Question

A mixture of \(\mathrm{N}_{2}(g)\) and \(\mathrm{H}_{2}(g)\) reacts in a closed container to form ammonia, \(\mathrm{NH}_{3}(g)\). The reaction ceases before either reactant has been totally consumed. At this stage \(3.0 \mathrm{~mol} \mathrm{} \mathrm{N}_{2}, 3.0 \mathrm{~mol} \mathrm{H}\), and \(3.0 \mathrm{~mol} \mathrm{} \mathrm{NH}_{3}\) are present. How many moles of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) were present originally?

Short answer

Initially, there were 4.5 moles of \(N_{2}\) and 7.5 moles of \(H_{2}\) present.

Step-by-step solution

Write the balanced chemical equation

The balanced chemical equation for the formation of ammonia from nitrogen gas and hydrogen gas is: \[N_{2}(g) + 3H_{2}(g) \rightarrow 2NH_{3}(g)\]

Determine the extent of reaction

At the end of the reaction, we have 3.0 moles of NH₃. According to the balanced chemical equation, every 2 moles of NH₃ produced require 1 mole of N₂ and 3 moles of H₂. Therefore, to produce 3.0 moles of NH₃, the reacted moles of N₂ and H₂ can be determined by: Reacted moles of N₂ = \( \frac{3.0 \, moles \, NH_{3}}{2 \,moles \, NH_{3}}\) x 1 mole N₂ = 1.5 moles N₂ Reacted moles of H₂ = \( \frac{3.0 \, moles \, NH_{3}}{2 \,moles \, NH_{3}}\) x 3 moles H₂ = 4.5 moles H₂

Calculate initial moles of N₂ and H₂

Since we know the reacted moles of N₂ and H₂, we can find the initial moles by adding those to the moles present at the end of the reaction. Initial moles of N₂ = Reacted moles of N₂ + Moles of N₂ present at the end Initial moles of N₂ = 1.5 moles + 3.0 moles Initial moles of N₂ = 4.5 moles Initial moles of H₂ = Reacted moles of H₂ + Moles of H₂ present at the end Initial moles of H₂ = 4.5 moles + 3.0 moles Initial moles of H₂ = 7.5 moles Hence, initially, there were 4.5 moles of N₂ and 7.5 moles of H₂.

Key concepts

Balanced Chemical Equation

Writing a balanced chemical equation is the first crucial step in solving any stoichiometry problem. It shows you the relationship between reactants and products, telling you exactly how much of each substance participates in the reaction. In this problem, the balanced chemical equation for ammonia synthesis is:\[N_{2}(g) + 3H_{2}(g) \rightarrow 2NH_{3}(g)\]This equation shows that one mole of nitrogen (\(N_{2}\)) reacts with three moles of hydrogen (\(H_{2}\)) to produce two moles of ammonia (\(NH_{3}\)). Each component of the equation must be in this exact proportion to reflect the conservation of mass, ensuring that no atoms are lost or gained during the reaction.

Ammonia Synthesis

Ammonia synthesis is an essential chemical process, mainly done using the Haber process. The goal is to combine nitrogen (from the air) with hydrogen (from natural gas) to produce ammonia. This process is critical for creating fertilizers and has industrial importance. In our reaction, we start by mixing nitrogen and hydrogen in a container. They then react to form ammonia gas. However, it is important to follow the correct stoichiometric proportions as defined by the balanced chemical equation to ensure efficiency. This reaction is limited by the availability of reactants and stops when one of them is consumed. In real industrial applications, unreacted nitrogen and hydrogen can even be recycled to improve yield.

Reactants and Products

Reactants are the starting materials in a chemical reaction, while products are the substances formed by the reaction. In the equation for ammonia synthesis, the reactants are nitrogen (\(N_{2}\)) and hydrogen (\(H_{2}\)), and the product is ammonia (\(NH_{3}\)).The transformation from reactants to products follows a fixed ratio (as shown in the balanced equation). Here:

• 1 mole of nitrogen reacts with 3 moles of hydrogen.
• This produces 2 moles of ammonia.

Understanding which substances are reactants and which are products is key to correctly applying stoichiometry in chemical calculations.

Mole Concept

The mole is a fundamental unit in chemistry used to express amounts of a chemical substance. It provides a bridge between the atomic scale and the macroscopic world. Using the mole concept, chemists can count specific numbers of atoms or molecules by weighing them. In this exercise, the mole concept helps us determine how much of each reactant was initially present based on the amount of product formed. For every 2 moles of ammonia produced, 1 mole of nitrogen and 3 moles of hydrogen are used. This arena of calculation allows you to deduce how much nitrogen and hydrogen were originally in the system by:

• Calculating how much reacted to form ammonia.
• Adding the remaining unreacted amounts to find starting totals.

Thus, the mole concept simplifies the balancing of equations and the quantitative interpretation of chemical reactions.