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

Dalton's atomic theory explains the decomposition of 1.000 g of water into 0.111 g of hydrogen and 0.889 g of oxygen, regardless of its source, through mass conservation and consistent mass ratios of elements. The decomposition reaction conserves mass, as the sum of hydrogen and oxygen produced equals the initial mass of water: \(0.111g_{H_{2}} + 0.889g_{O_{2}} = 1.000g_{H_{2}O}\). Additionally, the mass ratio of hydrogen to oxygen (\(\approx 0.125\)) remains the same for any source of water, further supporting Dalton's atomic theory.

Step-by-step solution

Understand the problem

We are given that when 1.000 g of water is decomposed, 0.111 g of hydrogen and 0.889 g of oxygen are obtained. We need to show that this outcome is consistent with Dalton's atomic theory, which states that the mass of the reactants should equal the mass of the products formed.

Mass conservation during the decomposition

If we decompose 1.000 g of water into its elements, the sum of the masses of hydrogen and oxygen produced should equal the mass of water that we started with, according to Dalton's theory. So, we have: Mass of hydrogen + Mass of oxygen = Mass of water \(0.111g_{H_{2}} + 0.889g_{O_{2}} = 1.000g_{H_{2}O}\) Thus, the mass is conserved during the decomposition of water, which is supported by Dalton's atomic theory.

Relative proportions of hydrogen and oxygen in water

Another aspect to consider is how the ratio of masses of hydrogen and oxygen remains the same, regardless of the source of the water. Let's calculate the mass ratio of hydrogen to oxygen: Ratio = (Mass of hydrogen) / (Mass of oxygen) \(= \frac{0.111g_{H_{2}}}{0.889g_{O_{2}}}\) \(≈ 0.125\) The mass ratio of hydrogen to oxygen is approximately 0.125. This holds true for any source of water, meaning that these proportions are consistent, which also supports Dalton's atomic theory. In conclusion, Dalton's atomic theory accounts for the fact that when 1.000 g of water is decomposed into its elements, 0.111 g of hydrogen and 0.889 g of oxygen are obtained regardless of the source of the water through mass conservation during reactions and consistent mass ratios of elements.