For `(A)+K_(2)CO_(3)+air overset(Heat)rarr(B)`
`(B)+CI_(2)rarr(C)`pink
Which of the following is correct ?

Options

A. X=black,`MnO_(2)`, Y=Blue, `CrO_(4)`, Z=`KMnO_(4)`
B. X=Green, `Cr_(2)O_(3)`, Y=Yellow, `K_(2)CrO_(4)`, Z=`K_(2)Cr_(2)O_(7)`
C. X=black, `MnO_(2)`, Y=green, `K_(2)MnO_(4)`, Z=`KMnO_(4)`
D. X=black, `Bi_(2)O_(3)`, Y=colourless, `KBiO_(2)`, Z=`KBiO_(3)`

Explanation

To solve the question, we need to identify the compounds involved in the reactions and their respective colors. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify Compound A
- **Given Reaction**: \( (A) + K_2CO_3 + \text{air} \overset{\text{Heat}}{\rightarrow} (B) \)
- **Analysis**: Compound A is likely to be manganese dioxide (MnO2) since it is a common reactant in reactions involving potassium carbonate and air.
- **Conclusion**: Compound A is MnO2.

### Step 2: Determine Compound B
- **Reaction**: When MnO2 reacts with \( K_2CO_3 \) in the presence of air and heat, it forms potassium manganate (K2MnO4) and releases carbon dioxide (CO2).
- **Balanced Reaction**:
\[ 2 \text{MnO}_2 + 4 \text{K}_2\text{CO}_3 + \text{O}_2 \rightarrow 2 \text{K}_2\text{MnO}_4 + 4 \text{CO}_2 \]
- **Conclusion**: Compound B is K2MnO4.

### Step 3: Identify Compound C
- **Given Reaction**: \( (B) + Cl_2 \rightarrow (C) \)
- **Analysis**: When K2MnO4 reacts with chlorine gas (Cl2), it forms potassium permanganate (KMnO4) and potassium chloride (KCl).
- **Balanced Reaction**:
\[ 2 \text{K}_2\text{MnO}_4 + \text{Cl}_2 \rightarrow 2 \text{KMnO}_4 + 2 \text{KCl} \]
- **Conclusion**: Compound C is KMnO4.

### Step 4: Determine the Colors of the Compounds
- **MnO2**: This compound is black in color.
- **K2MnO4**: This compound is green in color.
- **KMnO4**: This compound is pink in color.

### Final Summary of Compounds
- **Compound A (X)**: MnO2 (black)
- **Compound B (Y)**: K2MnO4 (green)
- **Compound C (Z)**: KMnO4 (pink)

### Conclusion
The correct option that matches the identified compounds and their colors is the third option, which states:
- X is black (MnO2)
- Y is green (K2MnO4)
- Z is pink (KMnO4)