1. Tardigrade
  2. Question
  3. Chemistry
  4. Ammonia under a pressure of 15 atm at 27oC is heated to 347oC in a closed vessel in the presence of a catalyst. Under the conditions, NH3 is partially decomposed according to the equation, 2NH3 leftharpoons N2 + 3H2. The vessel is such that the volume remains effectively constant whereas pressure increases to 50 atm. Calculate the percentage of NH3 actually decomposed.

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Q. Ammonia under a pressure of $15$ atm at $27^{o}C$ is heated to $347^{o}C$ in a closed vessel in the presence of a catalyst. Under the conditions, $NH_{3}$ is partially decomposed according to the equation,
$2NH_{3} \rightleftharpoons N_{2} + 3H_{2}$. The vessel is such that the volume remains effectively constant whereas pressure increases to $50\, atm$. Calculate the percentage of $NH_{3}$ actually decomposed.

Equilibrium

Solution:

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Initial pressure of $NH_{3}$ of a mole $= 15$ atm at $27°C$
The pressure of ‘a ’ mole of $NH_{3} - p$ atm at $347°C$
$\therefore \frac{15}{300}=\frac{P}{620}$
$\therefore P=3$atm
At constant volume and at $347^{o}C$, mole $\propto$ pressure a $\propto$ 31 (before equilibrium)
$\therefore a+ 2x \propto50 \left(after equilibrium\right)$
$\therefore \frac{a+2x}{a}=\frac{50}{31}$
$\therefore x=\frac{19}{62}a$
$\therefore \% of NH_{3}$ decomposed $=\frac{2x}{a}\times100 $
$=\frac{2\times19a}{62\times a}\times100=61.33\%$