Question

1.5 grams of metal hydroxide on strong heating gives 1 gram of metal oxide. Find the equivalent weight of metal.

Answer 1

Hint: We know that metal hydroxides decompose on heating to give metal oxides and water. So, one equivalent of the metal reacts with 1 mole of hydroxide ion. Similarly, one equivalent of the metal reacts with the\[\dfrac{1}{2}\] mole of oxygen atoms. So, we will calculate the equivalent weight of $O{H^ - }$ and ${O^ - }$ ions. Let ‘x’ be the equivalent weight of metal.

Complete step by step answer:
Given in the question,
Weight of metal hydroxide = 1.5 grams
Weight of metal oxide = 1 gram
Weight of water produced = 0.5 gram
Molecular mass of water \[({H_2}O) = \left( {1 \times 2} \right) + 16 = 18\]
The equivalent weight of an element is its gram atomic weight divided by its valence (combining power)
Equivalent mass of water \[({H_2}O) = \dfrac{{18}}{2} = 9\] gram
One equivalent of the metal reacts with 1 mole of hydroxide ion. Similarly, one equivalent of the metal reacts with the\[\dfrac{1}{2}\] mole of oxygen atoms.
1 mole of hydroxide $(O{H^ - }) = \left( {16 + 1} \right) = 17g$
\[\dfrac{1}{2}\] mole of Oxide ion $({O^ - }) = 8g$
Let the equivalent weight of metal be “x”.
$\dfrac{{weight\,of\,metal\,hydroxide}}{{weight\,of\,metal\,oxide}} =
\dfrac{{Equivalent\,mas\,of\,metal + Equivalent\,mass\,of\,O{H^ - }}}{{Equivalent\,mas\,of\,metal +
Equivalent\,mass\,of\,{O^ - }}}$
$\Rightarrow$ $\dfrac{{1.5}}{1} = \dfrac{{x + 17}}{{x + 8}}$
$\Rightarrow$ \[1.5\left( {x + 8} \right) = 1\left( {x + 17} \right)\]
$\Rightarrow$ \[1.5x + 12 = x + 17\]
$\Rightarrow$ \[0.5x = 5\]
$\Rightarrow$ \[x = {\text{1}}0g\]

Hence, the equivalent weight of metal is 10 grams.

Note: The example of metal hydroxide giving metal oxide on heating can be, sodium hydroxide (NaOH) decomposes to produce sodium oxide $(N{a_2}O)$ and water \[({H_2}O)\]. In the question, 18 grams of water \[({H_2}O)\] is released from 1.5 grams of metal hydroxide.