Question

An 18 g sample of water is decomposed into \(2 \mathrm{g}\) of hydrogen gas and \(16 \mathrm{g}\) of oxygen gas. What masses of hydrogen and oxygen gases would have been prepared from 27 g of water? What law of chemistry is used in solving this problem?

Short answer

3 g of hydrogen and 24 g of oxygen are produced from 27 g of water; this uses the Law of Definite Proportions.

Step-by-step solution

Understand the Problem

We are given an 18 g sample of water that yields 2 g of hydrogen gas and 16 g of oxygen gas upon decomposition. We need to determine the masses of hydrogen and oxygen gases produced from a 27 g sample of water. Also, identify the chemical law applied.

Identify Relevant Law

The law applied here is the Law of Definite Proportions, which states that a chemical compound always contains its component elements in a fixed ratio by mass.

Determine Proportions for Hydrogen

From the decomposition of 18 g of water, we get 2 g of hydrogen. Therefore, the proportion of hydrogen by mass is \( \frac{2}{18} \). Calculate the mass of hydrogen in 27 g of water using this proportion.

Calculate Mass of Hydrogen

Apply the proportion: \( \text{Mass of hydrogen in 27 g} = 27 \times \frac{2}{18} = 3 \text{ g} \).

Determine Proportions for Oxygen

Similarly, from 18 g of water, we get 16 g of oxygen. The proportion of oxygen by mass is \( \frac{16}{18} \). Calculate the mass of oxygen in 27 g of water using this proportion.

Calculate Mass of Oxygen

Apply the proportion: \( \text{Mass of oxygen in 27 g} = 27 \times \frac{16}{18} = 24 \text{ g} \).

Conclusion

From 27 g of water, 3 g of hydrogen gas and 24 g of oxygen gas are produced. The calculation is based on the Law of Definite Proportions.

Key concepts

Chemical Decomposition

Chemical decomposition is a process where a single compound breaks down into simpler substances. In the context of the exercise, water (H₂O) undergoes chemical decomposition to form hydrogen and oxygen gases. When water decomposes, it splits into its component elements, hydrogen (H₂) and oxygen (O₂), which are gases. This decomposition process requires energy, often in the form of electricity or heat, to overcome the energy barrier that keeps the molecules of water intact.
The decomposing of a substance is different from a mixture being separated because the component elements were chemically bonded together in a compound and now are released as separate elements. It's like unlocking a combination to open a lock, where specific conditions are required to separate the components. Understanding chemical decomposition helps us learn how substances transform and is crucial in industrial processes like electrolysis.
This process highlights how fixed proportions are consistently observed, supporting key chemical laws such as the one we use here.

Mass Ratios

Mass ratios are a way to understand how much of each element is present in a compound. They allow us to see the "recipe" for forming a compound by showing the relationship between the mass of its component elements. In the exercise, the mass ratio of hydrogen to oxygen in water is given as 2:16 or simplified 1:8.
This ratio comes from decomposing an 18 g sample of water, which produces 2 g of hydrogen and 16 g of oxygen. By maintaining this ratio, we can predict the amount of each gas yielded from any mass of water. For example, when decomposing 27 g of water, the same ratio tells us to expect 3 g of hydrogen and 24 g of oxygen.
These predictable mass ratios are a critical aspect of the Law of Definite Proportions, which ensures that no matter how much of a compound we have, the elements within are always in the same fixed ratio. This principle supports consistency and reproducibility in chemical reactions and calculations.

Hydrogen and Oxygen Gases

Hydrogen and oxygen gases are the elemental decomposition products of water. Each plays a significant role not just in chemistry but also in our everyday world.

• **Hydrogen (H₂)**: It is the lightest and most abundant element in the universe. Upon decomposition of water, the hydrogen gas formed is extremely flammable and used widely as a fuel, especially in the context of creating "clean energy" through hydrogen fuel cells.
• **Oxygen (O₂)**: This gas is essential for combustion and is vital for life as it is a major part of the air we breathe. The oxygen obtained from water decomposition is not only critical for respiration but also used industrially in welding and supporting combustion in rockets.

When water decomposes, the production of hydrogen and oxygen gases exemplifies how different the properties of elemental gases can be compared to their compound in water. While water is a liquid vital for life, the resulting hydrogen and oxygen gases have very different properties and uses. Understanding these gases helps appreciate the types of reactions and energy transformations that occur, providing context to how the Law of Definite Proportions holds true in real-world applications.