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The Solid State
Calculate the efficiency of packing in case of a metal crystal for ...

Calculate the efficiency of packing in c | Class 12 Chemistry Chapter The Solid State, The Solid State NCERT Solutions

Welcome to the NCERT Solutions for Class 12 Chemistry - Chapter The Solid State. This page offers a step-by-step solution to the specific question from Exercise 2, Question 10: . With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.

Question 10:

Calculate the efficiency of packing in case of a metal crystal for

(i) simple cubic

(ii) body-centred cubic

(iii) face-centred cubic (with the assumptions that atoms are touching each other).

Answer:

(i) Simple cubic:

Suppose the edge length of the unit cell = a

Radius of the sphere = r

Then,since the sphere are touching each other along the edge,therefore a = 2r

Now there are 8 spheres at the corners of the cube & each sphere at the corner is shared by 8 unit cells & the contribution per unit cell is 1/8 so that

Number of spheres per unit cell is 8 x 1/8 = 1

Volume of sphere =4/3πr³ & volume of cube = a³ = (2r)³ = 8r³

Now packing efficiency = (volume of one sphere / total volume of cubic unit cell) x 100

(4/3 πr³/ 8r³) x 100 = 52.4%

Therefore the volume occupied in simple cubic arrangement = 52.4%

(ii) Body centered cubic:

Let us suppose the edge leght = a & radius of each sphere = r then there are 8 spheres at the corners & 1 in the body of unit cell

Therefore number of spheres per unit cell = (8 x1/8) + 1 = 2

Now volume of unit cell = a³ = (4r / √3)³

and volume of a sphere = 4 / 3π^r3

Total volume of two spheres = 2 x 4/3πr³

Packing efficiency = (volume of two spheres in unit cell/total volume of unit cell ) x 100

= (2 x 4/3πr³ / (4r/√3)³ ) x 100 = 68%

Therefore volume occupied in bcc arrangement = 68%

(iii) Face centered:

let us suppose the edge length of the unit cell = a

Radius of each sphere = r

Now there are 8 spheres at the corner & 6 at the faces

Therefore number of spheres in unit cell = (8 x 1/8 + 6 x1/2) = 4

From the arrangement of fcc, we get a = 2√2r

Now volume of a unit cell = a³ = (2√2r)³ = 16√2r³

Total volume of 4 spheres = 4 x 4/3 πr³ = 16/3 πr³

Packing efficiency = (volume of 4 spheres in the unit cell/total volume of unit cell) x 100

= (16/3 πr³/16√2r³) x 100 = 74%

Therefore volume occupied in fcc = 74%

Other Questions of Chapter The Solid State

Ionic solids conduct electricity in molten state but not in solid state. Explain.

What type of solids are electrical conductors, malleable and ductile?

Ferric oxide crystallises in a hexagonal close-packed array of oxide ions with two out of every three octahedral holes occupied by ferric ions. Derive the formula of the ferric oxide.

If the radius of the octachedral void is r and radius of the atoms in close packing is R, derive relation between r and R.

Classify the following as amorphous or crystalline solids:
Polyurethane, naphthalene, benzoic acid, teflon, potassium nitrate, cellophane, polyvinyl chloride, fibre glass, copper.

Why do solids have a definite volume?

Why are solids rigid?

Explain how much portion of an atom located at

(i) corner and

(ii) body-centre

of a cubic unit cell is part of its neighbouring unit cell.

What type of stoichiometric defect is shown by:

(i) ZnS

(ii) AgBr

Classify each of the following as being either a p-type or an n-type semiconductor:

(i) Ge doped with In

(ii) B doped with Si.

Popular questions of class 12 Chemistry

How the following conversions can be carried out?

