Identify the postulate of Dalton's theory that is violated by the following observations: \(59.95 \%\) of one sample of titanium dioxide is titanium; \(60.10 \%\) of a different sample of titanium dioxide is titanium.

Understanding the composition of chemical compounds is a fundamental aspect of chemistry that was significantly influenced by John Dalton's Atomic Theory. Dalton proposed that compounds are made up of atoms, the smallest indivisible units of matter. These atoms combine to form molecules of the compound.

Dalton's theory suggested that each molecule of a compound consists of a specific combination of atoms from different elements. Moreover, these atoms are not just randomly thrown together; they combine in precise ratios. For example, water (H2O) always consists of two hydrogen atoms for every oxygen atom. This applies universally, meaning that no matter where you find a sample of water, its atomic composition remains constant.

The theory also implies that the properties of compounds are determined by the types of atoms they consist of and how these atoms are arranged. As a learner, picturing compounds as set patterns or structures of atoms can be a useful way to understand how their properties emerge from their atomic composition.

Among the most revolutionary ideas from Dalton's Atomic Theory is the concept that elements combine in whole-number ratios to form chemical compounds. What does this mean for students today? It signifies that when atoms unite, they do so in proportions that can be expressed as whole numbers, which is reflective of their discrete, particulate nature.

Let's take sodium chloride (table salt) as an example. For every sodium atom (Na) in salt, there is exactly one chloride atom (Cl) to form NaCl. This 1:1 ratio complies with Dalton's postulate and is true regardless of the sample size. If you had a larger sample, say you were to look at a mole of salt, which contains around 6.022 x 10²³ formula units, the ratio of sodium to chloride atoms would still be 1:1.

This concept introduces students to the orderly and predictable nature of chemical reactions. It also sets the stage for more complex stoichiometry calculations, where students learn to predict the amounts of reactants and products involved in chemical reactions.

A pivotal aspect of Dalton's Atomic Theory is the principle of fixed composition, which states that any given compound is formed by combining elements in a fixed ratio by mass, and this ratio is consistent for all samples of the compound. This means that no matter the source of the sample or the conditions under which it's examined, the ratio remains constant.

The exercise about the varying composition of titanium dioxide samples presents an apparent contradiction to this principle. In a real-world setting, such variations can be due to experimental error, the presence of isotopes, or impurities in the sample. However, for the purpose of this exercise, and within the scope of Dalton's original theory, the different mass percentages are not explained, thereby showing a limitation to the theory.

When studying compounds, especially for homework exercises, it is crucial to consider Dalton's fixed composition under ideal conditions. Recognizing that real samples can exhibit minor variations prepares students for understanding the complexity of real-world chemistry where pure substances and ideal conditions are the exceptions rather than the rule.