Analysis shows that a metal oxide has the empirical formula M_0.98 O_1.00. Calculate the percentage of M²⁺ and M³⁺ ions in this crystal.

Or

In an ionic compound the anion (N) form cubic close type of packing. While the cation (M⁺) ions occupy one third of the tetrahedal voids. Deduce the empirical formula of the compound and the coordination number of (M) ions.

Solution

Solution:

M_0.98 O_1.00 is non-stoichiometric compound and is a mixture of M²⁺ and M³⁺ ions.
Let x atoms of M³⁺ are present in the compound. This means that x M²⁺ have been replaced by M³⁺ ions.
∴ Number of M²⁺ ions = 0.96 – x.
For electrical neutrality, positive charge on compound

= negative charge on compound.
∴ 2(0.96 – x) + 3x = 2
1.92 – 2x + 3x = 2
or x = 2 – 1.92 = 0.08

∴ $% of M^{3 +} ions = \frac{0.08}{0.96} \times 100 = 8.33 %$

Thus, M²⁺ is 92% and M³⁺ is 8% in given sample having formula, M_0.96 O_1.00.

Or

The number of tetrahedral voids formed is equal

to twice the number of atoms of element N and only $\frac{1}{3} rd$ of these are occupied by the element M. Hence the ratio of number of atoms of M and is $2 \times (\frac{1}{3}) : 1 or 2 : 3 .$ So, the formula of the compound is M₂N₃.

Some More Questions From The Solid State Chapter

Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show clevage property?

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The Solid State

Some More Questions From The Solid State Chapter

Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show clevage property?

Classify the following solids in different categories based on the nature of intermolecular forces operating in them:
Potassium sulphate, tin, benzene, urea, ammonia, water, zinc
sulphate, graphite, rubidium, argon, silicon carbide.

Solid A is a very hard, electrical insulator in solid as well as in molten state and melts at extremely high temperature. What type of solid is it?

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Name the parameters that characterize a unit cell.

Distinguish between Hexagonal and monoclinic unit cells.

Distinguish between Face-centred and end-centred unit cells.

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

The Solid State

Some More Questions From The Solid State Chapter

Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show clevage property?

Classify the following solids in different categories based on the nature of intermolecular forces operating in them: Potassium sulphate, tin, benzene, urea, ammonia, water, zinc sulphate, graphite, rubidium, argon, silicon carbide.

Solid A is a very hard, electrical insulator in solid as well as in molten state and melts at extremely high temperature. What type of solid is it?

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

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

Give the significance of a 'lattice point'.

Name the parameters that characterize a unit cell.

Distinguish between Hexagonal and monoclinic unit cells.

Distinguish between Face-centred and end-centred unit cells.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Classify the following solids in different categories based on the nature of intermolecular forces operating in them:
Potassium sulphate, tin, benzene, urea, ammonia, water, zinc
sulphate, graphite, rubidium, argon, silicon carbide.