According to the law of definite composition, in a chemical compound the constituent elements are always present in definite proportions by which quantity?

Introduction / Context:
One of the fundamental laws of classical chemistry is the law of definite proportions, also called the law of constant composition. It describes how elements combine to form a given compound. This law helps explain why water from different sources always has the same basic composition and why a pure compound has a fixed formula. The question asks what kind of proportion remains fixed for the constituent elements in a compound according to this law, distinguishing it from other quantities such as volume or size.

Given Data / Assumptions:

• A chemical compound is formed when two or more elements chemically combine in fixed ratios.
• The law of definite proportions states that these ratios are constant for a given compound.
• Possible proportional quantities include mass, volume and number of particles.
• We assume conditions where the compound is pure and the formula is well defined.

Concept / Approach:
The law of definite proportions states that a chemical compound always contains the same elements in the same fixed proportion by mass, regardless of the sample size or source. For example, water always contains hydrogen and oxygen in a mass ratio of about 1 to 8. This is a mass ratio, not a volume ratio. While the number of moles of each element in a formula is also fixed, the law is traditionally stated in terms of mass because early chemists measured reactants and products by weighing them. The correct approach is to choose the quantity that is explicitly mentioned in the law, which is mass.

Step-by-Step Solution:
Step 1: Recall the statement of the law of definite proportions: a given compound always contains elements combined in the same proportion by mass. Step 2: Apply this to water, H2O. One mole of water has a mass of approximately 18 grams, with about 2 grams of hydrogen and 16 grams of oxygen, giving a fixed mass ratio of hydrogen to oxygen of 1 to 8. Step 3: No matter how much water you have, the ratio of mass of hydrogen to mass of oxygen remains the same. Step 4: Volume is not used in the law because the volume of gases or liquids can change significantly with temperature and pressure. Step 5: The size of atoms is not relevant to the law, and the number of moles is a different way of expressing composition that came later in chemistry history. Step 6: Therefore, the correct answer is that elements in a compound are always present in fixed proportions by mass.

Verification / Alternative check:
Consider carbon dioxide, CO2. Each mole of CO2 contains 12 grams of carbon and 32 grams of oxygen, giving a constant mass ratio of carbon to oxygen of 3 to 8. If you decompose CO2 from any source, such as respiration or combustion, you always obtain carbon and oxygen in this same mass ratio. Early quantitative experiments by chemists like Joseph Proust confirmed such constant mass ratios for many compounds, leading to the formulation of the law of definite proportions. This historical and experimental evidence supports mass as the correct quantity for the law.

Why Other Options Are Wrong:
Option B, volume, depends on physical conditions like temperature and pressure, especially for gases, so volume ratios are not constant for a given compound. Option C, physical size of atoms, is a microscopic property that does not directly define composition in the law. Option D, number of moles only, is related to the formula, but the classical statement of the law focuses on mass, and different formulas such as CO and CO2 have different mole ratios. Option E claims no option is correct, which contradicts the well established wording of the law. Only option A correctly states that elements in a compound are always present in definite proportions by mass.

Common Pitfalls:
A common confusion is mixing the law of definite proportions with the law of multiple proportions, which deals with different compounds formed by the same elements. Another pitfall is focusing on the chemical formula and mole ratios without connecting back to mass ratios, which were historically measured. To avoid errors, remember that definite proportions refer to constant mass ratios for a given compound, while mole ratios and subscripts in formulas are another, more modern way of expressing the same idea.

Final Answer:
According to the law of definite composition, in a compound the elements are always present in definite proportions by Mass.