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ExtremeBDS
2 months ago
5

The unit cell for cr2o3 has hexagonal symmetry with lattice parameters a = 0.4961 nm and c = 1.360 nm. If the density of this ma

terial is 5.22 g/cm3, calculate its atomic packing factor. The atomic weights of cr
Chemistry
2 answers:
alisha [2.9K]2 months ago
8 0

Answer:

The value of the atomic packing factor is 0.76

Explanation:

The area is

A = 6r²√3 = 6(a/2)²√3 = 1.5a²√3

For HCP, it holds that:

a = 2r

Substituting

A = 1.5 * (4.961x10⁻⁸)²√3 = 6.39x10⁻¹⁵ cm²

The volume of the cell can be computed as

V = A*c = 6.39x10⁻¹⁵ * 1.36x10⁻⁷ = 8.7x10⁻²² cm³

For n results in

n = (e * N * V)/(∑Ac + ∑An) = (5.22 * 6.022x10²³ * 8.7x10⁻²²)/(2 * 52 + (3 * 16) = 18 formula unit/unit cell

There are 18 units of Cr₂O₃ or equivalently 36 ions of Cr₂O₃. The overall volume computes as

V = 36 * (4π/3) * (rCr³) + 54 * (4π/3) * (rO³) = 36 * (4π/3) * (6.2x10⁻⁹)³ + 54 * (4π/3) * (1.4x10⁻⁸)³ = 6.57x10⁻²² cm³

The atomic packing factor becomes:

APF = 6.57x10⁻²²/8.7x10⁻²² = 0.76

KiRa [2.9K]2 months ago
6 0

To determine the packing factor, begin by calculating the area and volume of the unit cell.

The area is found using:

A=6R^{2}\sqrt{3}

In this case, R represents the radius and is connected to a as shown:

R=\frac{a}{2}

Substituting the value into the area formula,[ [TAG_14]]

A=6(\frac{a}{2})^{2}\sqrt{3}=1.5a^{2}\sqrt{3}

The value of a is 0.4961 nm

As, 1 nm=10^{-7}cm

Therefore, 0.4961 nm=4.961\times 10^{-8} cm

Substituting the value,[ [TAG_27]]

Area=1.5(4.961\times 10^{-8}cm)^{2}\sqrt{3}=6.39\times 10^{-15}cm^{2}

Next, the volume can be calculated by the following method:

V=Area\times c

The value of c is 1.360 nm or 1.360\times 10^{-7} cm

Inserting the value,[ [TAG_40]]

V=(6.39\times 10^{-15}cm^{2})\times (1.360\times 10^{-7} cm)=8.7\times 10^{-22}cm^{3}

Now, to determine the number of atoms in the unit cell, the following equation can be employed:

n=\frac{\rho N_{A}V_{c}}{A}

In this context, A represents the atomic mass of Cr_{2}O_{3} which is 151.99 g/mol.

Inserting all the necessary values,[ [TAG_53]]

n=\frac{(5.22 g/cm^{3})(6.023\times 10^{23} mol^{-1})(8.7\times 10^{-22}cm^{3})}{(151.99 g/mol)}\approx 18

Consequently, there will be 18 Cr_{2}O_{3} units within 1 unit cell.

Given, there are 2 chromium atoms and 3 oxygen atoms, thus, the total units for chromium and oxygen will be 2×18=36 and 3×18=54 respectively.

The atomic radii for Cr^{3+} and O^{2-} measure 62 pm and 140 pm respectively.

Transforming them into centimeters:

1 pm=10^{-10}cm

Therefore,

r_{Cr^{3+}}=6.2\times 10^{-9}cm

and,

r_{O^{2-}}=1.4\times 10^{-8}cm

The total volume of the sphere will be the combined volume of all cations and anions, thus,

V_{S}=V_{Cr^{3+}}+V_{O^{2-}}

Since, the volume of a sphere is V=\frac{4}{3}\pi r^{3},

V_{S}=36\left ( \frac{4}{3}\pi (r_{Cr^{3+})^{3}} \right )+54\left ( \frac{4}{3}\pi (r_{O^{2-})^{3}} \right )

Inputting the respective values,[ [TAG_93]]

V_{S}=36\left ( \frac{4}{3}(3.14) (6.2\times 10^{-9} cm)^{3}} \right )+54\left ( \frac{4}{3}(3.14) (1.4\times 10^{-8} cm)^{3}} \right )=6.6\times 10^{-22}\times 10^{-8}cm^{3}

The atomic packing factor reflects the ratio of the volume of spheres to the volume of the crystal, so,[ [TAG_98]]

packing factor=\frac{V_{S}}{V_{C}}=\frac{6.6\times 10^{-22}cm^{3}}{8.7\times 10^{-22}cm^{3}}=0.758

Thus, the atomic packing factor equals 0.758.

