1

### JEE Advanced 2021 Paper 1 Online

MCQ (More than One Correct Answer)
The correct statement(s) related to colloids is (are)
A
The process of precipitating colloidal sol by an electrolyte is called peptization.
B
Colloidal solution freezes at higher temperature than the true solution at the same concentration.
C
Surfactants form micelle above critical micelle concentration (CMC). CMC depends on temperature.
D
Micelles are macromolecular colloids.

## Explanation

Statements (b) and (c) are correct whereas statements (a) and (d) are incorrect.

(a) Process of precipitating colloidal sol is known as coagulation.

(b) Concentration of colloidal solutions is small due to large molar mass and thus, their colligative properties are very small compared to true solutions. Hence, these solution freezes at higher temperature.

(c) Micelles are formed at the critical micelle concentration (CMC) which depends to temperature.

(d) Micelles and macromolecular colloids are two different types of colloid.

2

### JEE Advanced 2020 Paper 1 Offline

MCQ (More than One Correct Answer)
The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

A
The empirical formula of the compound is MX.
B
The cation M and anion X have different coordination geometries.
C
The ratio of M$$-$$X bond length of the cubic unit cell edge length is 0.866.
D
The ratio of the ionic radii of cation M to anion X is 0.414.

## Explanation

(a) The empirical formula of the compound :

Contribution of M and X :

$${M_{\left( {2 \times {1 \over 2}} \right)}}{X_{\left( {4 \times {1 \over 4}} \right)}} \Rightarrow MX$$

(b) Coordination number of both M and X is 8.

(c) Distance between M and X

$$= \sqrt {{{{a^2}} \over 4} + {{{a^2}} \over 2}} = \sqrt {{3 \over 4}} a = {{\sqrt 3 } \over 2}a$$

$$\Rightarrow$$ 0.866 a

(d) $${r_M}\,:\,{r_X} = (\sqrt 3 - 1)\,:\,1 \Rightarrow 0.732:1$$, thus statement (d) is incorrect.
3

### JEE Advanced 2017 Paper 2 Offline

MCQ (More than One Correct Answer)
The correct statement(s) about surface properties is (are)
A
Adsorption is accompanied by decrease in ethalpy and decrease in entropy of the system
B
The critical temperatures of ethane and nitrogen are $$563$$ $$K$$ and $$126$$ $$K,$$ respectively. The adsorption of ethane will be more than that of nitrogen on same amount of activated charcoal at a given temperature
C
Cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is dispersion medium
D
Brownian motion of colloidal particles does not depend on the size of the particles but depends on viscosity of the solution

## Explanation

Option (A) : Correct. Adsorption is a surface phenomenon in which the concentration of the adsorbate increases only on the surface. It is always accompanied by a decrease in the entropy ($$\Delta$$S). Since adsorption is an exothermic process, the enthalpy change ($$\Delta$$H) of the system is also negative.

Option (B) : Correct. Easily liquefiable gases, that is, gases with high critical temperatures, are more readily adsorbed because van der Waals forces are stronger near the critical temperature. Thus, the adsorption of ethane will be more than that of nitrogen.

Option (C) : Cloud is an aerosol in which liquid is dispersed phase and gas is dispersion medium. Whereas, emulsion is liquid in liquid colloidal system.

Option (D) : Incorrect. Brownian movement varies with the size of the particles and viscosity of the solution. Smaller particles with lower viscosity show faster movement.

4

### JEE Advanced 2016 Paper 2 Offline

MCQ (More than One Correct Answer)
The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are) :
A
The number of the nearest neighbours of an atom present in the topmost layer is 12
B
The efficiency of an atom packing is 74%
C
The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively
D
The unit cell edge length is $$2 \sqrt 2$$ times the radius of the atom

## Explanation

Coordination number cannot be 12, for any atom in the topmost layer, as there is no layer above it. Thus, each atom is in contact with six atoms in the same layer and three atoms from the layer below it.

For cubic close packing, we have

Packing fraction = $${{Volume\,of\,four\,spheres\,in\,the\,unit\,cell} \over {Total\,volume\,of\,the\,unit\,cell}}$$

$$= 4 \times {{(4/3)\pi {r^3}} \over {16\sqrt 2 {r^3}}} = {\pi \over {3\sqrt 2 }} = 0.74 = 74\%$$

In fcc unit cell, the effective number of atoms is

One atom at each corner = 8 corner atoms $$\times {1 \over 8} = 1$$

Atoms at each of the six face centres :

6 face centered atoms $$\times {1 \over 2} = 3$$.

Number of octahedral voids = 4.

Number of tetrahedral voids = 8.

Therefore, per atom, there is one octahedral void and two tetrahedral voids.

In fcc (or ccp), the unit edge length is given by

$$\sqrt 2 a = 4r \Rightarrow a = {{4r} \over {\sqrt 2 }} = 2\sqrt 2 r$$

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