(i) Propene to propan-1-ol

(ii) Ethanol to but-1-yne

(iii) 1-Bromopropane to 2-bromopropane

(iv) Toluene to benzyl alcohol

(v) Benzene to 4-bromonitrobenzene

(vi) Benzyl alcohol to 2-phenylethanoic acid

(vii) Ethanol to propanenitrile

(viii) Aniline to chlorobenzene

(ix) 2-Chlorobutane to 3, 4-dimethylhexane

(x) 2-Methyl-1-propene to 2-chloro-2-methylpropane

(xi) Ethyl chloride to propanoic acid

(xii) But-1-ene to n-butyliodide

(xiii) 2-Chloropropane to 1-propanol

(xiv) Isopropyl alcohol to iodoform

(xv) Chlorobenzene to p-nitrophenol

(xvi) 2-Bromopropane to 1-bromopropane

(xvii) Chloroethane to butane

(xviii) Benzene to diphenyl

(xix) tert-Butyl bromide to isobutyl bromide

(xx) Aniline to phenylisocyanide

Give simple chemical tests to distinguish between the following pairs of compounds.

(i) Propanal and Propanone

(ii) Acetophenone and Benzophenone

(iii) Phenol and Benzoic acid

(iv) Benzoic acid and Ethyl benzoate

(v) Pentan-2-one and Pentan-3-one

(vi) Benzaldehyde and Acetophenone

(vii) Ethanal and Propanal

A 5% solution (by mass) of cane sugar in water has freezing point of 271 K. Calculate the freezing point of 5% glucose in water if freezing point of pure water is 273.15 K.

A solution of glucose in water is labelled as 10% w/w, what would be the molality and mole fraction of each component in the solution? If the density of solution is 1.2 g mL^-1, then what shall be the molarity of the solution?

Henry's law constant for CO₂ in water is 1.67 x 10⁸Pa at 298 K. Calculate the quantity of CO₂in 500 mL of soda water when packed under 2.5 atm CO₂pressure at 298 K.

Calculate the mass of a non-volatile solute (molar mass 40 g mol^-1) which should be dissolved in 114 g octane to reduce its vapour pressure to 80%.

The vapour pressure of pure liquids A and B are 450 and 700 mm Hg respectively, at 350 K. Find out the composition of the liquid mixture if total vapour pressure is 600 mm Hg. Also find the composition of the vapour phase.

Calculate the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride.

How many mL of 0.1 M HCl are required to react completely with 1 g mixture of Na₂CO₃ and NaHCO₃ containing equimolar amounts of both?

H₂S, a toxic gas with rotten egg like smell, is used for the qualitative analysis. If the solubility of H₂S in water at STP is 0.195 m, calculate Henry's law constant.

Recently Viewed Questions of Class 12 Chemistry

Henry's law constant for CO₂ in water is 1.67 x 10⁸Pa at 298 K. Calculate the quantity of CO₂in 500 mL of soda water when packed under 2.5 atm CO₂pressure at 298 K.

What are nucleic acids? Mention their two important functions.

What are the different oxidation states exhibited by the lanthanoids?

The reaction between A and B is first order with respect to A and zero order with respect to B. Fill in the blanks in the following table:

Experiment	A/ mol L^{- 1}	B/ mol L^{- 1}	Initial rate/mol L^{- 1} min^{- 1}
I	0.1	0.1	2.0 × 10^{- 2}
II	--	0.2	4.0 × 10^{- 2}
III	0.4	0.4	--
IV	--	0.2	2.0 × 10^{- 2}

Mention the conditions required to maximise the yield of ammonia.

Describe the oxidising action of potassium dichromate and write the ionicequations for its reaction with:

(i) iodide

(ii) iron

(II) solution and

(iii) H₂S

Write the structure of the major organic product in each of the following reactions:

How will you bring about the following conversions?

(i) Ethanol to but-1-yne

(ii) Ethane to bromoethene

(iii) Propene to 1-nitropropane

(iv) Toluene to benzyl alcohol

(v) Propene to propyne

(vi) Ethanol to ethyl fluoride

(vii) Bromomethane to propanone

(viii) But-1-ene to but-2-ene

(ix) 1-Chlorobutane to n-octane

(x) Benzene to biphenyl.

What is meant by hydroboration-oxidation reaction? Illustrate it with an example.

Write structures of the following compounds:

(i) 2-Chloro-3-methylpentane

(ii) 1-Chloro-4-ethylcyclohexane

(iii) 4-tert. Butyl-3-iodoheptane

(iv) 1,4-Dibromobut-2-ene

(v) 1-Bromo-4-sec. butyl-2-methylbenzene

Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about The Solid State.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

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