Potassium dichromate when heated with concentrated sulphuric acid and a soluble chloride, gives brown-red vapours of :

Potassium dichromate is represented as $$ K_2Cr_2O_7 $$. When it is heated with concentrated sulphuric acid ($$ H_2SO_4 $$) and a soluble chloride, such as potassium chloride ($$ KCl $$) or sodium chloride ($$ NaCl $$), a specific reaction occurs that produces chromyl chloride.

The balanced chemical equation for this reaction is:

$$ K_2Cr_2O_7 + 4KCl + 6H_2SO_4 \rightarrow 2CrO_2Cl_2 + 6KHSO_4 + 3H_2O $$

Let's verify the atom balance step by step. On the left side (reactants):

• Potassium ($$ K $$): $$ K_2Cr_2O_7 $$ has 2 K, and $$ 4KCl $$ has 4 K, so total $$ 2 + 4 = 6 $$ K atoms.
• Chromium ($$ Cr $$): $$ K_2Cr_2O_7 $$ has 2 Cr atoms.
• Chlorine ($$ Cl $$): $$ 4KCl $$ has 4 Cl atoms.
• Hydrogen ($$ H $$): $$ 6H_2SO_4 $$ has $$ 6 \times 2 = 12 $$ H atoms.
• Sulfur ($$ S $$): $$ 6H_2SO_4 $$ has 6 S atoms.
• Oxygen ($$ O $$): $$ K_2Cr_2O_7 $$ has 7 O, and $$ 6H_2SO_4 $$ has $$ 6 \times 4 = 24 $$ O, so total $$ 7 + 24 = 31 $$ O atoms.

On the right side (products):

• Chromyl chloride ($$ CrO_2Cl_2 $$): $$ 2CrO_2Cl_2 $$ has 2 Cr, $$ 2 \times 2 = 4 $$ O atoms (since each $$ CrO_2Cl_2 $$ has two O atoms), and $$ 2 \times 2 = 4 $$ Cl atoms (since each has two Cl atoms).
• Potassium hydrogen sulfate ($$ KHSO_4 $$): $$ 6KHSO_4 $$ has 6 K, 6 H, 6 S, and $$ 6 \times 4 = 24 $$ O atoms (since each $$ KHSO_4 $$ has four O atoms).
• Water ($$ H_2O $$): $$ 3H_2O $$ has $$ 3 \times 2 = 6 $$ H atoms and $$ 3 \times 1 = 3 $$ O atoms.

Summing the products:

• K: 6 atoms (from $$ 6KHSO_4 $$)
• Cr: 2 atoms (from $$ 2CrO_2Cl_2 $$)
• Cl: 4 atoms (from $$ 2CrO_2Cl_2 $$)
• H: 6 (from $$ 6KHSO_4 $$) + 6 (from $$ 3H_2O $$) = 12 atoms
• S: 6 atoms (from $$ 6KHSO_4 $$)
• O: 4 (from $$ 2CrO_2Cl_2 $$) + 24 (from $$ 6KHSO_4 $$) + 3 (from $$ 3H_2O $$) = 31 atoms

The atoms are balanced on both sides, confirming the equation.

Chromyl chloride ($$ CrO_2Cl_2 $$) is a volatile compound that appears as brown-red vapors. This reaction is the basis of the chromyl chloride test, used to detect chloride ions.

Now, evaluating the options:

• Option A ($$ CrO_3 $$): Chromium trioxide is a dark red solid, not a vapor, and is not formed in this specific reaction with chloride.
• Option B ($$ CrCl_3 $$): Chromium(III) chloride is a green solid and does not produce vapors.
• Option C ($$ CrO_2Cl_2 $$): Chromyl chloride matches the description of brown-red vapors.
• Option D ($$ Cr_2O_3 $$): Chromium(III) oxide is a green solid and does not form vapors.

Hence, the brown-red vapors are due to chromyl chloride ($$ CrO_2Cl_2 $$).

So, the answer is Option C.