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The Equivalent weight of an element is $13$. It forms an acidic oxide with which \[KOH\] forms a salt isomorphous with \[{K_2}S{O_4}\]​. The atomic weight of element is:
A. $13$
B. $26$
C. $52$
D. $78$

Last updated date: 25th Jun 2024
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Hint: If the compound formed by the element is isomorphous with then that means that the Valency of both Sulphur in \[{K_2}S{O_4}\] and the element in the acidic oxide formed should be identical. Upon finding the valency, we can find the atomic weight of the compound.

Formula used: $Atomic{{ }}weight = Equivalent{{ }}weight \times Valency$

Complete step by step answer:
To understand the question we must first understand the definition of isomorphous. Isomorphous can be defined as the condition where two compounds have similar morphology or shape. In other words, two compounds share similar geometry.
Let us consider the element given to be x. If this element is isomorphous then it will have the same valency as Sulphur and thus form a similar compound to \[{K_2}S{O_4}\]. This element x can react with \[KOH\]to form an acidic oxide. This reaction is:
$x + KOH \to {K_2}x{O_4}$
To find the valency we need to find the oxidation number of Sulphur in \[{K_2}S{O_4}\] . For this, we must consider the Oxidation state of sulphur to be an unknown variable $y$ . After that we must not down the oxidation state of $K$ and $O$ . The OS of $K$ is $ + 1$ and that of $O$ is $ - 2$ . Therefore, the addition of all the OS in the compound \[{K_2}S{O_4}\] is
  $2\left( { + 1} \right) + y + 4\left( { - 2} \right) = 0$
$2 + y - 8 = 0$
$y = 8 - 2$
$y = 6$
Therefore, the valency of both sulphur and element $x$ is $6$ . The equivalent weight is $13$ and valency is $6$ .
Now that we know valency and equivalent weight, we can find atomic weight using the formula mentioned above:
Atomic weight= Equivalent weight$ \times $Valency
= $13 \times 6 = 78$
This is the atomic weight of the element. If we can recall the periodic table, we will find out that the unknown element $x$ is $Mn$ . And the compound is \[{K_2}Mn{O_4}\].

Therefore, the answer will be option D that is $78$

Note: It is important to remember that isomorphous means the same shape or geometry. If two compounds have the same geometry then it is implied that the constituents of the compound may also possess a similar valency.