Problem 54 - Chemistry: The Central Science

Question

(a) If an electric car is capable of going \(225 \mathrm{~km}\) on a single charge, how many charges will it need to travel from Seattle, Washington, to San Diego, California, a distance of \(1257 \mathrm{mi}\), assuming that the trip begins with a full charge? (b) If a migrating loon flies at an average speed of \(14 \mathrm{~m} / \mathrm{s}\), what is its average speed in mi/hr? (c) What is the engine piston displacement in liters of an engine whose displacement is listed as 450 in. \(^{3}\) ? (d) In March 1989 the Exxon Valdez ran aground and spilled 240,000 barrels of crude petroleum off the coast of Alaska. One barrel of petroleum is equal to \(42 \mathrm{gal}\). How many liters of petroleum were spilled?

Step-by-Step Solution

Answer

(a) The electric car requires 9 full charges to travel from Seattle, Washington to San Diego, California. (b) The average speed of a migrating loon is approximately 31.32 mi/hr. (c) The engine piston displacement in liters is approximately 7.37 L. (d) Approximately 38,062,632 liters of petroleum were spilled in the Exxon Valdez incident.

Step 1: (a) Conversion of distance to charges needed

First, find out how many miles the electric car can travel on a single charge: 1 km = 0.621371 miles 225 km * 0.621371 miles/km = 139.808525 miles Now, divide the total miles (1257 mi) by the miles it can travel per charge (139.808525 mi): 1257 mi / 139.808525 mi/charge ≈ 8.99 charges Since the car cannot travel on a partial charge, it needs 9 full charges to complete the trip (assuming the trip starts with a full charge).

Step 2: (b) Conversion of m/s to mi/hr

To convert the average speed from m/s to mi/hr, use the following conversion factors: 1 m = 0.000621371 miles 1 hr = 3600 s 14 m/s * 0.000621371 mi/m * 3600 s/hr ≈ 31.318511 mi/hr The average speed of the migrating loon in miles per hour is approximately 31.32 mi/hr.

Step 3: (c) Conversion of cubic inches to liters

To convert the engine piston displacement from cubic inches to liters, use the following conversion factor: 1 in³ = 0.0163871 liters 450 in³ * 0.0163871 L/in³ ≈ 7.374195 L The engine piston displacement in liters is approximately 7.37 L.

Step 4: (d) Conversion of gallons to liters and calculation of petroleum spilled

To convert the petroleum spill from barrels to gallons to liters, use the following conversion factors: 1 barrel = 42 gallons 1 gallon = 3.78541 liters 240,000 barrels * 42 gal/barrel * 3.78541 L/gal ≈ 38,062,632 L Approximately 38,062,632 liters of petroleum were spilled in the Exxon Valdez incident.

Key Concepts

Distance Conversion in Chemistry

When dealing with chemical experiments or environmental studies, scientists often need to convert distances from one unit to another. In our example, the electric car's mileage on a single charge is given in kilometers, but the total distance for the trip is in miles. To solve for the number of charges, we convert kilometers to miles using the fact that 1 km is approximately equal to 0.621371 miles.

This step is crucial in chemistry for understanding the scale of reactions or the range of molecules' diffusion. For instance, in nanotechnology, one might need to convert nanometers to meters to appreciate the tiny scales at which these technologies operate. Similarly, environmental chemists might convert between miles and kilometers when measuring the spread of pollutants.

Using proper distance conversion ensures precise communication between international teams and accurate scientific analysis. It's important when documenting findings that can have global implications-for example, when calculating the distance pollutants travel in the atmosphere or the coverage area of an oil spill.

Speed Conversion in Chemistry

Speed conversion is particularly useful in kinetics, the study of the rates of chemical reactions. In the case of the migrating loon, the speed is converted from meters per second to miles per hour to match the units familiar to a particular audience or required by specific regulations or reports.

In a lab setting, chemists might measure reaction rates in one unit but need to report them in another, requiring a conversion similar to the one performed for the bird's average speed. For example, the diffusion speed of a gas might be observed in centimeters per second but reported in meters per hour in research papers. Knowing how to convert between these units is vital to accurately communicate findings and compare rates across different experiments and studies.

The ability to perform speed conversions allows chemists to relate their work to real-world contexts, such as environmental monitoring where wind speeds could be crucial in modeling the dispersion of pollutants.

Volume Conversion in Chemistry

Volume conversion is a fundamental skill in chemistry, as it allows for the quantification of substances in various states. Here, we see two examples: converting engine displacement from cubic inches to liters and gallons to liters for the volume of petroleum spilled.

Conversion factors like 1 in³ being equivalent to 0.0163871 liters and 1 gallon equaling 3.78541 liters are essential tools in a chemist's arsenal. Whether it's measuring reactants for a reaction, determining the yield of a product, or assessing the environmental impact of a spill, appropriate volume conversion ensures accuracy.

For chemists working in different industries or countries, the proficiency in converting volume units is indispensable. It's not just about getting the numbers right; it's also about adhering to legal standards and ensuring that data can be universally understood and applied to global challenges. In pharmaceuticals, for example, dosages are precise volumes often requiring conversion between metric and imperial units.

Problem-Solving in Chemistry

Problem-solving in chemistry entails a methodical approach to converting units, calculating concentrations, balancing reactions, and more. A chemist must appreciate the importance of dimensional analysis, which underlies all the conversions we've explored.

When incorporating problem-solving techniques, focus on clearly identifying what is given and what needs to be found and then setting up conversion factors to bridge the gap. This process requires a solid understanding of the relationships between different units. For example, knowing that volume can affect reaction rates or product yields in stoichiometric calculations.

Critical thinking and the application of chemistry principles to solve problems are at the heart of the scientific method. This includes everything from the synthesis of new compounds to the management of chemical spills, all of which rely on accurate data and calculations. Remember that in chemistry, as in these examples, context is key - understanding the purpose behind the calculations can often guide you to the correct method and solution.