An inorganic reaction sequence involving potassium dichromate is...

The given reaction sequence is the chromyl chloride test for chloride ions.

Reaction 1: Heating $\text{K}_2\text{Cr}_2\text{O}_7$ with $\text{NaCl}$ and conc. $\text{H}_2\text{SO}_4$ produces reddish-brown vapors of chromyl chloride.

$\text{K}_2\text{Cr}_2\text{O}_7 + 4\text{NaCl} + 6\text{H}_2\text{SO}_4 \rightarrow 2\text{KHSO}_4 + 4\text{NaHSO}_4 + 2\text{CrO}_2\text{Cl}_2 + 3\text{H}_2\text{O}$

Gas (X) is $\text{CrO}_2\text{Cl}_2$.

Reaction 2: Passing $\text{CrO}_2\text{Cl}_2$ gas into aqueous $\text{NaOH}$ gives a yellow solution of sodium chromate.

$\text{CrO}_2\text{Cl}_2 + 4\text{NaOH} \rightarrow \text{Na}_2\text{CrO}_4 + 2\text{NaCl} + 2\text{H}_2\text{O}$

Solution (Y) contains $\text{Na}_2\text{CrO}_4$.

Reaction 3: Adding lead acetate to the yellow solution forms a yellow precipitate of lead chromate.

$\text{Na}_2\text{CrO}_4 + (\text{CH}_3\text{COO})_2\text{Pb} \rightarrow \text{PbCrO}_4 + 2\text{CH}_3\text{COONa}$

Precipitate (Z) is $\text{PbCrO}_4$.

Oxidation state of Cr in $\text{CrO}_2\text{Cl}_2$:
Let the oxidation state of Cr be $x$.
$x + 2(-2) + 2(-1) = 0 \Rightarrow x = +6$

Answer: X = $\text{CrO}_2\text{Cl}_2$, Z = $\text{PbCrO}_4$, Oxidation state = +6