Question

What volume of hydrogen is required to react with \(12 \mathrm{~L}\) of oxygen under the same conditions? $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$

Short answer

The volume of hydrogen that would be required to react fully with 12 L of oxygen, under the given conditions, would be 24 L.

Step-by-step solution

Understand the stoichiometry

Firstly, understand the stoichiometry of the given balanced chemical equation. From the equation 2H2(g) + O2(g) -> 2H2O(g), we know that it takes 2 moles (or volumes since gases are under consideration) of hydrogen to react with 1 mole (or volume) of oxygen.

Calculating the Volume of Hydrogen

Taking the given volume of oxygen (12 L), and knowing that the ratio between hydrogen and oxygen volumes from the balanced reaction is 2:1, the volume of hydrogen needed can be determined by multiplying the given volume of oxygen by 2.

Result

Therefore, under the same conditions, 24 L of hydrogen gas are needed to react with 12 L of oxygen gas which is given

Key concepts

Chemical Reactions

In chemistry, a chemical reaction involves a process where substances, known as reactants, are transformed into different substances, called products. When hydrogen and oxygen gases react, they form water vapor. This process is a typical example of a chemical reaction, where new chemical bonds are formed, and old bonds are broken. Chemical reactions are governed by a variety of laws and principles that allow chemists to predict the outcomes and products of reactions:

• Every chemical reaction is associated with energy changes.
• Mass is conserved; no atoms are lost or gained during the reaction.

When hydrogen combusts in oxygen, energy is released, which is why these reactions are often employed in rockets as a source of propulsion. Understanding chemical reactions is crucial for manipulating and producing useful compounds from raw materials.

Gas Laws

Gas laws are essential for understanding how gases behave under different conditions of temperature and pressure. These laws are closely related to stoichiometry, especially when dealing with reactions involving gases.
Ideal Gas Law: Perhaps the most comprehensive of the gas laws, it relates all the key properties of a gas, combining Charles's Law, Boyle's Law, and Avogadro's Law into the equation \( PV = nRT \). This can be useful for calculating the behavior of gases when reacting.
Avogadro's Law: This law states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This principle is crucial in stoichiometry when calculating the volumes of gaseous reactants and products.

• For our example, the law implies that a gas's volume is directly proportional to the number of moles, given constant pressure and temperature.

Understanding these laws allows chemists to predict how changing conditions will affect a gas's volume, helping in the precise calculation as in the given exercise.

Balanced Chemical Equation

A balanced chemical equation is fundamental in stoichiometry because it represents the relationship between reactants and products in terms of molecules or moles. It ensures the conservation of mass and atoms throughout the reaction. Balancing involves having the same number of each type of atom on both sides of the equation.
Importance of Balancing: In the equation \(2 \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)\), balancing indicates that two molecules of hydrogen gas react with one molecule of oxygen gas to form two molecules of water vapor. This 2:1 hydrogen to oxygen ratio is crucial for determining the proportions of gases used in the reaction.

• A balanced equation allows us to use stoichiometry effectively to calculate the quantities of reactants needed and products formed.
• It helps ensure that calculations account for all atoms and molecules, maintaining consistency in chemical reactions.

For the exercise, balancing the chemical equation helped us know that 24 L of hydrogen gas react with 12 L of oxygen gas, reflecting the 2:1 ratio.