We are asked to calculate *K*_{p} for this reaction.

2AsH_{3}(*g*) ⇌ 2As(*s*) + 3H_{2}(*g*)

Step 1. Convert the pressures to atm

$\mathbf{392}\mathbf{.}\mathbf{0}\mathbf{}\overline{)\mathbf{torr}}\mathbf{}\mathbf{\times}\mathbf{}\frac{\mathbf{1}\mathbf{}\mathbf{atm}}{\mathbf{760}\mathbf{}\overline{)\mathbf{torr}}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{516}\mathbf{}\mathbf{atm}\phantom{\rule{0ex}{0ex}}\mathbf{488}\mathbf{.}\mathbf{0}\mathbf{}\overline{)\mathbf{torr}}\mathbf{}\mathbf{\times}\mathbf{}\frac{\mathbf{1}\mathbf{}\mathbf{atm}}{\mathbf{760}\mathbf{}\overline{)\mathbf{torr}}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{642}\mathbf{}\mathbf{atm}$

Step 2. Calculate x

Total pressure:

$\overline{){{\mathbf{P}}}_{{\mathbf{T}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{P}}}_{{\mathbf{AsH}}_{\mathbf{3}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{}}{{\mathbf{P}}}_{{\mathbf{H}}_{\mathbf{2}}}}\phantom{\rule{0ex}{0ex}}\mathbf{0}\mathbf{.}\mathbf{642}\mathbf{}\mathbf{atm}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{516}\mathbf{}\mathbf{atm}\mathbf{-}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{}\mathbf{}\mathbf{3}\mathbf{x}\phantom{\rule{0ex}{0ex}}\mathbf{0}\mathbf{.}\mathbf{642}\mathbf{}\mathbf{atm}\mathbf{-}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{516}\mathbf{}\mathbf{atm}\mathbf{}\mathbf{=}\mathbf{}\mathbf{x}\phantom{\rule{0ex}{0ex}}\mathbf{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{126}\mathbf{}\mathbf{atm}\phantom{\rule{0ex}{0ex}}$

The gas arsine, AsH_{3}, decomposes as follows:

2AsH_{3}(*g*) ⇌ 2As(*s*) + 3H_{2}(*g*)

In an experiment at a certain temperature, pure AsH _{3}(*g*) was placed in an empty, rigid, sealed flask at a pressure of 392.0 torr. After 48 hours the pressure in the flask was observed to be constant at 488.0 torr.

b. Calculate *K*_{p} for this reaction.

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