Problem 75 - Chemistry: The Central Science

Question

(a) What is a hydrocarbon? (b) Butane is the alkane with a chain of four carbon atoms. Write a structural formula for this compound, and determine its molecular and empirical formulas.

Step-by-Step Solution

Answer

A hydrocarbon is an organic compound composed only of hydrogen and carbon atoms, with alkanes being the simplest type containing only single bonds. Butane, an alkane, has the molecular formula \(C_4H_{10}\) and the structural formula CH3-CH2-CH2-CH3. Its empirical formula, representing the simplest whole number ratio of atoms, is \(C_2H_5\).

Step 1: (a) Definition of a Hydrocarbon

A hydrocarbon is an organic compound consisting only of hydrogen (H) and carbon (C) atoms. They can be found in various structures, such as linear chains, branched chains, and rings. The simplest type of hydrocarbons is alkanes, which only contain single bonds between carbon and hydrogen atoms.

Step 2: (b) Structural Formula for Butane

Butane is an alkane with a chain of four carbon atoms. The general formula of an alkane is \(C_nH_{2n+2}\), where n is the number of carbon atoms. In the case of butane, the formula will be \(C_4H_{10}\). The structural formula for butane is: H H H H | | | | C-C-C-C | | | | H H H H It can also be written more compactly as CH3-CH2-CH2-CH3 or simply as \(C_4H_{10}\).

Step 3: Molecular and Empirical Formulas for Butane

The molecular formula represents the actual number of atoms in a molecule. For butane, the molecular formula is \(C_4H_{10}\), as it has four carbon atoms and ten hydrogen atoms. The empirical formula represents the simplest whole number ratio of atoms in a compound. In the case of butane, you can observe that there is a 4:10 ratio between the number of carbon and hydrogen atoms in the molecule. You can simplify this ratio further by dividing both values by their greatest common divisor, which is 2. So, the simplified ratio becomes 2:5, which means that the empirical formula for butane is \(C_2H_5\).

Key Concepts

Alkanes

Alkanes are a fundamental group of hydrocarbons characterized by having only single bonds between carbon and hydrogen atoms. This makes them saturated hydrocarbons, meaning they have the maximum number of hydrogen atoms per carbon. Their general formula is given by \(C_nH_{2n+2}\), where \(n\) represents the number of carbon atoms in the molecule. Common examples include methane (\(CH_4\)), ethane (\(C_2H_6\)), and in our case, butane (\(C_4H_{10}\)).
Alkanes can be found in different forms:

• Linear chains: where carbon atoms are connected in a straight or continuous line.
• Branched chains: which have additional carbon branches off the main chain.
• Cyclic forms: where carbon atoms form a ring.

Understanding the structure and formula of alkanes is key, as it helps determine physical and chemical properties as well as the potential reactions they can undergo.

Molecular Formula

The molecular formula of a compound explicitly shows the number and type of atoms present in a molecule.
For example, butane, as an alkane with four carbon atoms, has a molecular formula of \(C_4H_{10}\). This tells us that each butane molecule contains exactly four carbon atoms and ten hydrogen atoms.
The molecular formula is crucial in identifying the composition of a substance. It helps scientists understand not only the type of elements present but also their ratio. This allows chemists to predict molecular weight, chemical behavior, and possible reactions when mixed with other substances. Molecular formulas are specific and crucial for understanding the precise nature of chemical substances.

Empirical Formula

The empirical formula of a chemical compound conveys the simplest whole number ratio of the atoms in the molecule. It simplifies the composition without considering the full molecular structure.
To determine the empirical formula of butane from the molecular formula \(C_4H_{10}\), you reduce the numbers to the smallest possible ratio. Here, there are four carbon atoms to ten hydrogen atoms, which can be simplified to a 2:5 ratio by dividing both numbers by the greatest common divisor, which is 2. Thus, the empirical formula for butane is \(C_2H_5\).
The empirical formula is often used for calculations in stoichiometry and to infer potential chemical behaviors. It tells us about relative quantities regardless of the actual molecular size, providing insights into both analysis and synthesis of chemical compounds.