In methane, one part hydrogen combines with three parts carbon by mass. If a sample of a compound containing only carbon and hydrogen contains 32.0 g of carbon and 8.0 g of hydrogen, could the sample be methane? If the sample is not methane, show that the law of multiple proportions is fol-lowed for methane and this other substance.

Verified step by step guidance

1. Determine the mass ratio of carbon to hydrogen in methane. Methane (CH₄) has a molar mass of 12.01 g/mol for carbon and 1.01 g/mol for hydrogen. Since there are four hydrogen atoms, the total mass of hydrogen in methane is 4.04 g/mol. Therefore, the mass ratio of carbon to hydrogen in methane is 12.01:4.04.
2. Calculate the mass ratio of carbon to hydrogen in the given sample. The sample contains 32.0 g of carbon and 8.0 g of hydrogen, so the mass ratio is 32.0:8.0.
3. Compare the mass ratios. Simplify both ratios to see if they are equivalent. The ratio for methane simplifies to approximately 3:1, while the ratio for the sample simplifies to 4:1.
4. Since the mass ratios are not the same, the sample is not methane. The sample has a different carbon to hydrogen ratio, indicating it is a different compound.
5. To show the law of multiple proportions, note that the ratio of the two mass ratios (4:1 for the sample and 3:1 for methane) is a simple whole number ratio, which is consistent with the law of multiple proportions.

Key Concepts

Law of Definite Proportions

The Law of Definite Proportions states that a chemical compound always contains its component elements in fixed ratio by mass. For methane (CH4), the ratio of carbon to hydrogen by mass is 12:4 or 3:1. This law helps determine if a given sample could be a specific compound based on its elemental composition.

Law of Multiple Proportions

The Law of Multiple Proportions states that when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other element are in a ratio of small whole numbers. This principle can be used to compare the ratios of carbon and hydrogen in methane and another compound to demonstrate that they adhere to this law.

Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements present. In the case of the sample with 32.0 g of carbon and 8.0 g of hydrogen, calculating the empirical formula will help determine if it corresponds to methane (CH4) or another compound, thus aiding in the analysis of its composition.