Chemistry: CUET Mock Test - 1

Unit cell is the smallest entity of a crystal lattice which, when repeated in space (3 dimensions) generates the entire crystal lattice. Lattice comprises of the unit cells which hold all the particles in a particular arrangement in 3 dimensions. Crystal is a piece of homogenous solid and Bravais indices are used to define planes in crystal lattices in the hexagonal system.

Explanation: In primitive unit cubic cell, each atom at the corner is shared between 8 adjacent unit cells. Thus, only 1/8th of an atom (or ion or molecule) belongs to a particular unit cell.

Only short range order is a feature of amorphous solids. Crystalline solids exhibit both short and long range order. Crystalline solids are formed by repetitive arrangement of unit cells.

An ideal solution is the solution in which each component obeys Raoult’s law under all conditions of temperature and concentrations. An ideal solution will satisfy the following conditions:
I. There will be no change in volume on mixing the components, i.e., ΔV_mixing = 0.
II. There will be no change in enthalpy (i.e., no heat is evolved or absorbed) when the two components are mixed, i.e., ΔH_mixing = 0.

According to classification of unit cells, a primitive unit cell is one which has all constituent particles located at its corners. BCC has one particle present at the center including the corners. FCC has an individual cell shared between the faces of adjacent cells. End centered cells have cells present at centers of two opposite faces.

In primitive cubic unit cell, atoms are present only at the corner of the cell. Thus, in actual, only 1/8th of an atom (or ion or molecule) belongs to a particular unit cell. Hence, the total number of atoms in primitive cubic unit cell 

Homogeneity refers to uniformity in composition, which is a characteristic property of crystalline solids. Isotropy is when the values of physical properties do not change with direction throughout the body of the solid. Crystalline solids are anisotropic because the composition of the solid changes with direction, hence the physical properties also change with direction.

An ideal solution may be defined as the solution in which no volume change and no enthalpy change take place on mixing the solute and the solvent in any proportion. Ethyl alcohol + Water is a Non-Ideal solution.

Coordination number of a unit cell is defined as the number of atoms/ions that surround the central atom/ion. In the case of BCC, the central particle is surrounded by 8 particles hence, 8.

In body-centered cubic unit cell, one atom is present at each of the corners and one atom at its body center.

• 
• 1 body-centered atom

Thus, the total number of atoms in body-centered cubic unit cell: 1+1=2 atoms.

When there is a fault in the arrangement of a constituent particle such as an atom, ion or molecule, and the fault exists at a point in the lattice structure, it is called as a point defect.

Quartz glass does not have a perfectly ordered structure, hence it is classified as an amorphous solid. The rest are crystalline solids due to ordered structures.

Simple cubic lattice results from 3D close packing from 2D square-packed layers. When one 2D layer is placed on top of the other, the corresponding spheres of the second layer are exactly on top of the first one. Since both have the same, exact arrangement it is AAA type.

In face-centered cubic unit cell, atoms are present at each of the corners and at the centre of the face of the cube.

Thus, the total number of atoms in face-centered cubic unit cell: 1+3=4 atoms.

A vacancy defect is when an atom, ion or molecule is absent from its position in the lattice. When this occurs for ionic solids, it is called a Schottky defect. Cations and anions are found to be absent in stoichiometric proportion so that the electrical neutrality of the crystal is maintained.

Non-Ideal solutions do not obey Raoult’s law. For Non-Ideal solutions, ΔV_mixing ≠ 0, ΔH_mixing ≠ 0. Non-ideal solutions form azeotropes or constant boiling mixtures, i.e., they have the same concentration in the vapour phase and the liquid phase.

For a crystal lattice, if there are N close-packed spheres the number of tetrahedral voids are 2N and number octahedral voids are N. For N=6, number of tetrahedral voids = 2 × 6 = 12.

There is a considerable size difference between Ag cation and Cl anion. Hence a Frenkel defect is more likely to occur than a Schottky defect.

Chlorobenzene + Bromobenzene is an example of an ideal solution. Chloroform + Benzene and Acetone + Aniline are examples of non-ideal solutions but they show negative deviations. Acetone + Carbon disulphide is an example of a non-ideal solution showing positive deviation.

Crystalline solids possess anisotropic nature within their structure. Anisotropy is the directional dependence of a property. Meaning, a property within the crystal structure will have different values when measured in different directions. Snowflake is a crystalline solid whereas the rest are amorphous solids.

An impurity defect occurs when a regular ion is replaced by some other type of ion, e.g. Na⁺ is replaced by K⁺. If the replacement occurs in the place of the regular cation, it is called a substitution impurity defect. If the replacement occurs in an interstitial position, it is called an interstitial impurity defect.

Crystalline solids have a perfectly ordered structure which collapses immediately at a specific temperature. Amorphous solids melt over a range of temperatures, not one specific value.

