A gas X undergoes first-order decomposition X(g) → Y(g) + Z(g) in a sealed rigid vessel with inert He. The initial total pressure is 360 kPa; after complete decomposition it is 600 kPa. At 15.0 min it

Question

A gas X undergoes first-order decomposition X(g) → Y(g) + Z(g) in a sealed rigid vessel with inert He. The initial total pressure is 360 kPa; after complete decomposition it is 600 kPa. At 15.0 min it is 480 kPa. What is the additional time after 15.0 min needed to reach total pressure 570 kPa?

TestHub · Accepted Answer

The original X partial pressure is 600 - 360 = 240 kPa; the initial inert pressure is 120 kPa. At any time p X ​ = 600 - Pₜₒₜₐₗ. At 15.0 min, p X ​ = 120 kPa, so one half-life is 15.0 min. At 570 kPa, p X ​ = 30 kPa = 240/8, reached after three half-lives, or 45.0 min from the start. Additional time is 45.0 - 15.0 = 30.0 min. Neither total pressure itself nor its ratio follows the first-order decay law in the presence of products and inert gas.

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