Question

Observations of the reaction between nitrogen gas and hydrogen gas show us that 1 volume of nitrogen reacts with 3 volumes of hydrogen to make 2 volumes of gaseous product, as shown below: Determine the formula of the product and justify your answer.

Short answer

The formula of the product is ammonia (NH_3), as it matches the given stoichiometry of the reaction: 1 volume of nitrogen (N_2) reacts with 3 volumes of hydrogen (H_2) to form 2 volumes of product, which follows the balanced equation N_2 (g) + 3 H_2 (g) -> 2 NH_3 (g).

Step-by-step solution

Identify the reactants and their stoichiometry

The reactants in the reaction are nitrogen gas (N_2) and hydrogen gas (H_2), and we are given their stoichiometry as 1 volume of nitrogen reacts with 3 volumes of hydrogen. So we can write the general balanced equation as: N_2 (g) + 3 H_2 (g) -> X Where X is the formula of the product.

Determine the product's formula based on possible compounds

Based on the reactants, the most likely product would be a compound containing both nitrogen and hydrogen atoms. We know that we are forming 2 volumes of this gaseous product. Since the reactants are diatomic molecules, let's assume that the product is also a molecule containing an equal number of nitrogen and hydrogen atoms. A possible candidate is ammonia (NH_3), which is a known compound formed from nitrogen and hydrogen. Let's see if the stoichiometry of the reaction would support this assumption.

Check if the stoichiometry matches for NH_3

If ammonia (NH_3) were the product of the reaction, the balanced chemical equation would be: N_2 (g) + 3 H_2 (g) -> 2 NH_3 (g) This equation indicates that 1 mole of nitrogen (N_2) reacts with 3 moles of hydrogen (H_2) to form 2 moles of ammonia (NH_3). Since the volume of a gas is directly proportional to the number of moles at constant temperature and pressure (Avogadro's Law), this balanced equation matches the given stoichiometry (1 volume of nitrogen reacting with 3 volumes of hydrogen to form 2 volumes of product). Therefore, the formula of the product is ammonia (NH_3).

Justify the answer

Based on the information given in the exercise, the reaction between nitrogen gas (N_2) and hydrogen gas (H_2) has a stoichiometry of 1:3:2, which matches that of the formation of ammonia (NH_3). Hence, the formula of the product is NH_3, and this result is consistent with the observation that 1 volume of nitrogen reacts with 3 volumes of hydrogen to make 2 volumes of the gaseous product.

Key concepts

Chemical Equation Balancing

Mastering chemical equation balancing is fundamental to understanding stoichiometry, which is the calculation of reactants and products in chemical reactions. When we balance a chemical equation, we ensure that the number of atoms for each element is the same on both sides of the equation, following the Law of Conservation of Mass.

For instance, when we analyze the reaction where nitrogen gas (N_2) combines with hydrogen gas (H_2) to produce a mysterious product, we start with a general equation like N_2 (g) + 3 H_2 (g) -> X. Here, the coefficients indicate the relative amounts of reactants needed. In this case, the '3' in front of H_2 means that three times as many hydrogen molecules are required compared to nitrogen molecules to form the product 'X'.

The process of balancing involves tweaking these coefficients until the number of atoms for each element is the same on both sides. For example, in the reaction above, if X is identified as ammonia (NH_3), we would balance the equation to N_2 (g) + 3 H_2 (g) -> 2 NH_3 (g), ensuring that the amount of nitrogen and hydrogen atoms are conserved, thus properly reflecting the law.

Gas Volume Relationships

Gas volume relationships play a crucial role in stoichiometry, especially when dealing with reactions involving gases. In the provided exercise, 1 volume of nitrogen reacts with 3 volumes of hydrogen to produce 2 volumes of a gaseous product. These relationships can be quite intuitive: the volumes of gases involved in the reaction correlate directly with their coefficients in the balanced chemical equation.

In the ammonia synthesis example, the direct volume ratio aligns perfectly with the balanced equation. Avogadro's Law provides the theoretical grounding for this relationship, asserting that equal volumes of gases at the same temperature and pressure contain the same number of particles (or moles). Simply put, under identical conditions, a volume ratio of 1:3:2 for nitrogen, hydrogen, and the ammonia product perfectly fits the balanced equation N_2 (g) + 3 H_2 (g) -> 2 NH_3 (g), our established stoichiometric model for this reaction.

Ammonia Synthesis

Ammonia synthesis is a classic example often used in chemistry education to illustrate chemical reactions, particularly because it demonstrates a simple stoichiometry and the practical application of gas volume relationships. The synthesis of ammonia is a reaction where nitrogen gas (N_2) combines with hydrogen gas (H_2) to form ammonia (NH_3), very relevant in the production of fertilizers and other chemicals.

The balanced equation for this synthesis, N_2 (g) + 3 H_2 (g) -> 2 NH_3 (g), shows the precise stoichiometry where one molecule of nitrogen reacts with three molecules of hydrogen to produce two molecules of ammonia. This process occurs under specific conditions of temperature and pressure, and in an industrial setting, is facilitated by a catalyst. Ammonia synthesis is vital not just in chemistry, but also for agricultural and industrial applications, making it an excellent case study for the practical application of stoichiometric principles.

Avogadro's Law

Avogadro's Law is a foundational principle in chemistry, stating that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. To put it another way, the volume of a gas is directly proportional to the number of moles (and thus the number of molecules) present, as long as the temperature and pressure remain constant.

This law helps us understand the gas volume relationships observed in reactions, such as the synthesis of ammonia. It tells us that for every one volume of nitrogen gas that reacts, we can expect a corresponding number of molecules to react with three volumes of hydrogen (since there are more hydrogen molecules present per volume), ultimately forming two volumes of ammonia. The beauty of Avogadro's Law is that it simplifies our understanding of gases in a reaction, allowing us to make these direct comparisons and confirm that the stoichiometry of the balanced equation is consistent with the observed volumes of reactants and products.