Question

How does Dalton's atomic theory account for the fact that when $1.000\mathrm{g}$ of water is decomposed into its elements, $0.111\mathrm{g}$ of hydrogen and $0.889\mathrm{g}$ of oxygen are obtained regardless of the source of the water?

Short answer

The constant mass ratio of hydrogen to oxygen obtained from the decomposition of water is $1:8$. This is consistent with Dalton's atomic theory, which states that elements combine in fixed ratios to form compounds. In water, two atoms of hydrogen combine with one atom of oxygen to form a molecule ($H_{2}O$). The constant mass ratio of $1:8$ demonstrates the law of constant composition, meaning the elements in a chemical compound always combine in the same mass proportions, regardless of the source or method of preparation.

Step-by-step solution

Calculate the ratio of hydrogen and oxygen masses

To understand how Dalton's atomic theory accounts for the constant ratio, we first need to find the ratio of the masses of hydrogen and oxygen obtained when water is decomposed. Given: Mass of water = $1.000\mathrm{g}$ Mass of hydrogen = $0.111\mathrm{g}$ Mass of oxygen = $0.889\mathrm{g}$ Ratio of hydrogen to oxygen mass = $\frac{\text{mass of hydrogen}}{\text{mass of oxygen}}$

Calculate the mass ratio

Substitute the given values and calculate the mass ratio. Ratio of hydrogen to oxygen mass = $\frac{0.111}{0.889}$ = $0.125$ or $1:8$ The constant mass ratio of hydrogen to oxygen obtained from the decomposition of water is $1:8$.

Relate the mass ratio to Dalton's atomic theory

According to Dalton's atomic theory, atoms combine in fixed ratios to form compounds. In the case of water, decomposing it results in the constant mass ratio of hydrogen (H) and oxygen (O) as $1:8$. This constant ratio can be explained by the fact that in water, H and O are combined in a fixed proportion. One molecule of water ($H_{2}O$) consists of two atoms of hydrogen and one atom of oxygen. The mass ratio obeys the law of constant composition, which states that a chemical compound always has the same elements combined in the same mass proportions, regardless of the source or method of preparation. In this case, the constant mass ratio of hydrogen to oxygen in water is due to the fixed atomic ratio of hydrogen and oxygen in water molecules according to Dalton's atomic theory.

Key concepts

Law of Constant Composition

The Law of Constant Composition is a fundamental principle in chemistry. It states that any given compound will always be made up of the same elements in the same proportion by mass, no matter how or where the compound is created. This means that the composition stays unchanged regardless of the sample's origin or the method used to produce it.
For example, when you decompose water, you will always get exactly the same mass ratio of hydrogen to oxygen. Whether the water is from a river or produced in a lab, it will behave the same way.
In the context of Dalton's Atomic Theory, this law shows that atoms of elements combine in consistent and fixed ratios to form compounds. For water, it implies that in every water molecule, two hydrogen atoms always bond with one oxygen atom. This consistency results in water always consisting of 88.9% oxygen and 11.1% hydrogen by mass.

Fixed Mass Ratio

The concept of a fixed mass ratio ties closely to Dalton's insight regarding compounds. They form due to the specific arrangement and combination of atoms in set ratios. In the case of water, it appears as a mass ratio of hydrogen to oxygen of 1:8.
This ratio does not change because of how hydrogen and oxygen atoms come together in a water molecule. Each molecule of water is made up of two hydrogen atoms and one oxygen atom. Because of this consistent atomic structure, water's mass ratio remains 1:8 regardless of the water's source.

• Mass of hydrogen in water = 0.111 g (or 11.1% by mass)
• Mass of oxygen in water = 0.889 g (or 88.9% by mass)

This illustrates the unwavering mass ratio due to the nature of atomic and molecular formation as explained by Dalton.

Decomposition of Water

The decomposition of water is an excellent demonstration of Dalton's Atomic Theory and the principles of stoichiometry. During decomposition, water breaks down into its elemental components – hydrogen and oxygen. This process unveils the constant mass ratio of these elements.
The measured quantities, where 1 g of water yields approximately 0.111 g of hydrogen and 0.889 g of oxygen, perfectly match the theoretical predictions of Dalton's concept of fixed atomic combinations. The early chemists confirmed the correctness of Dalton's theory through such observations. In decomposing water,

• Each water molecule breaks down into exactly two hydrogen atoms and one oxygen atom.
• This explains the precise 1:8 mass ratio between hydrogen and oxygen.

So when water is decomposed, regardless of its initial form or location, it confirms the unchangeable nature of chemical compounds as foreseen by Dalton's Atomic Theory.