Explanation:
The given reaction will be as follows.
[tex]NH_{3} \rightarrow 1/2N_{2} + 3/2H_{2}[/tex]
As all the ammonia has decomposed into nitrogen and hydrogen. Hence, there will be no ammonia left in the reaction.
Now, using Dalton's law, partial pressure of [tex]N_{2}[/tex] + partial pressure of [tex]H_{2}[/tex] = 821 mm Hg.
As there is 1/2 mole [tex]N_{2}[/tex] for 3/2 moles [tex]H_{2}[/tex], the partial pressure of [tex]N_{2}[/tex] is 1/3 the partial pressure of the [tex]H_{2}[/tex].
Let the partial pressure of [tex]N_{2}[/tex] will be x and partial pressure of [tex]H_{2}[/tex] is therefore 3x.
Hence, we will calculate the value of x as follows.
[tex]NH_{3} \rightarrow 1/2N_{2} + 3/2H_{2}[/tex]
x + 3x = 821 mm Hg
4x = 821 mm Hg
x = 205.25
Therefore, we can conclude that the partial pressure of [tex]N_{2}[/tex] is 205.25 mm Hg, partial pressure of [tex]H_{2}[/tex] is 615.75 mm Hg.