Ammonia under a pressure of $$15$$ atm at $$270C$$ is heated to $$3470C$$ in a closed vessel in the presence of a catalyst. Under the conditions, $$NH3$$ is partially decomposed according to the equation,$$NH3$$⇌$$N3$$ $$+$$ $$3H2$$. The vessel is such that the volume remains effectively constant whereas pressure increases to $$50$$ atm. Calculate the percentage of $$NH3$$ actually decomposed.

Question

Ammonia under a pressure of $$15$$ atm at $$270C$$ is heated to $$3470C$$ in a closed vessel in the presence of a catalyst. Under the conditions, $$NH3$$ is partially decomposed according to the equation,$$NH3$$⇌$$N3$$  $$+$$  $$3H2$$. The vessel is such that the volume remains effectively constant whereas pressure increases to $$50$$ atm. Calculate the percentage of $$NH3$$ actually decomposed.

Infinity Learn · Accepted Answer

$$NH3$$ ⇌ $$N3$$ $$+$$ $$3H2Initial$$ mole                  a           $$0$$          $$0Mole$$ at equiibrium  (a$$ $$-$$ $$2x)      x         $$3xInitial$$ pressure of $$NH3$$ of a mole $$=$$ $$15$$ atm at $$270C=300kThe$$ pressure of ‘a’ mole of $$NH3$$ $$=$$ p atm at   $$3470C=620K$$∴     $$15300$$ $$=$$ $$p620$$∴    p $$=$$ $$31$$ atmAt constant volume and at $$3470C$$, mole ∝ pressurea  ∝ $$31$$ (before$$ $$equilibrium)∴   a $$+$$ $$2x$$  ∝  $$50$$ (after$$ $$equilibrium)∴a $$+$$ $$2xa=5031$$∴    x $$=$$  $$1962$$ a∴   % of $$NH3$$  decomposed $$=$$ $$2xa$$× $$100=2$$× $$19a62$$×a× $$100$$ $$=$$ $$61.33$$%

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