`(x)+K_2CO_3+Airoverset("heat")rarr(Y)`
`(Y)+Cl_2rarr(Z) ` Pink
Which of the following is correct ?

Options

A. `X = "black" , Mn O_2 , Y = "Blue" ,K_2CrO_4,Z=KMnO_4`
B. `X = "green" , Cr_2 O_3, Y = "Yellow" ,K_2CrO_4,Z=K_2Cr_2O_7`
C. `X = "black" , MnO_2 Y = "green" ,K_2CrO_4,Z=K_2MnO_4,Z=KMnO_4`
D. `X=" black" , Bi_2O_3,Y = " colourless " KBiO_2,Z=KBiO_3`

Answer

To solve the problem step by step, we need to analyze the reactions given in the question and identify the compounds formed at each stage.

### Step 1: Identify the initial reactants and products
The first reaction is:
\[ (X) + K_2CO_3 + \text{Air} \xrightarrow{\text{heat}} (Y) \]
Here, \(X\) is a compound that reacts with potassium carbonate (\(K_2CO_3\)) and air (which contains oxygen) upon heating to form \(Y\).

### Step 2: Determine the identity of \(X\)
From the context of the problem, we can infer that \(X\) is likely a manganese compound, specifically manganese dioxide (\(MnO_2\)), which is known to be black in color.

### Step 3: Identify the product \(Y\)
When \(MnO_2\) reacts with \(K_2CO_3\) and oxygen, it forms potassium manganate (\(K_2MnO_4\)), which is typically green in color. Thus, we can write:
\[ MnO_2 + K_2CO_3 + O_2 \xrightarrow{\text{heat}} K_2MnO_4 \quad (Y) \]

### Step 4: Analyze the second reaction
The second reaction is:
\[ (Y) + Cl_2 \rightarrow (Z) \]
Here, \(Y\) (which we identified as \(K_2MnO_4\)) reacts with chlorine gas (\(Cl_2\)) to form \(Z\).

### Step 5: Identify the product \(Z\)
The reaction of potassium manganate with chlorine leads to the formation of potassium permanganate (\(KMnO_4\)), which is known to be pink in color. The balanced reaction can be represented as:
\[ K_2MnO_4 + Cl_2 \rightarrow 2KMnO_4 + 2KCl \quad (Z) \]

### Step 6: Summarize the findings
- \(X\) is \(MnO_2\) (black color)
- \(Y\) is \(K_2MnO_4\) (green color)
- \(Z\) is \(KMnO_4\) (pink color)

### Conclusion
The correct identification of the compounds based on the reactions is:
- \(X\) = \(MnO_2\) (black)
- \(Y\) = \(K_2MnO_4\) (green)
- \(Z\) = \(KMnO_4\) (pink)

Thus, the correct option that matches these findings is option number 3.