Question

What volume of nitrogen is required to react with \(9 \mathrm{~L}\) of hydrogen under the same conditions? $$ 3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$

Short answer

\(\therefore\) 3 L of Nitrogen gas is required to react completely with 9 L of Hydrogen gas.

Step-by-step solution

Understand the chemical equation

In the balanced chemical equation, \(3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\), 3 volumes (or moles) of hydrogen gas reacts with 1 volume (or mole) of nitrogen gas.

Apply Volume Ratio

Realize that volume ratio equals mole ratio for gases. Since the reaction says 3 volumes of hydrogen reacts with 1 volume of nitrogen, the volume ratio in this case is 3:1.

Calculation

Given that 9 L of hydrogen is used, the volume of nitrogen required can be found by cross-multiplying with the volume ratio, that is, \((9 \mathrm{L} \, \mathrm{H}_{2})\times (1 \mathrm{L} \, \mathrm{N}_{2})/(3 \mathrm{L} \, \mathrm{H}_{2}) = 3L N_{2}\).

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into different substances called products. In a chemical equation, you can see this transformation clearly indicated by reactants on the left side and products on the right side of the arrow. The equation must be balanced, meaning the number of atoms for each element must be equal on both sides of the equation. This reflects the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction.

• In the context of this exercise, the balanced chemical equation is: \(3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\).
• This shows that three molecules of hydrogen gas react with one molecule of nitrogen gas to form two molecules of ammonia gas.

Understanding balanced equations helps predict the quantities of reactants required and products formed, which is essential in stoichiometry.

Volume Ratio

The volume ratio in a chemical reaction involving gases is a crucial aspect of stoichiometry. For gases, the volume ratio is the same as their mole ratio due to Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.

• This principle allows us to use the coefficients in a balanced chemical equation as a direct comparison of volumes for gaseous reactants and products.
• In the given reaction, the volume ratio of hydrogen to nitrogen is 3:1. This means that three volumes of hydrogen are needed to react with one volume of nitrogen.

This understanding helps calculate the exact amount of each gas needed for a complete reaction without considering the specific amounts of moles or mass.

Gas Laws

Gas laws are essential for understanding the behavior of gases under different conditions. They help us relate pressure, volume, and temperature of a gas. For this problem, where the conditions are stated to be the same, Boyle's law, Charles's law, or Avogadro's law could be relevant, but mainly Avogadro's law simplifies calculations when dealing with gases' volumes in stoichiometric calculations.

• Avogadro's law: Equal volumes of gases, at the same temperature and pressure, have the same number of molecules.
• This law underpins the assumption that volume ratios are equivalent to mole ratios for gases.

By adhering to these laws, it becomes straightforward to use volume measurements to determine reactant or product quantities when all measurements occur under identical conditions.