Problem 8 - Chemistry: The Central Science in SI Units, Global Edition

Question

Indicate whether each statement is true or false. (a) Ethane has a higher molar mass than ethene. (b) For molecules of the same homologous family, the higher the molecular mass, the higher the boiling point. (c) The local geometry around the alkene group is T-shaped. (d) Butene has two structural isomers.

Step-by-Step Solution

Answer

(a) True, since the molar mass of ethane (30.08 g/mol) is higher than that of ethene (28.06 g/mol). (b) True, as boiling points generally increase with molecular mass in the same homologous family due to stronger London dispersion forces or van der Waals forces. (c) False, the local geometry around the alkene group is not T-shaped, but trigonal planar due to sp^2 hybridization of the carbon atoms. (d) True, butene has two structural isomers: 1-butene (CH2=CHCH2CH3) and 2-butene (CH3CH=CHCH3).

Step 1: (a) Analyzing statement A

Ethane (C2H6) has a molecular formula of CH3CH3 while ethene (C2H4) has a molecular formula of CH2CH2. To determine if the statement is true or false, we need to calculate the molar mass of ethane and ethene and compare their values. Molar mass of ethane = (2 * 12.01) + (6 * 1.01) = 30.08 g/mol Molar mass of ethene = (2 * 12.01) + (4 * 1.01) = 28.06 g/mol Since the molar mass of ethane (30.08 g/mol) is higher than that of ethene (28.06 g/mol), the statement (a) is true.

Step 2: (b) Analyzing statement B

Molecules of the same homologous family have the same general formula and functional group, and differ by a fixed increment of CH2 in their molecular formulas. Typically, as the molecular mass increases, the boiling point also increases due to stronger London dispersion forces or van der Waals forces present between larger molecules. Thus, statement (b) is true.

Step 3: (c) Analyzing statement C

The local geometry around an alkene group is determined by the bond angles and hybridization of the carbon atoms involved in the double bond. In the case of an alkene, the carbon atoms are sp^2 hybridized, resulting in a trigonal planar geometry surrounding the carbon atoms. This means the statement (c) is false, as the geometry is not T-shaped.

Step 4: (d) Analyzing statement D

Butene (C4H8) has the following two structural isomers, with the double bond occurring between different carbon atoms: 1. 1-butene (CH2=CHCH2CH3) 2. 2-butene (CH3CH=CHCH3) As there are indeed two structural isomers for butene, the statement (d) is true. #Summary of Results# (a) True (b) True (c) False (d) True

Key Concepts

Molecular Mass

Molecular mass, often called molar mass, is an important concept in understanding the properties of chemical substances. It is the mass of one mole of a substance, typically measured in grams per mole (g/mol). The molecular mass is calculated by summing up the atomic masses of all the atoms present in a molecule.
For the specific example of ethane (C\(_2\)H\(_6\)) and ethene (C\(_2\)H\(_4\)), we identify that:

• Ethane's molar mass is higher because it contains more hydrogen atoms than ethene.
• Ethane's molar mass: \((2 \times 12.01) + (6 \times 1.01) = 30.08 \text{ g/mol}\).
• Ethene's molar mass: \((2 \times 12.01) + (4 \times 1.01) = 28.06 \text{ g/mol}\).

This demonstrates that even a small difference in the number of atoms can affect a substance's molecular mass. Understanding this concept is crucial when comparing substances on a molecular level.

Boiling Point

Boiling point refers to the temperature at which a substance changes from a liquid to a gas. It is influenced by several factors such as molecular size and the type of intermolecular forces present. For molecules in the same homologous series, there is a direct correlation between molecular mass and boiling point.
As molecular mass increases, the boiling point generally increases as well. This is due to:

• Stronger London dispersion forces (van der Waals forces) present in larger molecules.
• More significant surface area contact between molecules, enhancing intermolecular attractions.

Thus, in hydrocarbons like the alkanes and alkenes, the trend is clear: heavier molecules require more energy to transition to the gas phase, which results in a higher boiling point.

Alkene Geometry

Alkene geometry is a fascinating topic often explored in organic chemistry. Alkenes are hydrocarbons containing at least one carbon-carbon double bond. Their geometry is determined by the hybridization of the carbon atoms involved in the bond, which, in the case of alkenes, is sp\(^2\) hybridization.
This means that:

• The carbon atoms in an alkene are arranged in a trigonal planar geometry.
• Each double-bonded carbon atom forms 120-degree bond angles.
• This geometry is not T-shaped but rather flat or planar.

This geometric configuration significantly affects the physical and chemical properties of alkenes. It also influences how alkenes interact with other molecules and how they react in chemical reactions.

Structural Isomers

Structural isomers are molecules with the same molecular formula but different structural arrangements of atoms. In the example of butene (C\(_4\)H\(_8\)), the possibility of having different arrangements arises from shifting the position of the double bond among the carbon atoms.
Butene illustrates this concept by having two isomers:

• 1-butene (CH\(_2\)=CH-CH\(_2\)-CH\(_3\)): where the double bond is at the end of the carbon chain.
• 2-butene (CH\(_3\)-CH=CH-CH\(_3\)): where the double bond is between the second and third carbon atoms.

This structural variance results in different physical and chemical properties between isomers, even though they share the same formula. Understanding structural isomers is key for predicting and rationalizing the behavior of organic compounds in different reactions and environments.