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 helow: Determine the formula of the product and justify your answer.

Short answer

The formula of the gaseous product formed in the reaction between nitrogen gas and hydrogen gas is ammonia (NH₃). This was deduced by using the given information about the volumes of the reactants and gaseous product, applying Avogadro's law, determining the stoichiometry, and analyzing the balanced chemical equation: \(N_2 + 3H_2 \rightarrow 2NH_3\).

Step-by-step solution

Analyze the given information about the volumes of the reactants and products.

We are given that 1 volume of nitrogen gas (N₂) reacts with 3 volumes of hydrogen gas (H₂) to form 2 volumes of gaseous product. We can represent this information in a reaction equation as follows: \(N_2 + 3H_2 \rightarrow 2P\) Here, P represents the gaseous product formed.

Apply the mole concept and gas laws.

By Avogadro's Law, equal volumes of gases under the same temperature and pressure conditions have the same number of moles. Therefore, the moles of nitrogen, hydrogen, and the product can be deduced using their respective given volumes. - Nitrogen gas: 1 volume = 1 mole of N₂ - Hydrogen gas: 3 volumes = 3 moles of H₂ - Gaseous product: 2 volumes = 2 moles of P

Determine the stoichiometry of the reaction.

We know the balanced chemical equation will have whole numbers as coefficients. Based on the moles calculated in Step 2, we can write the balanced equation as: \(N_2 + 3H_2 \rightarrow 2P\) Dividing the entire equation coefficients by the least of them (in this case 1): \(N_2 + 3H_2 \rightarrow 2P\)

Determine the formula of the product.

Considering the balanced equation with whole number coefficients, we have 1 mole of N₂ reacting with 3 moles of H₂ to form 2 moles of the gaseous product P. Since nitrogen and hydrogen are both diatomic, we can rewrite the equation as: \(N_2 + 3(H_2) \rightarrow 2NH_3\) Now, the product formed is ammonia (NH₃), and the balanced chemical equation for the reaction between nitrogen and hydrogen gases is: \(N_2 + 3H_2 \rightarrow 2NH_3\)

Justification:

We used the given information about the volumes of nitrogen, hydrogen, and the unknown product to deduce the formula of the product. Based on Avogadro's Law and the stoichiometry of the reaction, we determined that ammonia (NH₃) is the gaseous product formed when 1 mole of nitrogen gas reacts with 3 moles of hydrogen gas.

Key concepts

Avogadro's Law

Avogadro's Law plays a pivotal role in understanding chemical reactions involving gases. It states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules. In practice, this means that one volume of nitrogen will contain the same number of molecules as one volume of hydrogen if both are measured under identical conditions of temperature and pressure.

To put it simply, if we have two containers of different gases at the same temperature and pressure, and they occupy the same space (volume), they contain an equal number of molecules. This understanding is crucial when dealing with gas volume relationships in reactions. It allows chemists to predict how much product can be formed from given volumes of reactants, assuming the reaction occurs at constant temperature and pressure.

For instance, in the nitrogen and hydrogen reaction to form ammonia, we can confidently say that 1 volume of nitrogen will react with 3 volumes of hydrogen to produce 2 volumes of ammonia, only because Avogadro's Law assures us that these volumes are proportional to the number of particles involved in the reaction.

Mole Concept

The mole concept is a fundamental building block in chemistry, which provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure. A mole corresponds to Avogadro's number of particles, which is approximately 6.022x10²³ particles, be they atoms, molecules, ions, or electrons.

Understanding the mole is vital as it allows chemists to count particles by weighing them. This concept enables us to relate masses of different chemical substances to the number of particles or molecules in them and to interpret the reactant-product relationships in a chemical equation in terms of measurable quantities. In the context of our exercise, we apply the mole concept by associating volumes of gases with the number of moles, under the premise of Avogadro's Law, to identify the quantity of ammonia produced from nitrogen and hydrogen.

Balancing Chemical Equations

Balancing chemical equations is an essential skill in chemistry. It ensures that the law of conservation of mass is respected, implying that matter cannot be created or destroyed in a chemical reaction. To balance an equation, one must ensure that there are equal numbers of each type of atom on both sides of the reaction.

In our nitrogen and hydrogen reaction, we start with the simplest formula that describes the reactants and products and then adjust the coefficients to balance the atoms. We observe from the balanced equation that for every mole of nitrogen, we need three moles of hydrogen to produce two moles of ammonia. This balanced equation assures us that atoms are conserved during the reaction and thus reflects the true stoichiometric relationships between the reactants and products.

Gas Volume Relationships

Gas volume relationships refer to the way gas volumes can be used to deduce stoichiometric relationships in chemical reactions, particularly when all reactants and products are in the gaseous state. These relationships are directly derived from both Avogadro's Law and the ideal gas law.

For example, in the synthesis of ammonia from nitrogen gas and hydrogen gas, we can use the given volumes of reactants to predict the volume of product formed. If the temperature and pressure remain constant, the volume of gas gives a direct measure of the number of reactant and product molecules. In the provided exercise, one volume of nitrogen reacting with three volumes of hydrogen to produce two volumes of ammonia perfectly illustrates the concept of gas volume relationships in chemical reactions.