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The oxide that gives H$_2$O$_2$ on treatment with a dilute acid is:
(a) PbO$_2$
(b) Na$_2$O$_2$
(c) MnO$_2$
(d) BaO$_2$

Answer
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Hint Acid is a chemical which releases ${{H}^{+}}$ when the chemical is added to the water. Generally, sulphuric acid and nitric acid are called strong acids. By adding a large amount of water (dilution) to strong acid we can decrease the acidic strength and the formed acid is called dilute acid.

Complete step by step answer:
First, let us discuss the presence of a peroxide linkage. The sodium peroxide and barium peroxide contain peroxide (-O-O-) linkage, while the other given oxides do not contain a peroxide linkage.
Now, let us write the chemical reaction for each oxide with dilute acid. Consider dilute sulphuric acid as a dilute acid.
The first oxide is lead oxide, its chemical reaction is
\[\text{Pb}{{\text{O}}_{\text{2}}}\text{+dil}\text{.}{{\text{H}}_{2}}\text{S}{{\text{O}}_{4}}\to \text{PbS}{{\text{O}}_{4}}\text{+}{{\text{H}}_{2}}\text{O+}\frac{1}{2}{{\text{O}}_{2}}\]
The second oxide is sodium peroxide, its chemical reaction is
\[\text{N}{{\text{a}}_{2}}{{\text{O}}_{2}}+{{\text{H}}_{2}}\text{O}\to 2\text{NaOH+}{{\text{H}}_{2}}{{\text{O}}_{2}}\]
The third oxide is manganese oxide, its chemical reaction is
\[\text{Mn}{{\text{O}}_{2}}+\text{dil}\text{.}{{\text{H}}_{2}}\text{S}{{\text{O}}_{4}}\to \text{MnS}{{\text{O}}_{4}}\text{+}{{\text{H}}_{2}}\text{O+}\frac{1}{2}{{\text{O}}_{2}}\]
The fourth oxide is barium peroxide, its chemical reaction is
\[\text{Ba}{{\text{O}}_{2}}+\text{dil}\text{.}{{\text{H}}_{2}}\text{S}{{\text{O}}_{4}}\to \text{BaS}{{\text{O}}_{4}}\text{+}{{\text{H}}_{2}}{{\text{O}}_{2}}\]
From the reactions, we can conclude that the sodium peroxide, and barium peroxide forms a hydrogen peroxide; but sodium peroxide reacts with the water to form hydrogen peroxide.
So, in the last, we can say that the oxide that gives ${{\text{H}}_{2}}{{\text{O}}_{2}}$ on treatment with dilute acid is barium peroxide.

The correct option is (D).

Note: Don’t get confused between the different reactions of oxides, and peroxides with the dilute acid. Sodium peroxide has (-O-O-) linkage but it doesn’t show reaction with the dilute sulphuric acid, whereas it reacts with the water, and forms sodium hydroxide, and hydrogen peroxide. So we have considered the barium peroxide