Question

Which of the following have a triclinic system?
A. $K_{2}C{r}_2{O}_7$
B. $N{a}_{3}Al{F}_6$
C. $NaCl$
D. Quartz

Answer 1

Hint: Arrangement of ions or atoms of a crystalline solid in three dimensional structures is known as a crystal lattice. In simple words, a crystal lattice is an ordered array of points which describe the arrangement of atoms or ions in a solid. The crystal lattice is divided into seven basic crystal systems on the basis of the edge length and angles in the unit cell.

Complete answer: The seven basic crystal system of crystal lattice and the relation between the edge length and angles between vectors for each crystal system are as follows:

Crystal system	Edge length	Angles
Cubic	$a=b=c$	$\alpha =\beta =\gamma ={90}^o$
Tetragonal	$a=b\ne c$	$\alpha =\beta =\gamma ={90}^o$
Orthorhombic	$a\ne b\ne c$	$\alpha =\beta =\gamma ={90}^o$
Monoclinic	$a\ne b\ne c$	$\alpha =\beta ={90}^o$$\gamma \ne {90}^o$
Hexagonal	$a=b\ne c$	$\alpha =\beta ={90}^o$$\gamma ={120}^o$
Rhombohedral	$a=b=c$	$\alpha \ne \beta \ne \gamma \ne {90}^o$
Triclinic	$a\ne b\ne c$	$\alpha \ne \beta \ne \gamma \ne {90}^o$

From the above table, it is clear that in the triclinic crystal system, the crystal is composed of vectors of unequal length and angle between these vectors must not be equal and must not include a right angle. The three-dimensional structure of a triclinic system is described as follows:

Examples of triclinic crystal systems are: $K_2{S}_2{O}_8$ and $K_{2}C{r}_2{O}_7$.
The triclinic lattice is the least symmetric lattice among all crystal systems. It is the only lattice type which does not have any mirror planes within its structure.
Hence, among given options the compound which exists in the triclinic system is potassium dichromate i.e., $K_{2}C{r}_2{O}_7$.
Therefore, option (A) is the correct answer.

Additional information-
The compounds given in the options other than potassium dichromate exist as following crystal system:
$N{a}_{3}Al{F}_6$: It exists as a monoclinic crystal system. Other examples for monoclinic crystal systems are $KN{O}_2$ and $A{s}_4{S}_4$.
$NaCl$: It exists as a Cubic crystal system, specifically as a face centred cubic unit system. Other examples for cubic systems are $Au$, $Si$ and $CsCl$.
Quartz: It exists as a trigonal crystal system which is a structural category of hexagonal crystal system.

Note:
It is important to note that the seven crystal systems can further be arranged into fourteen different three-dimensional arrangements or structures which are known as Bravais lattice. Since, there is no point of symmetry in the triclinic system, so it has only one Bravais lattice structure.