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Which pair of substances gives the same gaseous product when these react with water
A. Ca and \[{\rm{Ca}}{{\rm{H}}_{\rm{2}}}\]
B. Na and \[{\rm{N}}{{\rm{a}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}}\]
C. K and \[{\rm{K}}{{\rm{O}}_{\rm{2}}}\]
D. Ba and \[{\rm{Ba}}{{\rm{O}}_{\rm{2}}}\]

Answer
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Hint: When a substance on reaction with water, the reaction is called hydrolysis.
Alkali metals and alkaline earth metals react with water giving rise to alkali metal hydroxides and alkaline earth metal hydroxides respectively.

Complete Step by Step Answer:
We are given a pair of substances and we have to find out which pair forms the same gaseous product when reacted with water.
The given metals Na and K are alkali earth metals and these react with water to give rise to alkali metal hydroxide.
Ca and Ba are alkaline earth metals and these react with water giving rise to alkaline earth metal hydroxide.

A. Ca and \[{\rm{Ca}}{{\rm{H}}_{\rm{2}}}\]
Calcium in reaction with water gives rise to calcium hydroxide and hydrogen gas.
The reaction happens as follows:
\[{\rm{Ca + }}{{\rm{H}}_{\rm{2}}}{\rm{O}} \to {\rm{Ca}}{\left( {{\rm{OH}}} \right)_{\rm{2}}}{\rm{ + }}{{\rm{H}}_{\rm{2}}}\]
Calcium hydride in reaction with water gives rise to calcium hydroxide and hydrogen gas.
The reaction happens as follows:
\[{\rm{Ca}}{{\rm{H}}_{\rm{2}}}{\rm{ + 2}}{{\rm{H}}_{\rm{2}}}{\rm{O}} \to {\rm{Ca}}{\left( {{\rm{OH}}} \right)_{\rm{2}}}{\rm{ + 2}}{{\rm{H}}_{\rm{2}}}\]
Both calcium and calcium hydroxide liberate hydrogen gas.
So, A is correct.

B. Na and \[{\rm{N}}{{\rm{a}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}}\]
Sodium in reaction with water gives rise to sodium hydroxide and hydrogen gas.
The reaction happens as follows:
\[{\rm{2Na + 2}}{{\rm{H}}_{\rm{2}}}{\rm{O}} \to 2{\rm{NaOH + }}{{\rm{H}}_{\rm{2}}}\]
Sodium peroxide in reaction with water gives rise to sodium hydroxide and hydrogen peroxide.
The reaction happens as follows:
\[{\rm{N}}{{\rm{a}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}}{\rm{ + 2}}{{\rm{H}}_{\rm{2}}}{\rm{O}} \to {\rm{2NaOH + }}{{\rm{H}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}}\]
So, sodium liberates hydrogen gas while sodium peroxide liberates oxygen gas.
So, B is incorrect.

C. K and \[{\rm{K}}{{\rm{O}}_{\rm{2}}}\]
Potassium in reaction with water gives rise to potassium hydroxide and hydrogen gas.
The reaction happens as follows:
\[{\rm{2K + 2}}{{\rm{H}}_{\rm{2}}}{\rm{O}} \to 2{\rm{KOH + }}{{\rm{H}}_{\rm{2}}}\]
Potassium superoxide in reaction with water gives rise to potassium hydroxide and hydrogen peroxide and liberates oxygen gas.
The reaction happens as follows:
\[{\rm{2K}}{{\rm{O}}_{\rm{2}}}{\rm{ + 2}}{{\rm{H}}_{\rm{2}}}{\rm{O}} \to {\rm{2KOH + }}{{\rm{H}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}{{\rm{O}}_{\rm{2}}}\]
So, potassium liberates hydrogen gas and potassium superoxide liberates oxygen gas.
So, C is incorrect.

D. Ba and \[{\rm{Ba}}{{\rm{O}}_{\rm{2}}}\]
Barium in reaction with water gives rise to barium hydroxide and hydrogen gas.
The reaction happens as follows:
\[{\rm{Ba + }}{{\rm{H}}_{\rm{2}}}{\rm{O}} \to {\rm{Ba}}{\left( {{\rm{OH}}} \right)_{\rm{2}}}{\rm{ + }}{{\rm{H}}_{\rm{2}}}\]
Barium peroxide in reaction with water gives rise to barium hydroxide and oxygen gas.
The reaction happens as follows:
\[{\rm{2Ba}}{{\rm{O}}_{\rm{2}}}{\rm{ + 2}}{{\rm{H}}_{\rm{2}}}{\rm{O}} \to {\rm{2Ba}}{\left( {{\rm{OH}}} \right)_{\rm{2}}}{\rm{ + }}{{\rm{H}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}}\]
Barium produces hydrogen gas when reacted with water and barium peroxide produces hydrogen peroxide when reacted with water.
So, D is incorrect.

So, option A is correct.

Note: It must be noted that out of the given options only calcium and calcium hydride liberate the same gas in reaction with water which is hydrogen gas. Sodium liberates hydrogen gas while sodium peroxide liberates oxygen gas in reaction to water. Potassium liberates hydrogen gas and potassium superoxide liberates oxygen gas. Barium liberates hydrogen gas when reacted with water and barium peroxide produces hydrogen peroxide and barium hydroxide when reacted with water.