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Response:

1. 16.54 grams.

2. 6.64 grams.

Clarification:

Greetings,

In this situation, the chemical reaction taking place is:

A+B\rightarrow C

Thus, based on the provided data, the theoretical yield of C can be determined as:

m_C^{theoretical}=\frac{12.9g}{0.78}=16.54g

Additionally, taking into account the principle of conservation of mass, the mass prior to the reaction is equal to the mass following the reaction, hence, the mass of B that was utilized amounts to:

m_B=m_C-m_A=16.54g-10.0g=6.64g

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6 0
2 months ago
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Answer: KOCH_2CH_3, CH_3CH_2COONa, NaOH are all ionic compounds.

Explanation:

Ionic compounds form when one atom transfers its valence electrons to another atom, resulting in partial opposite charges on the participating atoms, which creates a strong attractive force between them.

An ionic bond is typically established between a metal and a non-metal.

For instance, KOCH_2CH_3, CH_3CH_2COONa, NaOH are all ionic compounds.

Conversely, a covalent compound arises through the sharing of electrons among the atoms involved, where generally a non-metal bonds with the same or another non-metal.

For example, POCl_{3}, SOCl_{2} etc are all covalent compounds.

Therefore, we can affirm that KOCH_2CH_3, [tex]CH_3CH_2COONa, NaOH are indeed ionic compounds.

4 0
3 months ago
At the boiling point, the density of the liquid is 809 g/l and that of the gas is 4.566 g/l. how many liters of liquid nitrogen
KiRa [2933]

Result: 1.68 L of liquid nitrogen is generated during the gas liquefaction process.

Clarification:

This process involves transforming gaseous nitrogen into its liquid form.

The two states possess distinct densities, thus occupying varying volumes; however, the mass remains constant.

Step 1: Calculate the mass of nitrogen gas

Let’s determine the mass of nitrogen gas associated with 297 L.

The density formula is:

Density = \frac{Mass}{Volume}

With a density of nitrogen gas at 4.566 g/L and a volume of 297 L, we can compute the mass of nitrogen gas as follows:

Using these values yields:

Mass = Density \times Volume

Mass = \frac{4.566g}{L} \times 297L

Mass = 1356g

The mass of nitrogen gas calculates to be 1356 g.

Step 2: Derive the volume of liquid nitrogen from the mass obtained

The mass for liquid nitrogen remains the same.

With the density of liquid nitrogen at 809 g/L, we can substitute this into our formula to find the volume of liquid.

Volume = \frac{Mass}{Density}

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Therefore, the volume of liquid nitrogen is 1.68 L.


6 0
3 months ago
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Tems11 [2777]

Response:

Ethanol serves as a reducing agent.(C_2H_5OH)

The lowest integer coefficient for MnO_4^- in the balanced equation is 4

Clarification:

A redox reaction, or oxidation-reduction reaction, is defined as one in which oxidation and reduction processes occur simultaneously.

Oxidation is the process whereby a substance loses electrons, resulting in an increase in oxidation state. In contrast, reduction entails a substance gaining electrons, leading to a decrease in oxidation state.

Reducing agents enable other substances to undergo reduction while becoming oxidized themselves.

Conversely, oxidizing agents facilitate other substances' oxidation while being reduced in the process.

For the chemical reaction in question, the half-reaction would be:

Oxidation:

Reduction:

To balance the oxygen atoms on both sides

C_2H_5OH(aq)+MnO_4^-(aq)\rightarrow CH_3COOH(aq)+Mn^{2+}(aq)

For oxidation:

For reduction:

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MnO_4^-\rightarrow Mn^{2+}Then balance the hydrogen atoms on both sides.

  • For oxidation:
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C_2H_6O+H_2O\rightarrow C_2H_4O_2+4H^++4e^-

MnO_4^-+8H^++5e^-\rightarrow Mn^{2+}+4H_2O

In this redox process, ethanol acts as the reducing agent while the permanganate ion serves as the oxidizing agent.

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2 months ago
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