Question

Indicate whether each statement is true or false. (a) Pentane has a higher molar mass than hexane. (b) The longer the linear alkyl chain for straight- chain hydrocarbons, the higher the boiling point. (c) The local geometry around the alkyne group is linear. (d) Propane has two structural isomers.

Short answer

(a) False: Pentane has a molar mass of 72 g/mol, while hexane has a molar mass of 86 g/mol, making hexane's molar mass higher. (b) True: Boiling points of straight-chain hydrocarbons increase with increasing chain length due to increased London dispersion forces. (c) True: The local geometry around the alkyne group is linear, as the hybridization of each carbon atom in the triple bond is sp and the ideal bond angle is 180°. (d) False: Propane has only one structural isomer, which is itself.

Step-by-step solution

Statement (a): Pentane has a higher molar mass than hexane.

Pentane (C5H12) has 5 carbon atoms and 12 hydrogen atoms, while hexane (C6H14) has 6 carbon atoms and 14 hydrogen atoms. The molar mass of carbon is 12 g/mol, and the molar mass of hydrogen is 1 g/mol. Thus, the molar mass of pentane is (5 × 12) + (12 × 1) = 72 g/mol, and the molar mass of hexane is (6 × 12) + (14 × 1) = 86 g/mol. Since hexane has a higher molar mass than pentane, the statement is false.

Statement (b): The longer the linear alkyl chain for straight-chain hydrocarbons, the higher the boiling point.

Straight-chain hydrocarbons have increased boiling points with increasing chain length because of the increased London dispersion forces, which are caused by an increase in the electron cloud surrounding the hydrocarbon molecule. As the chain length in straight-chain hydrocarbons increases, the boiling point increases. The statement is true.

Statement (c): The local geometry around the alkyne group is linear.

An alkyne group consists of a triple bond between two carbon atoms, which comprises of one sigma bond and two π bonds. The hybridization of each carbon atom in the triple bond is sp, which consists of two electron domains. When there are only two electron domains surrounding an atom, the electron domain geometry is linear, and the ideal bond angle is 180°. Hence, the local geometry around the alkyne group is linear. The statement is true.

Statement (d): Propane has two structural isomers.

Propane has the molecular formula C3H8, consisting of three carbon atoms and eight hydrogen atoms. The simplest structure of propane is a straight-chain hydrocarbon, with the three carbon atoms bonded in a linear way. Due to the small size of the propane molecule, there are no other possible arrangements of carbon atoms without forming a different compound. Hence, propane has only one structural isomer, which is itself. The statement is false.

Key concepts

Molar Mass Comparison

Understanding molar mass is vital in organic chemistry. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It's calculated by summing the atomic masses of all atoms in a molecule. For instance, consider the molar mass comparison between pentane and hexane. Pentane (C5H12) has 5 carbon atoms and 12 hydrogen atoms, whereas hexane (C6H14) has 6 carbon atoms and 14 hydrogen atoms. Given the atomic masses of carbon (12 g/mol) and hydrogen (1 g/mol), pentane’s molar mass is calculated as \((5 \times 12) + (12 \times 1) = 72 \text{ g/mol}\), and that of hexane as \((6 \times 12) + (14 \times 1) = 86 \text{ g/mol}\).

This indicates hexane has a higher molar mass than pentane.

Alkane Boiling Points

The boiling point of an alkane depends on its molecular structure. For straight-chain alkanes, the boiling point generally increases with the length of the carbon chain. This pattern emerges because longer chains have a larger surface area leading to an increase in London dispersion forces—weak intermolecular attractions that occur due to temporary dipoles in the electron cloud surrounding a molecule.

As an example, when comparing butane (C4H10) to octane (C8H18), octane will have a higher boiling point due to its longer carbon chain and subsequently stronger London dispersion forces. This rule helps to deduce that, as given in the exercise, as the linear alkyl chain grows, so does the boiling point, making the statement that 'The longer the linear alkyl chain for straight-chain hydrocarbons, the higher the boiling point' true.

Alkyne Group Geometry

In organic chemistry, the geometry of molecular structures is key to understanding their properties. The alkyne group, characterized by a carbon-carbon triple bond, has a distinct linear geometry.

The triple bond consists of one sigma bond and two pi bonds, where the carbon atoms are sp hybridized. There are two electron domains around each carbon atom involved in the triple bond, translating to a linear spatial arrangement with a bond angle of approximately 180°. Thus, the local geometry around the alkyne group is indeed linear as stated in the exercise, providing a straightforward, predictable structure for these compounds.

Structural Isomers

Structural isomers are compounds with the same molecular formula but different arrangements of atoms. They can vary in the connectivity of their atoms or their spatial orientation. Isomers highlight the flexibility and diversity of organic structures.

Considering propane (C3H8), the molecule is too small to have alternative connectivity of atoms to form isomers; it has only a single structural form. This explains why the statement 'Propane has two structural isomers' is incorrect. However, larger alkanes with four or more carbon atoms can have structural isomers, indicating the complexity and the fascinating nature of organic chemistry.