Question

Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation:
${{N}_{2}}(g)+3{{H}_{2}}(g)\to 2N{{H}_{3}}(g)$
i. Calculate the mass of ammonia produced if $2.00\times {{10}^{3}}g$ dinitrogen reacts with $1.00\times {{10}^{3}}g$ of hydrogen.
ii. Will any of these reactants remain unreacted?
iii. If yes, which one and what would be its mass?

Answer 1

Solve this question by calculating the individual molar mass of the reacting species and relate them to find the grams used of the reacting species by elementary method.

Complete step by step answer:
Let us calculate the molar masses of the reacting substances and the product.
Molar mass of dinitrogen = 2$\times$Molar mass Nitrogen $= 2\times 14g = 28g$
Molar mass of dihydrogen = 2$\times$Molar mass Hydrogen = $2\times 1g = 2g$
Molar mass of ammonia = Molar mass Nitrogen$+$(3$\times$Molar mass of Hydrogen)$= 14+(3\times 1)g = 17g$.
- Now, let us balance the given stoichiometric equation.
${{N}_{2}}+3{{H}_{2}}\to 2N{{H}_{3}}$
- As we can see, 1 mole of dinitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia.
Therefore, we can write that -
28 g of ${{N}_{2}}$ reacts with 6 g of ${{H}_{2}}$ to produce 34 g of $N{{H}_{3}}$
1 g of ${{N}_{2}}$ will react with $\dfrac{6}{28} = 0.2g$ of ${{H}_{2}}$
i.) Given, $2.00\times {{10}^{3}}g$ dinitrogen reacts with $1.00\times {{10}^{3}}$g of hydrogen.
Therefore, 2000 g will nitrogen react with $\dfrac{6}{28}\times 2000g = 428.57g$ of hydrogen.
But, since the limiting reagent in this case is nothing but the nitrogen as it is consumed completely in the reaction leaving behind the rest of dihydrogen.
Thus, total amount of ammonia formed will be $\dfrac{2000\times 34}{28}=2428.57=2.43\times {{10}^{3}}g$

ii.) As we can see, we’ve been given 1000 g dihydrogen in the question. And only 428.57 g is used up in the reaction.
Therefore, yes – one reactant remains unreacted, i.e. Hydrogen
because limiting reagent in this case is nitrogen and it is consumed completely in the reaction leaving behind the rest of dihydrogen.

iii.) Mass of unreacted Hydrogen = $1000 - 428.57g = 571.43g$

Additional Information: Always remember to keep a check on all stoichiometric coefficients in a reaction. “The stoichiometric coefficient is the number written in front of atoms, ion and molecules in a chemical reaction to balance the number of each element on both the reactant and product sides of the equation.”

Note: Since dinitrogen is used up completely in this reaction, it is the limiting reagent.
“The limiting reagent (or limiting reactant or limiting agent) in a chemical reaction is the substance that is totally consumed when the chemical reaction is completed. The amount of product formed is limited by this reagent, since the reaction cannot continue without it.”