Problem 86 - Chemistry: The Central Science

Question

Using the following list of normal boiling points for a series of hydrocarbons, estimate the normal boiling point for octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\) : propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8},-42.1{ }^{\circ} \mathrm{C}\right)\), bu- tane \(\left(\mathrm{C}_{4} \mathrm{H}_{10},-0.5^{\circ} \mathrm{C}\right)\), pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}, 36.1^{\circ} \mathrm{C}\right)\), hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}, 68.7^{\circ} \mathrm{C}\right)\), heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}, 98.4{ }^{\circ} \mathrm{C}\right) .\) Explain the trend in the boiling points.

Step-by-Step Solution

Answer

The estimated normal boiling point of octane (\(\mathrm{C}_8\mathrm{H}_{18}\)) is around \(128.1\,^{\circ}\mathrm{C}\). The boiling points of hydrocarbons increase with the number of carbons, due to larger molecular size and stronger intermolecular forces (dispersion forces), which require more energy to separate the molecules.

Step 1: Collect data

Organize the given boiling points of hydrocarbons in a table: | Hydrocarbon | Boiling Point (°C) | |-------------|-------------------| | C3H8 | -42.1 | | C4H10 | -0.5 | | C5H12 | 36.1 | | C6H14 | 68.7 | | C7H16 | 98.4 |

Step 2: Observe the trend

Analyze the data to observe the trend of boiling points as the number of carbons in the hydrocarbons increases. As we can see, the boiling point tends to increase in a linear manner from propane to heptane.

Step 3: Extrapolate the trend

To estimate the boiling point of octane (C8H18), we can extrapolate the trend that we observed for the other hydrocarbons. Calculate the increase in boiling point from heptane to octane. A crude estimation can be calculated from the increase between hexane and heptane: Difference between hexane and heptane boiling points: \(98.4\,^{\circ}\mathrm{C} - 68.7 \,^{\circ}\mathrm{C} = 29.7\,^{\circ}\mathrm{C}\) Assuming this trend continues, we can add the calculated difference to the boiling point of heptane to estimate the boiling point of octane: Estimate for octane boiling point: \(98.4\,^{\circ}\mathrm{C} + 29.7\,^{\circ}\mathrm{C} \approx 128.1\,^{\circ}\mathrm{C}\) So, the estimated normal boiling point of octane would be around \(128.1\,^{\circ}\mathrm{C}\).

Step 4: Explain the trend

The boiling points of hydrocarbons depend mainly on the following factors: size of the molecule, shape of the molecule, and strength of the intermolecular forces (dispersion forces). Dispersion forces are generally stronger as the molecules get larger which in turn increases boiling points. In this series of hydrocarbons, as the number of carbons in the chain increases, the molecular size also increases. This results in stronger intermolecular forces between the hydrocarbon molecules, specifically dispersion forces. Due to these stronger forces, more energy is required to separate the molecules, leading to a higher boiling point. Consequently, there is a trend of increasing boiling points as the number of carbons in the hydrocarbon chain increases.

Key Concepts

Hydrocarbon Boiling Points

Understanding the boiling points of hydrocarbons is essential when studying organic chemistry. The boiling point is the temperature at which a substance changes from a liquid to a gas, and for hydrocarbons, this varies greatly with molecular structure. Hydrocarbons are compounds composed solely of carbon and hydrogen. Simple hydrocarbons like methane have very low boiling points, while larger ones like octane have much higher boiling points.

The size of the molecule is a crucial factor influencing the boiling point. As hydrocarbons increase in carbon chain length, their surface area grows, and they exhibit greater van der Waals forces, which are weak intermolecular attractions. This increased attraction requires more heat energy to overcome, thus elevating the boiling point. Therefore, a hydrocarbon with a longer carbon chain will generally have a higher boiling point than one with a shorter carbon chain, as seen with the transition from butane to octane in our exercise.

Intermolecular Forces

Intermolecular forces are the interactions that occur between molecules and are a key factor in determining boiling points. There are several types of intermolecular forces, with dispersion forces (or London forces) being the predominant type in hydrocarbons. Despite being the weakest intermolecular force, dispersion forces are significant as they are present in all molecules, and their strength increases with the size and shape of the molecule.

Dispersion forces result from the movement of electrons that create temporary dipoles within molecules. Larger hydrocarbons have more electrons and a greater surface area that can interact, resulting in stronger dispersion forces. This is the main reason larger hydrocarbons, such as octane in our example, have a higher boiling point than smaller ones like propane.

Trend Analysis

Trend analysis is a key scientific and mathematical method, particularly useful in chemistry, for predicting unmeasured aspects of a substance based on the observed properties of related substances. By analyzing the pattern in boiling points of a series of hydrocarbons, we can predict with reasonable accuracy the boiling point of unlisted members of the series, such as octane.

This process involves plotting boiling points against the number of carbon atoms and examining the trajectory of the resulting line. If the points form a consistent and predictable pattern, this pattern can be extended to estimate the boiling points of similar compounds. In the case of hydrocarbons, this trend is typically linear, with longer carbon chains correlating with higher boiling points. By extrapolating the linear trend observed from propane to heptane, we can estimate the boiling point of octane to further support our understanding of hydrocarbon behaviors.