Question

Several samples of methane gas, the primary component of natural gas, are decomposed into carbon and hydrogen. The masses of the carbon and hydrogen are then weighed, and the results are tabulated as shown here. Which of these does not follow the law of constant composition? a. \(4.0\) grams hydrogen and \(12.0\) grams carbon b. \(1.5\) grams hydrogen and \(4.5\) grams carbon c. \(7.0\) grams hydrogen and \(17.0\) grams carbon d. 10 grams hydrogen and 30 grams carbon

Short answer

Sample c (7.0 grams hydrogen and 17.0 grams carbon) does not follow the law of constant composition, as its ratio of hydrogen to carbon is different from that of the other samples.

Step-by-step solution

Understand the Law of Constant Composition

The Law of Constant Composition, also known as the Law of Definite Proportions, states that a chemical compound always contains exactly the same proportion of elements by mass. To check if the samples follow this law, calculate the ratio of the mass of hydrogen to the mass of carbon for each sample and compare them.

Calculate the Mass Ratios

Divide the mass of hydrogen by the mass of carbon for each sample to find the ratio:(a) Ratio for sample a: \(\frac{4.0 \text{ g H}}{12.0 \text{ g C}} = \frac{1}{3}\)(b) Ratio for sample b: \(\frac{1.5 \text{ g H}}{4.5 \text{ g C}} = \frac{1}{3}\)(c) Ratio for sample c: \(\frac{7.0 \text{ g H}}{17.0 \text{ g C}} = \approx 0.412\)(d) Ratio for sample d: \(\frac{10 \text{ g H}}{30 \text{ g C}} = \frac{1}{3}\)Samples a, b, and d have the same ratio of hydrogen to carbon, conforming to the law of constant composition.

Identify the Anomalous Sample

Sample c has a different ratio of hydrogen to carbon (approximately 0.412) compared to the constant ratio of 1:3 observed in samples a, b, and d. Therefore, sample c does not follow the Law of Constant Composition.

Key concepts

Chemical Compound Proportions

When studying chemistry, students learn that the composition of chemical compounds is incredibly consistent. This remarkable feature is governed by the Law of Constant Composition, which outlines how a chemical compound always features the exact elements in the same proportions by mass, regardless of the size of the sample or where the compound was sourced from. Taking methane gas as an example, its composition by mass should always be representative of its chemical formula, CH₄.

Understanding this is crucial when predicting how substances will behave when interacting with other chemicals. Consistent compound proportions also lend themselves to predictable physical and chemical properties, which allows chemists to identify substances and design reactions. Therefore, if a sample of methane does not conform to the established proportions, it suggests that either the sample is not pure methane, or there was an error in measuring the masses of carbon and hydrogen.

Mass Ratios in Chemistry

Delving into the world of chemical equations and reactions requires a solid grasp of mass ratios. In other words, chemists use mass ratios to describe the quantitative relationships between the amounts of substances involved in chemical reactions. For instance, in methane (CH₄), the mass ratio of hydrogen to carbon is a fixed value which can be determined experimentally.

In our exercise, careful calculation of the H to C mass ratios for different samples should ideally yield the same number if they are consistent with methane's chemical makeup. If students learn to apply this concept thoroughly by calculating and comparing these ratios, as shown in the provided solution, they can diagnose which samples align with methane's known composition and identify any outliers that do not fit this pattern. This skill is fundamental not only for validating the composition of compounds but also for stoichiometry in reactions where precise proportions dictate the outcome.

Chemical Law Validation

The significance of chemical laws goes beyond academic exercises; they provide a framework by which we can validate our understanding of the physical world. The Law of Constant Composition is routinely validated in laboratory settings where precise measurements can either reaffirm the law or expose deviations that could point to experimental errors or new phenomena.

For students, exercises like the decomposition of methane reinforce how to empirically validate chemical laws. By conducting measurements and calculations, they are practicing the scientific method—observing, hypothesizing, experimenting, and concluding. When a discrepancy arises, such as with sample c in our exercise, it's an invitation for inquiry. Was there an error in measurement, or is the sample not pure? Questions like these drive the scientific endeavor forward, and the pursuit of these answers strengthens our understanding and application of scientific laws like the Law of Constant Composition.