Question

Which of the following compounds of carbon and hydrogen have identical empirical formulas: \(\mathrm{CH}_{4}, \mathrm{C}_{2} \mathrm{H}_{4}\), \(\mathrm{C}_{3} \mathrm{H}_{6}, \mathrm{C}_{4} \mathrm{H}_{12}, \mathrm{C}_{6} \mathrm{H}_{6}\) ?

Short answer

C2H4 and C3H6 are the two compounds that have identical empirical formulas.

Step-by-step solution

Calculate Ratios

First, calculate the ratio of carbon to hydrogen in each compound. For CH4, the ratio is 1:4. For C2H4, the ratio is 2:4 or 1:2 on simplifying. C3H6 has a ratio of 3:6, or 1:2. The ratio in C4H12 is 4:12, or 1:3 and C6H6 has a 1:1 ratio.

Compare Ratios

Now we compare the simplified ratios. C2H4 and C3H6 both have a ratio of 1:2, so their empirical formulas are identical. No other compound shares this ratio.

Key concepts

Chemical Compound Ratios

Understanding the ratios of elements within chemical compounds is crucial when determining their empirical formulas. Empirical formulas represent the simplest whole number ratio of the atoms within a compound. To find these ratios, like in our exercise involving carbon and hydrogen compounds, we must divide the number of atoms of each element by the largest number that will yield whole numbers. For example, methane ((CH_4)) has one carbon atom to four hydrogen atoms (a 1:4 ratio).
In practice, it's essential first to identify the subscripts in the molecular formulas. Then, we look for the greatest common divisor that can be used to simplify these subscripts to their smallest possible whole numbers. This step is what takes us from a molecular formula, which shows the exact number of each atom, to the empirical formula that reflects the proportion of elements.
Consider the compound (C_6H_6); despite having more atoms, the ratio simplifies to a strikingly simple 1:1 ratio. The diversity of compounds and the simplicity of their empirical formulas showcase the elegance and efficiency of the chemical world, revealing how nature can create a variety of substances from the same basic building blocks—following a simple set of rules.

Simplifying Chemical Formulas

Simplifying chemical formulas is the process of reducing them to their simplest form—or their empirical formula. While the molecular formula gives us the exact number of each type of atom present, the empirical formula breaks this down to the simplest whole number ratio. To illustrate, ethene ((C_2H_4)) can be simplified to a 1:2 carbon to hydrogen ratio, demonstrating its empirical formula to be(CH_2).
Simplification is akin to reducing fractions in mathematics. For example, if a chemical formula has a ratio of 2:4, similar to reducing the fraction 2/4, we would divide both numbers by 2 to get the empirical formula with a 1:2 ratio. This process is invaluable in chemistry as it allows chemists to communicate substances succinctly and compare different compounds more effectively.
It's important to bear in mind that different compounds can have the same empirical formula while being distinct substances—for instance, ethene and propene. This phenomenon is called isomerism and signifies the variety and complexity of organic compounds. Understanding and applying these simplification principles, as seen in our example exercise, are fundamental skills for anyone delving into the chemical sciences.

Carbon and Hydrogen Compounds

Compounds consisting of only carbon and hydrogen are known as hydrocarbons. These are the simplest forms of organic compounds and exist in various structures, which drastically change their physical and chemical properties. Despite their structural diversity, the empirical formula for these compounds is often deceptively simple as it just represents the lowest whole number ratio of carbon to hydrogen atoms.
Hydrocarbons can be classified into alkanes, alkenes, and alkynes based on the types of bonds between carbon atoms. For instance, alkanes have single bonds as in butane ((C_4H_{10})), alkenes have double bonds as in ethene ((C_2H_4)), and alkynes have triple bonds as in acetylene ((C_2H_2)). When comparing their empirical formulas, we notice patterns in the ratios regardless of these different bonding arrangements.
A fascinating aspect of carbon and hydrogen compounds is that they can exhibit isomerism, meaning compounds have the same molecular formula but differ structurally and functionally. This adds another layer of complexity, as structural isomers have the same empirical formula, highlighting that empirical formulas alone don't always convey the complete picture of a compound's nature. As illustrated in our exercise, identifying empirical formulas is just the beginning—it's the intricate dance between structure and formula that makes organic chemistry so intriguing.