Question:
A solid having density of $9 \times 10^3 \; kg \; m^{-3}$ forms face centred cubic crystals of edge length $200 \sqrt{2}$ pm. What is the molar mass of the solid ?
[Avogadro constant $\simeq 6 \times 10^{23} \, mol^{-1}, \pi \simeq 3]$
A solid having density of $9 \times 10^3 \; kg \; m^{-3}$ forms face centred cubic crystals of edge length $200 \sqrt{2}$ pm. What is the molar mass of the solid ?
[Avogadro constant $\simeq 6 \times 10^{23} \, mol^{-1}, \pi \simeq 3]$
Updated On: Aug 17, 2024
- ${0.0216 \; kg \; mol^{-1}}$
- ${0.0305 \; kg \; mol^{-1}}$
- ${0.4320\; kg \; mol^{-1}}$
- ${0.0432\; kg \; mol^{-1}}$
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The Correct Option is B
Solution and Explanation
Formula for density,
Density, $d =\frac{ Z \times M }{ a ^{3} \times N _{ A }}$
where,
$d =$ density of the unit cell
$M =$ Molar mass of the molecule
$a^{3}=$ volume of the unit cell
$N _{ A }=$ Avogadro number
Here, for FCC unit cell, $Z = 4$
Subsituting the values we get,
$9 \times 10^{3}=\frac{4 \times M }{\left(200 \sqrt{2} \times 10^{-12}\right)^{3} \times 6.0 \times 10^{23}}$
$\Rightarrow M =0.0305 \,kg .mol ^{-1}$
Density, $d =\frac{ Z \times M }{ a ^{3} \times N _{ A }}$
where,
$d =$ density of the unit cell
$M =$ Molar mass of the molecule
$a^{3}=$ volume of the unit cell
$N _{ A }=$ Avogadro number
Here, for FCC unit cell, $Z = 4$
Subsituting the values we get,
$9 \times 10^{3}=\frac{4 \times M }{\left(200 \sqrt{2} \times 10^{-12}\right)^{3} \times 6.0 \times 10^{23}}$
$\Rightarrow M =0.0305 \,kg .mol ^{-1}$
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Concepts Used:
Solid State
Solids are substances that are featured by a definite shape, volume, and high density. In the solid-state, the composed particles are arranged in several manners. Solid-state, in simple terms, means "no moving parts." Thus solid-state electronic devices are the ones inclusive of solid components that don’t change their position. Solid is a state of matter where the composed particles are arranged close to each other. The composed particles can be either atoms, molecules, or ions.
Types of Solids:
Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;
- Amorphous solids behave the same as super cool liquids due to the arrangement of constituent particles in short-range order. They are isotropic and have a broad melting point (range is about greater than 5°C).
- Crystalline solids have a fixed shape and the constituent particles are arranged in a long-range order.