`Cl_(2)(g)+Ba(OH)_(2) to X(aq.)+BaCl_(2)+H_(2)O`
`X+H_(2)SO_(4) to Y+BaSO_(4)`
`Y underset(Deltagt365K)overset(Delta) Z+H_(2)O+O_(2)`
Y and Z are respectively:

Options

A. `HClO_(4), ClO_(2)`
B. `HClO_(3), ClO_(2)`
C. `HClO_(3), ClO_(6)`
D. `HClO_(4), Cl_(2)O_(7)`

Answer

To solve the problem step by step, we will analyze each reaction and identify the compounds involved.

### Step 1: Identify X from the first reaction
The first reaction given is:
\[ \text{Cl}_2(g) + \text{Ba(OH)}_2 \rightarrow X(aq) + \text{BaCl}_2 + \text{H}_2\text{O} \]

When chlorine gas reacts with barium hydroxide, it forms barium chlorate and barium chloride along with water. The balanced reaction can be written as:
\[ \text{Cl}_2 + \text{Ba(OH)}_2 \rightarrow \text{Ba(ClO}_3\text{)}_2 + \text{BaCl}_2 + \text{H}_2\text{O} \]

From this, we can conclude that:
\[ X = \text{Ba(ClO}_3\text{)}_2 \]

### Step 2: Identify Y from the second reaction
The second reaction involves the compound X reacting with sulfuric acid:
\[ X + \text{H}_2\text{SO}_4 \rightarrow Y + \text{BaSO}_4 \]

Substituting \( X \) into the equation:
\[ \text{Ba(ClO}_3\text{)}_2 + \text{H}_2\text{SO}_4 \rightarrow Y + \text{BaSO}_4 \]

This reaction produces barium sulfate and hydrochloric acid. The balanced reaction gives us:
\[ \text{Ba(ClO}_3\text{)}_2 + \text{H}_2\text{SO}_4 \rightarrow 2 \text{HClO}_3 + \text{BaSO}_4 \]

Thus, we find:
\[ Y = \text{HClO}_3 \]

### Step 3: Identify Z from the third reaction
The third reaction involves the decomposition of Y:
\[ Y \xrightarrow{\Delta, T > 365K} Z + \text{H}_2\text{O} + \text{O}_2 \]

Substituting \( Y \):
\[ \text{HClO}_3 \xrightarrow{\Delta, T > 365K} Z + \text{H}_2\text{O} + \text{O}_2 \]

The decomposition of chloric acid (HClO3) produces chlorine dioxide (ClO2), water, and oxygen gas. The balanced reaction is:
\[ 2 \text{HClO}_3 \rightarrow 2 \text{ClO}_2 + \text{H}_2\text{O} + \frac{1}{2} \text{O}_2 \]

Thus, we find:
\[ Z = \text{ClO}_2 \]

### Final Answer
Therefore, the compounds Y and Z are:
- \( Y = \text{HClO}_3 \)
- \( Z = \text{ClO}_2 \)