2003 AIPMT Some Basic Concepts of ChemistryStoichiometry and Limiting Reagent Medium Question 42 of 49 in Some Basic Concepts of Chemistry

In Haber process 30 litres of dihydrogen and 30 litres of dinitrogen were taken for reaction which yielded only 50% of the expected product. What will be the composition of gaseous mixture under the above condition in the end :

A 20 litres ammonia, 20 litres nitrogen, 20 litres hydrogen
B 10 litres ammonia, 25 litres nitrogen, 15 litres hydrogen
C 20 litres ammonia, 10 litres nitrogen, 30 litres hydrogen
D 20 litres ammonia, 25 litres nitrogen, 15 litres hydrogen

The answer is B.

Solution

$N_2 + 3H_2 \rightarrow 2NH_3$; by Gay-Lussac's law, volumes react in the ratio 1 : 3 : 2.
30 L of $H_2$ needs only 10 L of $N_2$, while 30 L of $N_2$ would need 90 L of $H_2$. So $H_2$ is the limiting reagent.
Expected product: 30 L $H_2$ would give 20 L $NH_3$.
Only 50% is obtained: $NH_3$ formed $= 10$ L.
To form 10 L $NH_3$: $N_2$ used $= 5$ L and $H_2$ used $= 15$ L.
Remaining: $N_2 = 30 - 5 = 25$ L, $H_2 = 30 - 15 = 15$ L.
Final mixture: 10 litres ammonia, 25 litres nitrogen and 15 litres hydrogen.

Concept Limiting reagent with percentage yield

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