3)πr^3]/[ 8r^3x8^½]

= 2π/(3x8^½)

<h2>d) Fraction of empty space </h2>

Fraction of empty space = 1 - PE = 1 - 2π/(3x8^½) = 1 – 0.740 480

= 0.259 52

You might be interested in

Sodium sulfate is slowly added to a solution containing 0.0500 M Ca 2 + ( aq ) and 0.0390 M Ag + ( aq ) . What will be the conce

levacccp [35]

The given question is incomplete. The complete question is as follows.

Sodium sulfate is slowly added to a solution containing 0.0500 M $Ca^{2+}(aq)$ and 0.0390 M $Ag^{+}(aq)$ . What will be the concentration of $Ca^{2+}$ (aq) when $Ag_{2}SO_{4}(s)$ begins to precipitate? What percentage of the $Ca^{2+}(aq)$ can be separated from the Ag(aq) by selective precipitation?

Explanation:

The given reaction is as follows.

$Ag_{2}SO_{4} \rightleftharpoons 2Ag^{+} + SO^{2-}_{4}$

$[Ag^{+}]$ = 0.0390 M

When $Ag_{2}SO_{4}$ precipitates then expression for $K_{sp}$ will be as follows.

$K_{sp} = [Ag^{+}]^{2}[SO^{2-}_{4}]$

$1.20 \times 10^{-5} = (0.0390)^{2} \times [SO^{2-}_{4}]$

$[SO^{2-}_{4}]$ = 0.00788 M

Now, equation for dissociation of calcium sulfate is as follows.

$CaSO_{4} \rightleftharpoons Ca^{2+} + SO^{2-}_{4}$

$K_{sp} = [Ca^{2+}][SO^{2-}_{4}]$

$4.93 \times 10^{-5} = [Ca^{2+}] \times 0.00788$

$[Ca^{2+}]$ = 0.00625 M

Now, we will calculate the percentage of $Ca^{2+}$ remaining in the solution as follows.

$\frac{0.00625}{0.05} \times 100$

= 12.5%

And, the percentage of $Ca^{2+}$ that can be separated is as follows.

100 - 12.5

= 87.5%

Thus, we can conclude that 87.5% will be the concentration of $Ca^{2+}(aq)$ when $Ag_{2}SO_{4}(s)$ begins to precipitate.

4 0

3 years ago

Write the isotopic symbol for the following (show your work) a) An isotope of iodine whose atoms have 78 neutrons b) An isotope

morpeh [17]

Answer:

For a: The isotopic representation of iodine is $_{53}^{131}\textrm{I}$

For b: The isotopic representation of cesium is $_{55}^{137}\textrm{Cs}$

For c: The isotopic representation of strontium is $_{38}^{52}\textrm{Sr}$

Explanation:

The isotopic representation of an atom is: $_Z^A\textrm{X}$

where,

Z = Atomic number of the atom

A = Mass number of the atom

X = Symbol of the atom

For a:

We are given:

Number of neutrons = 78

Atomic number of iodine = 53 = Number of protons

Mass number = 53 + 78 = 131

Thus, the isotopic representation of iodine is $_{53}^{131}\textrm{I}$

For b:

We are given:

Number of neutrons = 82

Atomic number of cesium = 55 = Number of protons

Mass number = 55 + 82 = 137

Thus, the isotopic representation of cesium is $_{55}^{137}\textrm{Cs}$

For c:

We are given:

Number of neutrons = 52

Atomic number of strontium = 38 = Number of protons

Mass number = 38 + 52 = 90

Thus, the isotopic representation of strontium is $_{38}^{52}\textrm{Sr}$

3 0

3 years ago

When diluting an acid with water always remember to:.

Alex777 [14]

Measure how much water has gone in, so you know the concentration.

3 0

2 years ago

What is the heaviest element that is made in nature on the periodic table

ANTONII [103]

It would be uranium

5 0

3 years ago

Read 2 more answers

PLEASE HELP A HOMIIE

Allushta [10]

Answer:

Its the first one. The cells are arranged for structure.

Explanation:

Animal cells do not need to maintain a shape since out bodies do it for us. Plant cells need something for structure.

8 0

3 years ago