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).
(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
Or
(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 / 3πr3
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%
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.
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
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 CO2 pressure 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?
If NaCl is doped with 10-3mol % of SrCl2, what is the concentration of cation vacancies?
Give plausible explanation for each of the following:
(i) Cyclohexanone forms cyanohydrin in good yield but 2, 2, 6 trimethylcyclohexanone does not.
(ii) There are two -NH2 groups in semicarbazide. However, only one is involved in the formation of semicarbazones.
(iii) During the preparation of esters from a carboxylic acid and an alcohol in the presence of an acid catalyst, the water or the ester should be removed as soon as it is formed.
Give two examples to show the anomalous behaviour of fluorine.
Arrange the compounds of each set in order of reactivity towards SN2 displacement:
(i) 2-Bromo-2-methylbutane, 1-Bromopentane, 2-Bromopentane
(ii) 1-Bromo-3-methylbutane, 2-Bromo-2-methylbutane, 3-Bromo-2- methylbutane
(iii) 1-Bromobutane, 1-Bromo-2,2-dimethylpropane, 1-Bromo-2-methylbutane, 1-Bromo-3-methylbutane.
A reaction is first order in A and second order in B.
(i) Write the differential rate equation.
(ii) How is the rate affected on increasing the concentration of B three times?
(iii) How is the rate affected when the concentrations of both A and B are doubled?
What type of bonding helps in stabilising the ∝-helix structure of proteins?
The decomposition of dimethyl ether leads to the formation of CH4, H2and CO and the reaction rate is given by
Rate = k [CH3OCH3]3/2
The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e.,
Rate = k (PCH3OCH3)3/2
If the pressure is measured in bar andtime in minutes, then what are the units of rate and rate constants?
What is a biodegradable polymer? Give an example of a biodegradable aliphatic polyester.
Explain why propanol has higher boiling point than that of the hydrocarbon, butane?
How do you explain the absence of aldehyde group in the pentaacetate of D-glucose?
Which aerosols deplete ozone?