Question

The formula of metallic hydroxide (eq. wt.=$150$) is ${\text{M}}{\left( {{\text{OH}}} \right)_{\text{2}}}{\text{.x}}{{\text{H}}_{\text{2}}}{\text{O}}$. If the atomic weight of the metal is $176$ then the value of x will be,
A. $2$
B.$5$
C.$3$
D.$6$

Answer 1

Hint: We will determine the molecular weight of the metal hydroxide by multiplying the equivalent weight by valency. From the total weight, subtract the weight of metal and hydroxide ions. The left weight will be of x water molecules. By dividing the weight of one water molecule we can determine the number of water molecules.

Complete step by step solution:
The molecular weight is determined as the product of equivalent weight and valency.
The formula of equivalent weight is as follows:
${\text{Molecular}}\,{\text{weight}}\,{\text{(M)}}\,\,{\text{ = }}\,\,{\text{equivalent}}\,{\text{weight}}\, \times {\text{valency}}\,{\text{(n)}}$
The metal hydroxide dissociates as follows:
${\text{M}}{\left( {{\text{OH}}} \right)_{\text{2}}}{\text{.x}}{{\text{H}}_{\text{2}}}{\text{O}}\, \to \,{{\text{M}}^{2 + }}\, + \,{\text{2}}\,{\text{O}}{{\text{H}}^ - }\, + \,{\text{x}}{{\text{H}}_{\text{2}}}{\text{O}}$
Metal loses two electrons so the valency of metal hydroxide is two.
So, the molecular mass of metal hydroxide is,
Substitute $150$for equivalent weight and two for valency.
${\text{Molecular}}\,{\text{weight}}\,{\text{(M)}}\,\,{\text{ = }}\,\,{\text{150}}\, \times {\text{2}}$
${\text{Molecular}}\,{\text{weight}}\,{\text{(M)}}\,\,{\text{ = }}\,300$
The weight of the metal is $176$so, the remaining weight is of two hydroxide and x water molecules. The remaining weight is,
Remaining weight $ = 300 - 176$
Remaining weight $ = 124$
$124$ is the weight of two hydroxide and x water molecules.
The molecular mass of hydroxide ion is $17$ so, the weight of two hydroxide ions is,
Weight of two hydroxide ions $ = 17\, \times 2$
Weight of two hydroxide ions $ = 34$
Subtract the weight of two hydroxide from the remaining weight to determine the mass of x water molecules.
The mass of water molecules $ = 124 - 34$
The mass of water molecules $ = 90$
The weight of one water molecule is$18$. So, weight$18$correspond to one water molecule so, weight $90$will corresponds to,
${\text{18}}\,{\text{ = }}\,{\text{1}}\,{{\text{H}}_{\text{2}}}{\text{O}}$
${\text{90}}\,\,{\text{ = }}\,5\,{{\text{H}}_{\text{2}}}{\text{O}}$
So, five molecules of water will weigh $90$ the value of x is $5$.

Therefore, option (B) $5$ is correct.

Note: Valency is the charge or oxidation number of the atom. In the case of acids, the valency is determined as the number of protons donated. In the case of oxidation number one, the equivalent weight will be equal to atomic weight. The molecular weight is determined as the sum of atomic weight of all atoms.