Solid $ KCl $ , when heated with solid $ {K_2}C{r_2}{O_7} $ and concentrated $ {H_2}S{O_4} $ , gives red vapours $ \left( a \right) $ that turn $ NaOH $ solution yellow $ \left( b \right) $ . the yellow solution, when acidified with acetic acid and treated with lead acetate, gives yellow precipitate $ \left( c \right) $ . Which of the following is true with respect to $ a $ , $ b $ and $ c $ ?
(A) $ a $ and $ b $ contain $ CrO_4^{2 - } $
(B) $ a $ and $ c $ contain $ CrO_4^{2 - } $
(C) $ a $ , $ b $ and $ c $ contain $ CrO_4^{2 - } $
(D) $ a $ , $ b $ and $ c $ contain $ Cr\left( {VI} \right) $

Hint: This question gives the knowledge about the multistep reaction and a precipitate reaction. A multistep reaction is the reaction which completes through various steps. Precipitation reactions are the reactions which occur when two soluble salts containing solutions combine to form an insoluble salt.

Complete step by step solution:
It is a multistep reaction. A multistep reaction is the reaction which completes through various steps.
In the first step, when concentrated sulphuric acid and solid potassium chloride reacts with potassium dichromate it leads to the formation of chromyl chloride which produces red vapours. In this step, the oxidation state of chromium atoms is $ + 6 $ .
The reaction for this step is as follows:
 $ {K_2}C{r_2}{O_7} + 4KCl + 3{H_2}S{O_4} \to 2Cr{O_2}C{l_2} + 3{K_2}S{O_4} + 3{H_2}O $
In the second step, it further turns the sodium hydroxide solution yellow. In this step, the oxidation state of chromium atoms is $ + 6 $ .
The reaction for this step is as follows:
 $ Cr{O_2}C{l_2} + 4NaOH \to N{a_2}Cr{O_4} + 2NaCl + 2{H_2}O $
In the next step, it is acidified using acetic acid and then treated with lead acetate and produces yellow precipitate. In this step, the oxidation state of chromium atoms is $ + 6 $ .
The reaction for this step is as follows:
 $ N{a_2}Cr{O_4} + Pb{\left( {C{H_3}COO} \right)_2} \to PbCr{O_4} + C{H_3}COONa $
Therefore, option $ D $ is correct.

Additional Information
Precipitation reactions are the reactions which occur when two soluble salts containing solutions combine to form an insoluble salt. That insoluble salt is called precipitate. Precipitate reactions are very helpful in determining the presence of different ions in the solution. A precipitate is generally insoluble in the solution. Precipitation reactions are generally double displacement reactions.
The components which get precipitated during the reactions are generally reactants which can be present in any state solid, liquid or gas.
The most common example of precipitation reaction is the reaction between silver nitrate and potassium chloride which leads to the formation of a solid precipitate of silver chloride. The reaction is as follows:
 $ AgN{O_3} + KCl \to AgCl + KN{O_3} $ .

Note
Always remember that the precipitation reactions are the double displacement reactions. And also remember that precipitates are insoluble in the solution. These reactions are carried out under certain conditions.