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

Expert verified
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 (\(H_2O\)). 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

01

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 = \(\frac{\text{mass of hydrogen}}{\text{mass of oxygen}}\)
02

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 \(1:8\).
03

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 (\(H_2O\)) 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.

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