Problem 98 - Chemistry

Question

Consider the reaction of hydrogen gas with oxygen gas: $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$

Step-by-Step Solution

Answer

The given reaction represents a chemical reaction of hydrogen and oxygen forming water. The mole ratio of hydrogen gas to oxygen gas to water vapor in the reaction is 2:1:2, showing the stoichiometry of the reaction.

Step 1: Understanding the Given Chemical Reaction

The given chemical equation is \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2}\mathrm{O}(g)\). In this reaction, two moles of hydrogen gas react with one mole of oxygen gas to form two moles of water vapor.

Step 2: Chemical Law Behind

This reaction follows the Law of Conservation of Mass, meaning that the number of atoms of each element entering the reaction equals the number of atoms of the same element exiting the reaction.

Step 3: Stoichiometry of the Reaction

Looking closely at the stoichiometry of the reaction, for every 2 moles of hydrogen gas reacting, 1 mole of oxygen gas is required and this results in 2 moles of water vapor. So, the mole ratio of hydrogen:oxygen:water is 2:1:2.

Key Concepts

Stoichiometry

Stoichiometry is a key concept in chemistry that involves the quantitative relationships between the reactants and products in a chemical reaction. It is essentially a chemical recipe that tells you how much of each ingredient you need and what you will end up with.
In the given chemical reaction, \[2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2}\mathrm{O}(g),\]stoichiometry helps to determine how much hydrogen gas (\( \mathrm{H}_2 \)) and how much oxygen gas (\( \mathrm{O}_2 \)) is needed to produce water vapor (\( \mathrm{H}_2\mathrm{O} \)).
The stoichiometric coefficients (the numbers in front of the chemical formulas) indicate the proportions of each substance involved in the reaction. In this case:

• 2 moles of \( \mathrm{H}_2 \) react with
• 1 mole of \( \mathrm{O}_2 \) to produce
• 2 moles of \( \mathrm{H}_2\mathrm{O} \).

Understanding stoichiometry allows chemists to calculate the quantities and predict the amounts of substances consumed and produced. This is crucial when scaling reactions for practical uses, such as in manufacturing or laboratory settings.

Law of Conservation of Mass

The Law of Conservation of Mass is a fundamental principle stating that mass is neither created nor destroyed during a chemical reaction. In simpler terms, the total mass of reactants equals the total mass of products.
Using our example reaction:\[2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2}\mathrm{O}(g),\]we can see this law in action. The reaction starts with hydrogen gas and oxygen gas, and it produces water vapor.
The mass of two molecules of \( \mathrm{H}_2 \) and one molecule of \( \mathrm{O}_2 \) combines to form the same mass distributed in the two molecules of \( \mathrm{H}_2\mathrm{O} \).

• 2 moles \( \mathrm{H}_2 \) (4 atoms of hydrogen)
• 1 mole \( \mathrm{O}_2 \) (2 atoms of oxygen)

producing:

• 2 moles \( \mathrm{H}_2\mathrm{O} \) (4 hydrogen atoms and 2 oxygen atoms)

This ensures that every atom that starts in the reaction can be accounted for in the final products.

Mole Ratio

Mole ratio is a vital concept in chemistry, allowing chemists to predict and understand how different amounts of molecules interact in a balanced chemical equation.
In our given reaction example:\[2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2}\mathrm{O}(g),\]the mole ratio helps to balance the equation and shows a clear relationship between the reactants and products.
This particular reaction gives a mole ratio of:

• Hydrogen to Oxygen: 2:1
• Hydrogen to Water: 2:2, simplifying to 1:1
• Oxygen to Water: 1:2

By using these ratios, if you know the amount of \( \mathrm{H}_2 \) you have, you can easily find out how much \( \mathrm{O}_2 \) you need, and how much \( \mathrm{H}_2\mathrm{O} \) will be produced. This is extremely useful for planning chemical reactions or making calculations in lab experiments.