Problem 60 - Chemistry: The Central Science in SI Units, Global Edition

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. \({ }^{3} ?(\mathbf{d})\) In March \(1989,\) the Exxon Valdezranagroundand spilled 240,000 barrels of crude petroleum off the coast of Alaska. One barrel of petroleum is equal to 42 gal. How many liters of netroleum were spilled?

Step-by-Step Solution

Answer

The electric car will need 9 charges to travel from Seattle to San Diego. The migrating loon has an average speed of approximately 31.32 mi/hr. The engine piston displacement is approximately 7.37 L. The Exxon Valdez spilled approximately 38,122,308 L of petroleum.

Step 1: Convert miles to kilometers

We are given the distance from Seattle to San Diego as 1257 mi. To convert this distance to kilometers, use the following conversion: 1 mi = 1.60934 km So, the distance in kilometers is: \(1257 \mathrm{~mi} \times 1.60934 \frac{\mathrm{km}}{\mathrm{mi}} \approx 2023.42 \mathrm{~km}\)

Step 2: Calculate the number of charges required

The electric car can travel up to 225 km on a single charge. To find out how many charges are needed to travel 2023.42 km, divide the total distance by the distance per charge and round up to the nearest whole number: Number of charges = \(\left\lceil\frac{2023.42 \mathrm{~km}}{225 \mathrm{~km}}\right\rceil \approx 9\) So, the electric car will need 9 charges to travel from Seattle to San Diego. ##Part (b)##

Step 1: Convert meters per second to miles per hour

The migrating loon flies at an average speed of 14 m/s. To convert this speed to miles per hour, use the following conversion: 1 m/s = 2.23694 mi/hr So, the average speed in miles per hour is: \(14 \frac{\mathrm{m}}{\mathrm{s}} \times 2.23694 \frac{\mathrm{mi/hr}}{\mathrm{m/s}} \approx 31.32 \mathrm{~mi/hr}\) ##Part (c)##

Step 1: Convert cubic inches to liters

The engine piston displacement is given as 450 in^3. To convert this volume to liters, use the following conversion: 1 in^3 = 0.0163871 L So, the engine piston displacement in liters is: \(450 \mathrm{~in^3} \times 0.0163871 \frac{\mathrm{L}}{\mathrm{in^3}} \approx 7.37 \mathrm{~L}\) ##Part (d)##

Step 1: Convert barrels to gallons

240,000 barrels of crude petroleum were spilled. One barrel is equal to 42 gallons. So, the total gallons of petroleum spilled is: \(240{,}000 \mathrm{~barrels} \times 42 \frac{\mathrm{gal}}{\mathrm{barrel}} = 10{,}080{,}000 \mathrm{~gal}\)

Step 2: Convert gallons to liters

To convert the gallons of petroleum to liters, use the following conversion: 1 gal = 3.78541 L So, the total liters of petroleum spilled is: \(10{,}080{,}000 \mathrm{~gal} \times 3.78541 \frac{\mathrm{L}}{\mathrm{gal}} \approx 38{,}122{,}308 \mathrm{~L}\)

Key Concepts

Electric Car Range Calculation

Electric car range calculation involves determining how far a car can travel on a single charge. This concept is important for planning long road trips.
To solve such a problem, start by converting measurements of distance if they are not in the same unit. For example, if the distance between two cities is given in miles but the car's range is in kilometers, a conversion is necessary. You can use the conversion factor:

• 1 mile = 1.60934 kilometers

Multiply the distance in miles by this factor to find out the distance in kilometers. Once the conversion is done, divide the total distance by the range of the car in kilometers per charge. This will result in the number of charges needed. Round up to the nearest whole number, because partial charges are not practical in planning. This type of calculation helps drivers ensure they have enough time and places to recharge their vehicles, making long trips feasible even in an electric car.

Speed Conversion

Understanding speed conversion is crucial when dealing with different metrics globally. This ensures you are following speed limits, planning travel times effectively, and comprehending scenario-based problems.
Consider a scenario where you need to convert speed from meters per second (m/s) to miles per hour (mi/hr). The formula for conversion is:

• 1 m/s = 2.23694 mi/hr

To convert a speed given in meters per second to miles per hour, simply multiply by this factor. For instance, a flying speed of 14 m/s would be converted by multiplying by 2.23694, resulting in approximately 31.32 mi/hr.
Speed conversion is particularly useful in understanding different speed limits in countries using the metric system versus those using the imperial system.

Engine Piston Displacement

Engine piston displacement is an important parameter in understanding an engine's capacity and power. It's often expressed in cubic inches (in³) for certain vehicles and must be converted to liters (L) for international standards.
To convert cubic inches to liters, use the conversion:

• 1 in³ = 0.0163871 L

For instance, if an engine displacement is provided as 450 in³, the volume in liters is calculated by multiplying by 0.0163871, resulting in about 7.37 liters.
Knowing the engine displacement in liters is essential for understanding fuel consumption rates and comparing different engines across regions using diverse standards.

Volume Conversion

Volume conversion is frequently needed in chemistry and environmental science, such as when dealing with oil spills. Understanding conversions among barrels, gallons, and liters ensures accuracy when communicating such quantities.
A typical conversion is from barrels to gallons, as seen in oil industry standards. One barrel of crude petroleum equals:

• 42 gallons

Once you have the volume in gallons, convert to liters by using:

• 1 gallon = 3.78541 liters

For example, if 240,000 barrels were spilled, this equals 10,080,000 gallons. To find the liters, multiply by 3.78541, which equals roughly 38,122,308 liters.
Accurate conversion of volumes ensures proper reporting and dealing with resources, from environmental incidents to manufacturing processes.