Question

Oil spreads on water to form a film about \(100 \mathrm{~nm}\) thick (two significant figures). How many square kilometers of ocean will be covered by the slick formed when one barrel of oil is spilled (1 barrel \(=31.5\) U.S. gal)?

Short answer

Answer: The oil slick will cover approximately 1.19 square kilometers of the ocean's surface.

Step-by-step solution

Write down the given information

The thickness of the oil film is \(100 \mathrm{~nm}\) (nanometers), and the volume of one barrel of oil is \(31.5\) U.S. gallons. First of all, we need to convert these values into meters and cubic meters, respectively.

Convert units

1 nanometer = \(10^{-9}\) meters. So, the thickness of the oil slick in meters is: \(100 \mathrm{~nm} = 100 \times 10^{-9} \mathrm{~m} = 1 \times 10^{-7} \mathrm{~m}\) 1 U.S. gallon is equal to \(3.78541 \times 10^{-3}\) cubic meters. So, the volume of one barrel of oil in cubic meters is: \(31.5 \mathrm{~gal} = 31.5 \times 3.78541 \times 10^{-3} \mathrm{~m^3} = 0.119 \mathrm{~m^3}\)

Find the surface area

Let the surface area of the ocean covered by the oil slick be A. Since volume is equal to area multiplied by thickness (height) of the oil slick, we can find A using the following equation: \(Volume = Area \times Thickness\) Substitute the given values and solve for A: \(0.119 \mathrm{~m^3} = A \times 1 \times 10^{-7} \mathrm{~m}\) \(A = \frac{0.119}{1 \times 10^{-7}} \mathrm{~m^2} = 1.19 \times 10^{6} \mathrm{~m^2}\)

Convert the surface area to square kilometers

1 square meter is equal to \(10^{-6}\) square kilometers. So, the surface area A in square kilometers is: \(1.19 \times 10^{6} \mathrm{~m^2} = 1.19 \times 10^{6} \times 10^{-6} \mathrm{~km^2} = 1.19 \mathrm{~km^2}\) The oil slick formed when one barrel of oil is spilled will cover approximately \(1.19 \mathrm{~km^2}\) of the ocean's surface.

Key concepts

Unit Conversion

Converting units is a fundamental skill in chemistry and other scientific disciplines. When working with measurements, you often need to switch between different unit systems to calculate and compare effectively. In this context, we have oil measurements in nanometers for thickness and gallons for volume.

• 1 nanometer (nm) is equal to \(10^{-9}\) meters. It's a very tiny measurement, which is important in fields like nanotechnology.
• 1 U.S. gallon equals approximately 3.78541 liters, which is also equivalent to \(3.78541 \times 10^{-3}\) cubic meters.

By knowing these conversions, we converted the oil film thickness to meters and the oil volume to cubic meters. This allowed us to perform calculations in consistent units, which is crucial for accuracy.

Volume and Surface Area Relationship

The relationship between volume and surface area is a key aspect of this problem. When oil spills on water, it disperses to cover the surface.

• Volume (\(V\)) of oil is distributed over a surface area (\(A\)) with a certain thickness (\(T\)).
• The relationship can be expressed as: \(V = A \times T\).

Using this equation, you can calculate how much area the oil will cover by dividing the volume by the thickness of the oil film.In our case, with a volume of 0.119 cubic meters and a thickness of \(1 \times 10^{-7}\) meters, you arrive at a surface area of \(1.19 \times 10^{6}\) square meters. This highlights how even a small volume can cover a large area, given the thinness of the film.

Measurement Units

Understanding and using the correct measurement units helps ensure precision in scientific problems. Different types of measurements require different unit types, and conversions might be necessary between systems like the metric and imperial systems.

• Length is often measured in meters, with variants like nanometers for extremely small measurements.
• Volume might be in liters or cubic meters, depending on the context.

Correct use of measurement units aids in communicating scientific findings clearly and helps maintain consistency across calculations, as seen when converting gallons to cubic meters in the solution. This is extremely important as errors in unit conversion can drastically affect the outcome of calculations.

Oil Spill Environmental Impact

Oil spills have significant environmental impacts, spreading rapidly over large areas and potentially affecting marine life and ecosystems. The computed spread area of 1.19 square kilometers from one barrel of oil illustrates a substantial effect.

• Oil can damage fish and other aquatic life by obstructing breathing and reducing light penetration.
• Seabirds and marine mammals might be directly exposed, hindering their insulation and buoyancy mechanisms.

Understanding the extent of coverage, as shown by calculations, aids in predicting containment efforts and environmental assessments. Calculating the area provides early insights into potential cleanup requirements and impact mitigation strategies.