Problem 4 - Chemistry and Chemical Reactivity

Question

In the synthesis of ammonia, if \(-\Delta\left[\mathrm{H}_{2}\right] / \Delta t=4.5 \times 10^{-4}\) \(\mathrm{mol} / \mathrm{L} \cdot \mathrm{min},\) what is \(\Delta\left[\mathrm{NH}_{3}\right] / \Delta t ?\) \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\)

Step-by-Step Solution

Answer

The rate of change of ammonia concentration is \(3.0 \times 10^{-4}\) mol/L·min.

Step 1: Understand the Given Information

We are given the rate of change of hydrogen concentration as \(-\frac{\Delta[\mathrm{H}_2]}{\Delta t} = 4.5 \times 10^{-4}\) mol/L·min. We need to find the rate of change of ammonia concentration, \(\frac{\Delta[\mathrm{NH}_3]}{\Delta t}\), for the reaction \(\mathrm{N}_2(\mathrm{g}) + 3 \mathrm{H}_2(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_3(\mathrm{g})\).

Step 2: Relate the Rates of Reaction

Using the stoichiometry of the balanced chemical equation, we see that for every 3 moles of \(\mathrm{H}_2\) consumed, 2 moles of \(\mathrm{NH}_3\) are produced. Thus, the rate of change of \(\mathrm{NH}_3\) is \(\frac{2}{3}\) times the rate of change of \(\mathrm{H}_2\).

Step 3: Calculate the Rate of Change of NH3

Using the relationship from Step 2, calculate the rate of change of \(\mathrm{NH}_3\):\[\frac{\Delta[\mathrm{NH}_3]}{\Delta t} = \frac{2}{3} \times \left(4.5 \times 10^{-4}\right) = 3.0 \times 10^{-4}\, \text{mol/L·min}\]

Step 4: Provide the Final Answer

The rate of change of ammonia concentration is \(3.0 \times 10^{-4}\) mol/L·min.

Key Concepts

Stoichiometry

Stoichiometry is the field of chemistry that deals with the relationships between the quantities of reactants and products in chemical reactions. It involves using balanced chemical equations to make predictions about the relative amounts of substances consumed and produced. In essence, stoichiometry allows chemists to quantify how much of each component is involved in a reaction.

An essential concept of stoichiometry is the mole ratio, derived from the coefficients in a chemical equation. For the synthesis of ammonia, as shown through the reaction model:

• \[\text{N}_2(g) + 3\, \text{H}_2(g) \rightarrow 2\, \text{NH}_3(g)\]

We see a ratio of 1:3:2 among nitrogen, hydrogen, and ammonia. This ratio tells us that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia.

By understanding this concept, we can use stoichiometry to calculate unknown quantities in a reaction, like the rate of change of a product or reactant. This is achieved by forming equations based on the given relationships and solving for the desired variables. Stoichiometric calculations assure that chemical equations are accurately balanced and that the conservation of mass is adhered to.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction reaches a state where the concentrations of reactants and products remain constant over time. This does not mean that the reaction has stopped; rather, it has reached a balanced state where the rate of the forward reaction equals the rate of the reverse reaction.

In the context of ammonia synthesis, this balance is particularly important. At equilibrium, the synthesis of ammonia can be represented by the equation:

• \[\text{N}_2(g) + 3\, \text{H}_2(g) \rightleftharpoons 2\, \text{NH}_3(g)\]

Here, the double arrow indicates that the reaction can proceed in both directions. Equilibrium can be shifted by changing conditions such as temperature or pressure. According to Le Chatelier's Principle, the system will adjust to counteract the effect of the change, thus altering the concentrations to re-establish equilibrium.

Understanding chemical equilibrium and its dynamic nature is crucial for industrial processes like the synthesis of ammonia, ensuring that production is efficient and sustainable. It provides insights into maximizing yield and optimizing reaction conditions.

Ammonia Synthesis

Ammonia synthesis is an industrial process where nitrogen and hydrogen gases react to form ammonia. This process is commonly known as the Haber-Bosch process, named after the scientists who developed it. Ammonia plays a vital role in the production of fertilizers, making this method critical to global agriculture.

The Haber-Bosch process is carried out at high temperatures and pressures to maximize the yield of ammonia. The chemical equation for the reaction is:

• \[\text{N}_2(g) + 3\, \text{H}_2(g) \rightarrow 2\, \text{NH}_3(g)\]

Several factors influence the efficiency of ammonia synthesis, such as catalyst activity, temperature, pressure, and the recycling of unconverted gases. A good catalyst, typically iron with promoters, enhances the reaction rate without being consumed, facilitating a higher yield.

Optimizing the conditions for ammonia synthesis involves balancing kinetic and thermodynamic considerations, ensuring that the process is not only efficient but also economically viable. Understanding the nuances of this synthesis is fundamental for chemists and engineers working to meet the growing global demand for agricultural inputs.