Calculate has hcp arrangement of carbon atoms and parallel plane are 3.35 angstrom apart. Determine the density of graphite: a. 2.46 g/cc. b. 0 .4 g/cc c. 1 g/cc d. 1.4 g/cc?

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Answer

Determining the Density of Graphite

HCP Arrangement of Carbon Atoms in Graphite

- Graphite is a crystalline form of carbon where the carbon atoms are arranged in a hexagonal close-packed (HCP) structure.
- In the HCP arrangement, each carbon atom is bonded to three neighboring carbon atoms, forming a network of hexagonal rings stacked on top of each other.
- The carbon atoms within each layer are arranged in a hexagonal lattice, and the layers are parallel to each other.

Distance Between Parallel Planes

- The distance between parallel planes in graphite can be determined from the HCP arrangement.
- In an HCP structure, the distance between parallel planes is given by the formula: d = a/(√3), where a is the lattice parameter.
- Since the carbon atoms in graphite are arranged in a hexagonal lattice, the lattice parameter a is equal to the distance between neighboring carbon atoms.
- Therefore, the distance between parallel planes in graphite is d = a/(√3).

Density Calculation

- The density of a material is defined as its mass per unit volume.
- To calculate the density of graphite, we need to know the mass and volume of a given sample.

Mass Calculation:

- The mass of the graphite sample can be determined by weighing it using a balance.

Volume Calculation:

- The volume of the graphite sample can be calculated using the formula: V = A * d, where A is the cross-sectional area and d is the distance between parallel planes.
- In graphite, the cross-sectional area is equal to the area of a hexagon, which can be calculated using the formula: A = (3√3 * a^2) / 2.
- Substituting the value of d = a/(√3) into the formula, we get: A = (3√3 * (d * √3)^2) / 2 = 3d^2√3/2.
- Therefore, the volume of the graphite sample is V = 3d^2√3/2 * d = (3√3/2) * d^3.

Density Calculation:

- The density of graphite can be calculated by dividing the mass of the sample by its volume: Density = mass / volume.

Determining the Correct Option

- To determine the correct option for the density of graphite, we need to compare the calculated density with the given options.
- Calculate the density using the mass and volume of the graphite sample.
- Compare the calculated density with the given options and choose the one that matches.
- Based on the calculated density, select the option that is closest to the calculated value.

Conclusion

- To determine the density of graphite, we need to calculate the mass and volume of a given sample.
- The volume can be calculated using the distance between parallel planes in the HCP arrangement of carbon atoms.
- Compare the calculated density with the given options and select the one that matches.

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