Problem 24 - Chemistry The Science in Context

Question

During the Haber process for synthesizing ammonia, \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g),\) the rate of formation of ammonia is twice the rate at which nitrogen is consumed. Does this mean that the mass of the reaction mixture increases as the reaction proceeds--seemingly defying the law of conservation of mass? Explain why or why not.

Step-by-Step Solution

Answer

Answer: No, the mass of the reaction mixture does not increase during the Haber process, and the law of conservation of mass is not violated. This is because the mass of the consumed nitrogen gas combined with the mass of the used hydrogen gas is equal to the mass of the formed ammonia, and the total mass of reactants is equal to the total mass of products.

Step 1: Understand the given information

First, let's understand the given information. The reaction during the Haber process is represented as $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g).$$ We are also given that the rate of formation of ammonia is twice the rate at which nitrogen is consumed. In other words, the rate at which ammonia (\(\mathrm{NH}_3\)) forms is 2 times the rate at which nitrogen gas (\(\mathrm{N}_2\)) is used up.

Step 2: Calculate the mass of each compound

Next, calculate the mass of each compound involved in the reaction. The molar mass of nitrogen gas (\((N_2)\)) is \(2 \times 14 = 28\,\text{g/mol}\), whereas the molar mass of hydrogen gas (\((H_2)\)) is \(2 \times 1 = 2\,\text{g/mol}\). For ammonia (\(\mathrm{NH}_3\)), the molar mass is \(14 + 3 \times 1 = 17\,\text{g/mol}\). This information will be useful in determining whether the mass increases during the reaction.

Step 3: Analyze the mass conservation in the reaction

Now let's analyze the mass conservation in this reaction. According to the stoichiometry of the reaction, $$1\, \text{mol}\, \mathrm{N}_{2} + 3\, \text{mol}\, \mathrm{H}_{2} \rightarrow 2\, \text{mol}\, \mathrm{NH}_{3}.$$ In terms of mass, going from the left side of the reaction to the right side, we have: \(28\,\text{g}\, \mathrm{N}_{2} + 6\,\text{g}\, \mathrm{H}_{2} \rightarrow 34\,\text{g}\, \mathrm{NH}_{3}\). This shows that the mass of the reactants equals the mass of the products, simultaneously fulfilling the given rate condition and the law of conservation of mass.

Step 4: Explain why the mass of the reaction mixture does not increase

The mass of the reaction mixture does not increase during the process because the mass of the consumed nitrogen gas, combined with the mass of the used hydrogen gas, is equal to the mass of the formed ammonia. This holds true for the given condition that the rate of ammonia formation is twice the rate of nitrogen consumption. The law of conservation of mass remains upheld in this reaction because the total mass of reactants is equal to the total mass of products. In conclusion, the mass of the reaction mixture does not increase during the Haber process, and the law of conservation of mass is not violated in this reaction.

Key Concepts

Rate of Reaction

The rate of reaction is a critical concept in understanding chemical processes like the Haber process, which synthesizes ammonia from nitrogen and hydrogen gases. It refers to how quickly reactants are transformed into products. In the Haber process, the rate at which ammonia (\(\mathrm{NH}_{3}\)) forms is given as twice the rate at which nitrogen gas (\(\mathrm{N}_{2}\)) is consumed.
This information indicates that the amount of ammonia increases rapidly compared to nitrogen. Each factor affecting reaction rate, such as temperature and pressure, can alter the speed of reaction and must be considered to maximize yield.
When analyzing reaction rates, chemists use stoichiometric coefficients from balanced chemical equations to relate rates of different substances. For instance, in the Haber process, the formation of 2 moles of ammonia comes with the consumption of just 1 mole of nitrogen and 3 moles of hydrogen. This means we can correlate the rates through stoichiometric relationships rather than mass, bridging the observable rate information with the theoretical stoichiometry.

Law of Conservation of Mass

The law of conservation of mass states that mass cannot be created or destroyed in a closed system through chemical reactions. This fundamental principle applies flawlessly to the Haber process in the synthesis of ammonia.
Given the reaction: \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g),\) it's essential to realize that, although the appearance changes, total mass remains constant. For instance, 28 grams of nitrogen gas and 6 grams of hydrogen gas result in 34 grams of ammonia.
The crucial idea here is mass equality between reactants and products, ensuring no mass is lost or gained throughout the reaction. Despite differing rates of consumption and formation, the initial mass balance meticulously equates with the final product mass, confirming this law.

Stoichiometry

Stoichiometry provides a methodical way to quantify relationships between reactants and products in chemical reactions, as seen in the Haber process. It uses ratios derived from balanced chemical equations to predict the amounts needed or produced in a reaction.
For example, in the equation \(\mathrm{N}_{2}(g)+3\mathrm{H}_{2}(g) \rightarrow 2\mathrm{NH}_{3}(g),\) stoichiometry dictates that one mole of nitrogen reacts with three moles of hydrogen to produce two moles of ammonia. These ratios allow for precise calculations of reactant and product quantities, crucial for industrial applications where maximizing yield and efficiency is vital.
By understanding these stoichiometric coefficients, we can also appreciate how differing rates of formation, as noted in the Haber process, align with these predetermined ratios. Stoichiometry thus ensures that despite these variances in reaction rates, precise measured reactions occur without mystery.