Problem 97 - Chemistry and Chemical Reactivity

Question

About two centuries ago, Benjamin Franklin showed that 1 teaspoon of oil would cover about 0.5 acre of still water. If you know that \(1.0 \times 10^{4} \mathrm{m}^{2}=2.47\) acres, and that there is approximately \(5 \mathrm{cm}^{3}\) in a teaspoon, what is the thickness of the layer of oil? How might this thickness be related to the sizes of molecules?

Step-by-Step Solution

Answer

The oil layer thickness is approximately \(2.47 \times 10^{-9}\) m, which is similar to molecular size.

Step 1: Convert Area to Square Meters

First, we need to convert the area covered by the oil from acres to square meters using the given conversion factor. We have 0.5 acre, and we know that 1 acre is equivalent to \( \frac{1.0 \times 10^4 \ \text{m}^2}{2.47} \). Hence, the area covered by the oil is: \[\frac{1.0 \times 10^4 \ \text{m}^2}{2.47} \times 0.5 = \frac{5.0 \times 10^3 \ \text{m}^2}{2.47} \approx 2023.32 \ \text{m}^2\]

Step 2: Convert Volume to Cubic Meters

Next, we convert the volume of oil from cubic centimeters to cubic meters. We know that 1 cm³ equals \(1 \times 10^{-6}\) m³, and a teaspoon is approximately 5 cm³: \[5 \ \text{cm}^3 = 5 \times 10^{-6} \ \text{m}^3\]

Step 3: Calculate the Thickness of the Oil Layer

Use the formula for volume, \( V = A \times h \), where \( V \) is the volume, \( A \) is the area, and \( h \) is the thickness. Rearrange this to find \( h \): \[h = \frac{V}{A} = \frac{5 \times 10^{-6} \ \text{m}^3}{2023.32 \ \text{m}^2} \approx 2.47 \times 10^{-9} \ \text{m}\]This thickness suggests that the oil layer is extremely thin, likely on the order of magnitude of molecular sizes.

Key Concepts

Molecular Layer Thickness

Understanding the thickness of a molecular layer is essential in surface chemistry. In the context of this exercise, we aim to find out how thinly a layer of molecules, like oil, can spread over a surface. When we say that a layer is a few molecules thick, we mean it is extremely thin—sometimes as thin as a single molecule.

In the exercise, the thickness of the oil layer was calculated using the volume and the area it covered. The thinness can be compared to the size of molecules themselves. With a calculated thickness of approximately \(2.47 \times 10^{-9} \ \text{m}\), this means our layer is roughly as thick as certain molecules, reinforcing the concept of a molecular monolayer.

This monolayer concept is fundamental in surface chemistry applications such as coatings, where a single layer of molecules may significantly alter surface properties like friction and hydrophobicity.

Volume Conversion

Volume conversion is crucial when dealing with different measurement units. In the exercise, the volume is given in cubic centimeters (cm³), which is commonly used in kitchen measurements, such as teaspoons. However, scientific calculations often require us to convert to cubic meters (m³).

To convert from cm³ to m³, use the factor \(1 \ \text{cm}^3 = 1 \times 10^{-6} \ \text{m}^3\). So, when we convert 5 cm³ (the volume of one teaspoon) to cubic meters, the result is \(5 \times 10^{-6} \ \text{m}^3\).

Being able to perform such conversions accurately ensures that calculations are precise and meaningful, especially when estimating physical properties like the thickness of a layer.

Area Conversion

Area conversion is another vital component in surface chemistry calculations. In this exercise, the area covered by the oil spill is initially given in acres, a unit more commonly used in land measurements.

The challenge is converting acres to the more universally used square meters (m²) for scientific calculations. Here, the conversion factor is provided: 1 acre equals approximately \(4046.86 \ \text{m}^2\). For a 0.5 acre area, the conversion to square meters is done using this exact factor, resulting in \(2023.32 \ \text{m}^2\).

Converting area this way allows for uniformity in calculations, making it easier to use measurements in different systems, facilitating global scientific communication and understanding.

Benjamin Franklin

Benjamin Franklin, a prominent figure in American history, was also a pioneering scientist with a keen interest in chemistry and natural phenomena. This historical context enriches the understanding of his experiment with oil on water.

Franklin's experiment, where he spread a teaspoon of oil over water to observe its surface coverage, was a demonstration of the concept of molecular layer thickness. His keen observation of how a tiny amount of oil could spread so thinly over a large area was an early exploration into surface chemistry.

In analyzing these phenomena, Franklin contributed to the foundational understanding of molecules and their interactions at surfaces, helping to pave the way for modern chemistry. His work illustrates how curiosity and a simple experiment can lead to broader scientific insights.