What will be the volume of ammonia gas when [tex]$100 cm^3$[/tex] of nitrogen reacts with [tex]$150 cm^3$[/tex] of hydrogen? Which is the limiting reactant? (All gases are measured at the same temperature and pressure.)
Answer (2)
The volume of ammonia gas produced is 100 cm³, and the limiting reactant is hydrogen. Hydrogen is identified as the limiting reactant because the volume ratio of nitrogen to hydrogen is less than the stoichiometric requirement. Therefore, 150 cm³ of hydrogen will react completely to produce 100 cm³ of ammonia.
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Write the balanced chemical equation: N 2 ( g ) + 3 H 2 ( g ) → 2 N H 3 ( g ) .
Determine the limiting reactant: The ratio of N 2 to H 2 is 1:1.5, which is less than the stoichiometric ratio of 1:3, so hydrogen is the limiting reactant.
Calculate the volume of ammonia produced: 150 c m 3 of H 2 produces 3 2 × 150 c m 3 = 100 c m 3 of N H 3 .
The volume of ammonia produced is 100 c m 3 , and the limiting reactant is hydrogen.
Explanation
Problem Analysis We are given that 100 c m 3 of nitrogen reacts with 150 c m 3 of hydrogen, and we need to find the volume of ammonia gas produced and identify the limiting reactant. All gases are measured at the same temperature and pressure.
Balanced Chemical Equation The balanced chemical equation for the reaction between nitrogen and hydrogen to produce ammonia is: N 2 ( g ) + 3 H 2 ( g ) → 2 N H 3 ( g ) This equation tells us that 1 volume of nitrogen reacts with 3 volumes of hydrogen to produce 2 volumes of ammonia.
Identifying the Limiting Reactant To determine the limiting reactant, we compare the volume ratios of nitrogen and hydrogen to the stoichiometric ratio. The stoichiometric ratio of N 2 to H 2 is 1:3. The given volume ratio is 100 c m 3 : 150 c m 3 , which simplifies to 1:1.5. Since 1.5 < 3, hydrogen is the limiting reactant. This means that all of the hydrogen will be used up in the reaction, and there will be some nitrogen left over.
Calculating the Volume of Ammonia Now, we calculate the volume of ammonia produced based on the limiting reactant (hydrogen). From the balanced equation, 3 volumes of H 2 produce 2 volumes of N H 3 . Therefore, 150 c m 3 of H 2 will produce ( 2/3 ) ∗ 150 c m 3 of N H 3 .
V N H 3 = 3 2 × 150 c m 3 = 100 c m 3 So, the volume of ammonia produced is 100 c m 3 .
Final Answer The volume of ammonia gas produced is 100 c m 3 , and the limiting reactant is hydrogen.
Examples
In the Haber-Bosch process, nitrogen and hydrogen react to produce ammonia, which is a crucial component of fertilizers. Understanding limiting reactants and volume relationships helps optimize ammonia production in industrial settings. For example, if a factory has 300 cubic meters of nitrogen and 800 cubic meters of hydrogen, they can calculate that hydrogen is the limiting reactant and that approximately 533 cubic meters of ammonia can be produced.
