Ethane and ethylene are two gases containing only hydrogen and carbon atoms. In a certain sample of ethane, \(4.53 \mathrm{~g}\) of hydrogen is combined with \(18.0 \mathrm{~g}\) of carbon. In a sample of ethylene, \(7.25 \mathrm{~g}\) of hydrogen is combined with \(43.20 \mathrm{~g}\) of carbon. (a) Show how the data illustrate the law of multiple proportions. (b) Suggest reasonable formulas for the two compounds.

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the reactants and products in a chemical reaction. This field is fundamental for understanding chemical formulas and reactions. When we look at a chemical equation, stoichiometry tells us how much of each substance is involved, allowing us to predict the amounts of products formed from given amounts of reactants.

For instance, when discussing the ethane and ethylene problem, stoichiometry helps us determine how the mass of hydrogen relates to the mass of carbon in these compounds. By using stoichiometric calculations, such as the hydrogen to carbon ratio, we can infer how these elements combine in different proportions to form distinct chemical compounds, which is a core aspect when discussing the law of multiple proportions.

Chemical formulas represent the composition of molecules and ionic compounds in terms of chemical symbols. A chemical formula shows the elements in the compound and the relative ratio of these elements. For example, the chemical formula for water, H₂O, tells us that each molecule consists of two hydrogen atoms and one oxygen atom.

In the context of ethane and ethylene, knowing the chemical formula is crucial for understanding the constitution of these compounds. Chemical formulas provide us with a straightforward representation that reflects the underlying stoichiometric principles governing the composition of these molecules.

The hydrogen to carbon ratio is a specific example of stoichiometric ratios and it denotes the number of hydrogen atoms for every carbon atom in a compound. This ratio is particularly important in organic chemistry where compounds are primarily made up of hydrogen and carbon, such as hydrocarbons.

In our problem, calculating the hydrogen to carbon ratio for ethane and ethylene and then comparing them shows how the law of multiple proportions is at play. By expressing the elemental composition as a ratio, it simplifies understanding the different ways in which hydrogen and carbon can combine to form various substances, each with unique properties and structures.

The empirical formula of a compound provides the simplest whole-number ratio of elements in a compound. It's essential for the calculation to start with the mass of each element, as seen in the problem we're tackling with ethane and ethylene. To calculate an empirical formula, one must:

• Convert the mass of each element to moles by dividing by the atomic mass.
• Divide the mole quantities by the smallest number of moles to get a simple whole number ratio.

After determining the simplest ratio, we deduce the empirical formula. In our case, the empirical formula is a crucial step in establishing the law of multiple proportions and finding the most reasonable formula for ethane (C₂H₆) and ethylene (C₂H₄), based on the calculated hydrogen to carbon mass ratios.