The given figure represents an orthorhombic unit cell. Experimentally, it is determined that for orthorhombic unit cells a ≠ b ≠ c. All sides are unequal. It results from extension of cube along two pairs of orthogonal sides by two distinct factors.

Stainless steel is an interstitial alloy. Carbon atoms are introduced into interstitial spaces of iron lattice as an impurity. Further alloying sees the introduction of nickel, chromium in the interstitial spaces.

The description is of a BCC. For BCC, each atom at the corner is shared by 8 unit cells. One atom at the center wholly belongs to the corresponding unit cell.
Therefore, total number of atoms of A present 
Total number of atoms of B present=1
Therefore, A:B=1:1 implying the formula of the compound is AB.

HNO₃ + Water, HCl + Water and Acetic acid + Pyridine are non-ideal solutions showing negative deviations. Carbon tetrachloride + Toluene is an example of non-ideal solution showing positive deviation.

The number of tetrahedral voids form is equal to twice the number of atoms of element X. Number of atoms of Y is 3/4th the number of tetrahedral voids i.e. 3/2 times the number of atoms of X. Therefore, the ratio of numbers of atoms of X and Y are 2:3, hence X₂Y₃.

The interactions between the components of a non-ideal solution showing negative deviation are greater than the pure components. The change in volume and enthalpy after mixing is negative, i.e., ΔV_mixing = -ve, ΔH_mixing = -ve.

Since particles are assumed to be spheres and volume of one sphere is 4/3 πr³, total volume of all particles in  since a BCC has 2 particles per cell.

H₂O + C₂H₅OH forms an azeotrope with a boiling point of 351.15 K. CHCl₃ + C₂H₅ OH forms an azeotrope with a boiling point of 332.3 K. HCl + H₂O forms an azeotrope with a boiling point of 383 K. Benzene + Toluene is an ideal solution and hence does not form an azeotrope.

Atomic mass of Al = 27g/mole (contains 6.022 x 10²³ Al atoms)
Since it exhibits FCC, there are 4 Al atoms/unit cell.
If 27g Al contains 6.022 x 10²³ Al atoms then 54g Al contains 1.2044 x 10²⁴atoms.
Thus, if 1 unit cell contains 4 Al atoms then number of unit cells containing 1.2044 x 10²⁴ atoms=(1.2044 x 10²⁴ x 1)/4 = 3.011 × 10²³ unit cells.

Azeotropes have the same concentration in the vapour phase and the liquid phase. In case of minimum boiling azeotropes, the boiling point of the azeotrope is lesser than the boiling point of either of the pure components. In case of maximum boiling azeotropes, the boiling point of the azeotrope is higher than the boiling point of either of the pure components.

For body-centered unit cells, the relation between radius of a particle ‘r’ and edge length of unit cell ‘a’ is given as  is the radius of the metal atom.

The Gibbs free energy of a system at any moment in time is defined as the enthalpy of the system minus the product of the temperature times the entropy of the system. For ideal solutions, the value of the Gibbs Free energy is always negative as mixing of ideal solutions is a spontaneous process.

A unit cell is characterized by six parameters i.e. the three common edge lengths a, b, c and three angles between the edges that are α, β, γ. These are referred to as inter-axial lengths and angles, respectively. The position of a unit cell can be determined by fractional coordinates along the cell edges.

Observed pressure = 76 torr
According to Raoult’s law,
p_A = x_A x p_A⁰ = 5/15 x 64 = 21.33 torr
p_B = x_B x p_B⁰ = 10/15 x 76 = 50.67 torr
Therefore, pressure expected by Raoult’s law = 21.33 + 50.67 = 72 torr.
Thus, observed pressure (70 torr) is less than the expected value. Hence, the solution shows negative deviation.

Edge length (a) = 500 pm = 500 x 10^-12 m
Atomic mass (M) = 110 g/mole = 110 x 10^-3 kg/mole
Avogadro’s number (NA) = 6.022 x 10²³/mole
z = 4 atoms/cell
The density, d of a metal is given as 

Each point of the particle’s position is referred to as ‘lattice point’ or ‘lattice site’. Every lattice point represents one constituent particle which may be an atom, ion or molecule.

A colligative property is identified by the fact that it has no dependence on the nature of the particles of solute. However, in the case of viscosity it really depends on the solute that is added to the solvent. Thus, the change in viscosity after addition of a non-volatile solute cannot be considered to be a colligative property.

Given, P⁰water = 31 kPa
Concentration of solution, c = 2 molal = 2 moles of glucose/kg of water
From law of relative lowering of vapor pressure, ΔP/P⁰ = X₂, where X₂ is the mole fraction of glucose in the solution.
Mass of water = 1 kg = 1000 g
Molecular weight of water = 18 g/mole
Moles of water = 1000/18 = 55.556 moles
X₂ = 2/(2 + 55.556) = 0.035
ΔP = 31 kPa x 0.035 = 1.085 kPa
Final pressure = 31 kPa – 1.085 kPa = 29.915 kPa.