Core Syllabus Module

States of Matter

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Generate random timed arrays filtered strictly by States of Matter weightage mappings.

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Target Advanced

JEE Advanced 2014

LEVELJEE Advanced

Comprehension Passage

X and Y are two volatile liquids with molar weights of

10 g mol^{- 1}

and

40 g mol^{- 1}

respectively. Two cotton plugs, one soaked in X and the other soaked in Y, are simultaneously placed at the ends of a tube of length

L = 24 cm

, as shown in the figure. The tube is filled with an inert gas at

1 atmosphere

pressure and a temperature of

300 K

. Vapours of X and Y react to form a product which is first observed at a distance

d cm

from the plug soaked in X. Take X and Y to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.

Question 1:

The value of $d$ in cm (shown in the figure), as estimated from Graham's law, is - [JEE(Advanced) 2014]

The experimetnal value of $d$ is found to be smaller than the estimate obtained using Graham's law. This is due to - [JEE(Advanced) 2014]

(A)

Larger mean free path for X as compared to that of Y

(B)

Larger mean free path for Y as compared to that of X

(C)

Increased collision frequency of Y with the inert gas as compared to that of X with the inert gas

(D)

Increased collision frequency of X with the inert gas as compared to that of Y with the inert gas

JEE Advanced 2021

LEVELJEE Advanced

For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity) , the packing fraction is approximately (packing fraction = $\frac{Packing efficiency}{100}$ )

Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to

Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?

The cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In the first cylinder, the masses of He and Ar are $m_{1}$ and $m_{2}$ , respectively. In the second cylinder, the masses of He and Ar are $m_{2}$ and $m_{1}$ , respectively the molar mass of Ar is 10 times the molar mass of He. The external pressure applied by the piston on the first cylinder needs to be 5 times that on the second cylinder so that the volume of the gas mixtures in both the cylinders are equal at the same temperature. Assuming He and Ar behaves like ideal gases, the value of $(m_{1} / m_{2})$ is _____.

JEE Advanced 2016

LEVELJEE Advanced

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is

JEE Advanced 2023

LEVELJEE Advanced

Atoms of metals x, y, and z form face-centred cubic (fcc) unit cell of edge length $L_{x}$ , body-centred cubic (bcc) unit cell of edge length $L_{y}$ , and simple cubic unit cell of edge length $L_{z}$ , respectively. If $r_{z} = \frac{3}{2} r_{y}$ ; $r_{y} = \frac{8}{3} r_{x}$ ; $M_{z} = \frac{3}{2} M_{y}$ and $M_{z} = 3 M_{x}$ , then the correct statement (s) is (are) [Given : $M_{x}$ , $M_{y}$ , and $M_{z}$ are molar masses of metals x, y, and z, respectively. $r_{x}$ , $r_{y}$ , and $r_{z}$ are atomic radii of metals x, y, and z, respectively.]

* Multiple Correct Options

(A)

Packing efficiency of unit cell of x > Packing efficiency of unit cell of y > Packing efficiency of unit cell of z

(B)

L_{y} > L_{z}

(C)

L_{x} > L_{y}

(D)

Density of x > Density of y

JEE Advanced 2018

LEVELJEE Advanced

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in $m^{3}$ ) of the compartment A after the system attains equilibrium is_______.

JEE Main 2020

LEVELJEE Advanced

A crystal is made up of metal ions $M_{1}$ and $M_{2}$ and oxide ions. Oxide ions form a ccp lattice structure. The cation $M_{1}$ occupies $50%$ of octahedral voids and the cation $M_{2}$ occupies $12.5%$ of tetrahedral voids of oxide lattice. The oxidation numbers of $M_{1}$ and $M_{2}$ are, respectively

(A)

+ 2, + 4

(B)

+ 1, + 3

(C)

+ 3, + 1

(D)

+ 4, + 2

JEE Main 2021

LEVELJEE Advanced

KBr is doped with $1 0^{- 5}$ mole per cent of $SrBr_{2}$ . The number of cationic vacancies in $1 g$ of KBr crystal is ......... $1 0^{14}$ (Round off to the nearest integer). [Atomic mass : $K = 39.1 u$ , $Br = 79.9 u$ , $N_{A} = 6.023 \times 1 0^{23}$ ]

JEE Main 2020

LEVELJEE Advanced

An element with molar mass $2.7 \times 1 0^{- 2} kg mol^{- 1}$ forms a cubic unit cell with edge length $405 pm$ . If its density is $2.7 \times 1 0^{3} kg m^{- 3}$ , the radius of the element is approximately ............ $\times 1 0^{- 12} m$ (to the nearest integer).

