Question

Two samples of carbon tetrachloride are decomposed into their constituent elements. One sample produces 38.9 g of carbon and 448 \(\mathrm{g}\) of chlo- rinc, and the other sample produces 14.8 \(\mathrm{g}\) of carbon and 134 \(\mathrm{g}\) of chlorine. Are these results consistent with the law of definite proportions? Show why or why not.

Short answer

The two mass ratios are 448 g chlorine / 38.9 g carbon = 11.52 and 134 g chlorine / 14.8 g carbon = 9.05, which are not equal. Therefore, these results are not consistent with the Law of Definite Proportions.

Step-by-step solution

- Calculate the Mass Ratios

First, find the mass ratios of chlorine to carbon for each sample by dividing the mass of chlorine by the mass of carbon. This will give the ratio of chlorine to carbon by mass for both samples.

- Compare the Ratios

After calculating the ratios for both samples, compare them to see if they are the same. The Law of Definite Proportions states that a chemical compound always contains exactly the same proportion of elements by mass. Therefore, if the ratios are the same, the results are consistent with the law.

- Conclude Consistency with the Law

If the obtained mass ratios are equal (or very close within experimental error), then the conclusion is that the samples are consistent with the Law of Definite Proportions. If they differ significantly, they would not be consistent with the law.

Key concepts

Chemical Compound Composition

Understanding the chemical compound composition is key to grasping the basics of chemistry. It refers to the parts that make up a compound and how these are proportionally arranged. A chemical compound is made up of two or more different types of atoms joined together by chemical bonds.

For instance, water (H₂O) consists of two hydrogen atoms and one oxygen atom. The ‘2’ in H₂O represents that there are two atoms of hydrogen for every one atom of oxygen, indicating the fixed composition. Similarly, carbon tetrachloride (CCl₄) has one atom of carbon bonded to four atoms of chlorine.

When compounds are decomposed, like in the exercise, they break down into their constituent elements. The mass of each element can then be used to verify whether the compound's composition aligns with established laws of chemistry, such as the Law of Definite Proportions, which tells us that regardless of the size of the sample, the proportion by mass of the elements in a chemical compound is always the same.

Mass Ratio in Chemistry

The mass ratio in chemistry is a crucial concept when it comes to understanding the composition of compounds. It expresses the relationship between the masses of different elements in a compound.

In a laboratory, if we break down a chemical compound, like carbon tetrachloride, we would end up with a specific amount of carbon and chlorine. The mass ratio can be calculated by dividing the mass of one element by the mass of another. For the purpose of the textbook exercise, we computed the ratios of chlorine to carbon by dividing their respective masses.

For example, the first mass ratio is calculated by:\[\begin{equation}\frac{448 \mathrm{g} \text{ of chlorine}}{38.9 \mathrm{g} \text{ of carbon}}\end{equation}\]The exact ratio is not as important as the question of whether this ratio remains constant across different samples of carbon tetrachloride. This constancy is what the Law of Definite Proportions is about, and it's a fundamental principle that allows chemists to understand and predict the behavior of chemical compounds.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in chemical reactions. The term is derived from two Greek words: ‘stoicheion’, meaning element, and ‘metron’, meaning measure.

In practice, stoichiometry enables chemists to predict the amounts of substances consumed and produced in a given reaction. It's based on the conservation of mass and the concept of moles, which is a unit of measure in chemistry representing a specific number of molecules.

The stoichiometric coefficients in a chemical equation represent the ratio in which molecules combine or result from the reaction. For example, the stoichiometry of the combustion of methane (CH₄) is represented by the equation:\[\begin{equation}CH₄ + 2O₂ → CO₂ + 2H₂O\end{equation}\]Here, 1 molecule of methane reacts with 2 molecules of oxygen to yield 1 molecule of carbon dioxide and 2 molecules of water. By understanding stoichiometry, students can grasp the 'how much' aspect of chemical reactions, which is crucial for practical applications such as pharmaceuticals, materials science, and energy production.