Question

Assuming all gases are at the same temperature and pressure, how many milliliters of nitrogen gas react to give \(45.0 \mathrm{~mL}\) of ammonia gas? $$3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$$

Short answer

22.5 mL of nitrogen gas is needed.

Step-by-step solution

Understand the chemical equation

First, examine the balanced chemical equation: \(3 \mathrm{H}_{2}(g) + \mathrm{N}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g)\). This equation tells us that 1 mole of nitrogen gas \(\mathrm{N}_2\) reacts with 3 moles of hydrogen gas \(\mathrm{H}_2\) to produce 2 moles of ammonia gas \(\mathrm{NH}_3\).

Set up the volume ratio

Since the reaction takes place at the same temperature and pressure, the volume ratio of gases is equal to the mole ratio. From the equation, the mole (and volume) ratio of \(\mathrm{N}_2\) to \(\mathrm{NH}_3\) is 1:2.

Calculate the required volume of nitrogen gas

We have 45.0 mL of ammonia gas. According to the ratio, it takes 1 volume of \(\mathrm{N}_2\) to produce 2 volumes of \(\mathrm{NH}_3\). Therefore, the volume of \(\mathrm{N}_2\) needed is half the volume of \(\mathrm{NH}_3\). Calculate: \( \frac{45.0 \mathrm{~mL}}{2} = 22.5 \mathrm{~mL} \).

Key concepts

Understanding Chemical Reactions

Chemical reactions are processes where reactants transform into products. In a reaction, chemical bonds are broken and new ones are formed, resulting in substances with different properties and compositions. The primary focus in a chemical reaction is the conversion process. Reactants, the substances we start with, react together typically under specific conditions.
Products are the substances formed as a result of the reaction. In our example, the reaction involves hydrogen gas (\(\mathrm{H}_2\)) and nitrogen gas (\(\mathrm{N}_2\)) combining to form ammonia gas (\(\mathrm{NH}_3\)). This particular reaction is important because it illustrates how different elements come together to create a compound with new properties.

• Reactants: The starting materials (in this case, \(\mathrm{H}_2\) and \(\mathrm{N}_2\)).
• Products: The substances formed (here, \(\mathrm{NH}_3\)).
• Reaction Conditions: These involve temperature, pressure, and the state of reactants and products (all gases in this reaction).

Gas Laws and Their Role

Gas laws are a set of laws that describe how gases behave under different conditions of temperature, volume, and pressure. These laws are essential for understanding reactions involving gases, like the production of ammonia gas in our example. The key gas law relevant here is Avogadro's Law, which states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules.
This principle allows us to equate the volume ratio of gases to their mole ratio when they are at the same temperature and pressure.

• Avogadro's Law: This law is crucial for setting up the volume ratio since it directly ties the physical volume of a gas in a container to its chemical mole quantities.
• Ideal Gas Behavior: Real gases behave ideally under many conditions, allowing the use of these laws for calculations without major deviations.
• Volume Ratios: In reactions, gases react in simple whole-number volume ratios if they follow Avogadro's Law.

Balanced Equations and Stoichiometry

Balanced equations are pivotal in stoichiometry, the area of chemistry that deals with the quantitative relationships between reactants and products. A balanced chemical equation ensures that matter is conserved during a reaction.
In our reaction of creating ammonia, the balanced equation is \(3 \mathrm{H}_2(g) + \mathrm{N}_2(g) \rightarrow 2 \mathrm{NH}_3(g)\). This equation reflects the precise stoichiometric ratios needed for the reaction to occur without any leftover reactants, ensuring efficiency.

• Equal Atoms: The number of each type of atom on the reactant side must equal the number on the product side.
• Stoichiometric Coefficients: These numbers (like the 3, 1, and 2 in our equation) indicate the proportions in which the molecules or moles are present.
• Using Ratios: In stoichiometry, these coefficients are essential for calculating the exact amounts of reactants needed and products formed as shown when calculating the volume of \(\mathrm{N}_2\) from \(\mathrm{NH}_3\) volume.