JEE Main 2021

LEVELJEE Advanced

Two flasks I and II shown below are connected by a valve of negligible volume. When the valve is opened, the final pressure of the system in bar is $x \times 1 0^{- 2}$ . The value of $x$ is ............. . (Integer answer) [Assume, Ideal gas, $1 bar = 1 0^{5} Pa$ , molar mass of $N_{2} = 28.0 g mol^{- 1}$ ; $R = 8.31 J mol^{- 1} K^{- 1}$ ]

JEE Main 2021

LEVELJEE Advanced

Ga (atomic mass 70 u) crystallises in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is ...... $\times 1 0^{21}$ . (Round off to the nearest integer).

JEE Main 2015

LEVELJEE Advanced

The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is

(A)

ion-ion interaction

(B)

ion-dipole interaction

The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is (Edge length is represented by 'a')

(A)

0.134 a

(B)

0.027 a

(C)

0.047 a

(D)

0.067 a

JEE Advanced 2025

LEVELJEE Main

The correct statements (s) about intermolecular forces is(are)

* Multiple Correct Options

(A)

The potential energy between two point charges approaches zero more rapidly than the potential energy between a point dipole and a point charge as the distance between them approaches infinity.

(B)

The average potential energy of two rotating polar molecules that are separated by a distance

r

has

1/ r^{3}

dependence.

(C)

The dipole-induced dipole average interaction energy is independent of temperature.

(D)

Nonpolar molecules attract one another even though neither has a permanent dipole moment.

JEE Advanced 2025

LEVELJEE Main

Molar volume ( $V_{m}$ ) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_{m}$ as the variable. The ratio (in $mol dm^{- 3}$ ) of the coefficient of $V_{m}^{2}$ to the coefficient of $V_{m}$ for a gas having van der Waals constants $a = 6.0 dm^{6} atm mol^{- 2}$ and $b = 0.060 dm^{3} mol^{- 1}$ at $300 K$ and $300 atm$ is _______. Use: Universal gas constant (R) = $0.082 dm^{3} atm mol^{- 1} K^{- 1}$

LEVELJEE Main

For one mole of a van der Waals gas when b = 0 and T=300K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm. liter² mol⁻²) is

A closed vessel with rigid walls contains 1 mol of $_{92}^{238} U$ and 1 mol of air at 298 K. Considering complete decay of $_{92}^{238} U$ to $_{82}^{206} Pb$ , the ratio of the final pressure to the initial pressure of the system at 298 K is -

JEE Advanced 2015

LEVELJEE Main

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with $m$ fraction of octahedral holes occupied by aluminium ions and $n$ fraction of tetrahedral holes occupied by magnesium ions $m$ and $n$ respectively, are -

(A)

\frac{1}{2}, \frac{1}{8}

(B)

1, \frac{1}{4}

(C)

\frac{1}{2}, \frac{1}{2}

(D)

\frac{1}{4}, \frac{1}{8}

Micro-Topic Strategy Matrix

Gaseous State

Liquid State

Solid State

Chapter Elite-20 Challenge Zone

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of d in cm (shown in the figure), as estimated from Graham's law, is - [JEE(Advanced) 2014]

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The experimetnal value of d is found to be smaller than the estimate obtained using Graham's law. This is due to - [JEE(Advanced) 2014]

Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to

Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Ga (atomic mass 70 u) crystallises in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is ...... ×1021. (Round off to the nearest integer).

The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is

The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is (Edge length is represented by 'a')

The correct statements (s) about intermolecular forces is(are)

For one mole of a van der Waals gas when b = 0 and T=300K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm. liter² mol⁻²) is

The value of $d$ in cm (shown in the figure), as estimated from Graham's law, is - [JEE(Advanced) 2014]

The experimetnal value of $d$ is found to be smaller than the estimate obtained using Graham's law. This is due to - [JEE(Advanced) 2014]

Ga (atomic mass 70 u) crystallises in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is ...... $\times 1 0^{21}$ . (Round off to the nearest integer).