The problem asks to identify the final products, Y and Z, from a series of reactions. Let's break down the process step-by-step.

Step 1: Identify Gas W

The first step is the heating of potassium chlorate ($KCl{O_3}$) in the presence of a catalytic amount of manganese dioxide ($Mn{O_2}$). This is a classic laboratory method for the preparation of oxygen gas.

The balanced chemical equation for this reaction is: $2KClO_3(s) \xrightarrow{MnO_2, \Delta} 2KCl(s) + 3O_2(g)$ Thus, the gas W is oxygen ($O_2$).

Step 2: Identify Compound X

Next, an excess amount of gas W (oxygen, $O_2$) reacts with white phosphorus ($P_4$). When phosphorus burns in an excess of air or oxygen, it forms phosphorus pentoxide.

The balanced chemical equation is: $P_4(s) + 5O_2(g, \text{excess}) \to P_4O_{10}(s)$ Phosphorus pentoxide exists as a dimer, $P_4O_{10}$. So, compound X is phosphorus pentoxide ($P_4O_{10}$).

Step 3: Identify Compounds Y and Z

Finally, compound X ($P_4O_{10}$) reacts with pure nitric acid ($HN{O_3}$). Phosphorus pentoxide is a very powerful dehydrating agent. It reacts with nitric acid by removing water from it to form the anhydride of nitric acid, which is dinitrogen pentoxide ($N_2O_5$). In this process, $P_4O_{10}$ itself gets hydrated to form metaphosphoric acid ($HPO_3$).

The dehydration of nitric acid can be represented as: $2HNO_3 \xrightarrow{-H_2O} N_2O_5$ The overall balanced reaction between phosphorus pentoxide and nitric acid is: $P_4O_{10}(s) + 4HNO_3(l) \to 2N_2O_5(g) + 4HPO_3(l)$ The products of this reaction are dinitrogen pentoxide ($N_2O_5$) and metaphosphoric acid ($HPO_3$). Therefore, Y and Z are $N_2O_5$ and $HPO_3$.

Step 4: Compare with Options

Let's check the given options: A: ${N_2}{O_3}$ and ${H_3}P{O_4}$ - Incorrect. B: ${N_2}{O_5}$ and $HP{O_3}$ - Correct. The products are dinitrogen pentoxide and metaphosphoric acid. C: ${N_2}{O_4}$ and $HP{O_3}$ - Incorrect. D: ${N_2}{O_4}$ and ${H_3}P{O_3}$ - Incorrect.

The pair of compounds formed is ($N_2O_5$, $HPO_3$), which corresponds to option B. The question asks for Y and Z respectively, and option B provides the correct pair of substances.