Question

105\. Suppose your car is rated at \(45 \mathrm{mi} /\) gal for highway use and 38 \(\mathrm{mi} /\) gal for city driving. If you wanted to write your friend in Spain about your car's mileage, what ratings in kilometers per liter would you report?

Short answer

The car's mileage ratings in kilometers per liter would be approximately 19.13 km/L for highway use and 16.15 km/L for city driving.

Step-by-step solution

Convert highway mileage from miles per gallon to kilometers per gallon

To convert highway mileage from miles per gallon to kilometers per gallon, we will multiply the mileage by the conversion factor of miles to kilometers: \(45 \frac{mi}{gal} * 1.60934 \frac{km}{mi}\). \(45 \frac{mi}{gal} * 1.60934 \frac{km}{mi} = 72.4203 \frac{km}{gal}\)

Convert highway mileage from kilometers per gallon to kilometers per liter

To convert highway mileage from kilometers per gallon to kilometers per liter, we will divide the value by the conversion factor between gallons and liters: \(72.4203 \frac{km}{gal} * \frac{1}{3.78541} \frac{gal}{L}\). \(72.4203 \frac{km}{gal} * \frac{1}{3.78541} \frac{gal}{L} = 19.1322 \frac{km}{L}\)

Convert city mileage from miles per gallon to kilometers per gallon

To convert city mileage from miles per gallon to kilometers per gallon, we will multiply the mileage by the conversion factor of miles to kilometers: \(38 \frac{mi}{gal} * 1.60934 \frac{km}{mi}\). \(38 \frac{mi}{gal} * 1.60934 \frac{km}{mi} = 61.155 \frac{km}{gal}\)

Convert city mileage from kilometers per gallon to kilometers per liter

To convert city mileage from kilometers per gallon to kilometers per liter, we will divide the value by the conversion factor between gallons and liters: \(61.155 \frac{km}{gal} * \frac{1}{3.78541} \frac{gal}{L}\). \(61.155 \frac{km}{gal} * \frac{1}{3.78541} \frac{gal}{L} = 16.1526 \frac{km}{L}\) So for the car's mileage ratings in kilometers per liter, you would report approximately 19.13 km/L for highway use and 16.15 km/L for city driving to your friend in Spain.

Key concepts

Unit Conversion

Understanding unit conversions is essential in various scientific calculations and everyday situations. In the context of fuel efficiency, converting miles per gallon (mpg) to kilometers per liter (km/L) allows for meaningful comparisons across different regions using different measurement units. At its core, unit conversion is the process of multiplying or dividing a numerical value by conversion factors to change the units while keeping the same physical quantity.

When converting mpg to km/L, two important conversion factors are used: the length unit conversion (miles to kilometers) and the volume unit conversion (gallons to liters). This process involves multiplying the mpg value by the number of kilometers in a mile (1.60934 km/mi) and then dividing by the number of liters in a gallon (3.78541 L/gal). The result gives us the fuel efficiency in km/L, which can be more relatable for regions where the metric system is the standard.

Miles per Gallon to Kilometers per Liter

Fuel efficiency measurements often use the metric system outside the United States. Thus, the conversion from miles per gallon to kilometers per liter becomes particularly useful. This conversion involves two primary steps:

Firstly, convert miles to kilometers by multiplying the given mpg by the factor 1.60934, since there are 1.60934 kilometers in one mile. Secondly, convert gallons to liters by dividing the kilometers per gallon result by 3.78541, the number of liters in one gallon. This sequential operation ensures that the resulting fuel efficiency reflects the same distance traveled and fuel consumed, but in different units of measurement.

Therefore, by converting 45 mpg and 38 mpg to km/L, a more universally understandable measure is obtained, which in this case is approximately 19.13 km/L for highway use and 16.15 km/L for city driving.

Chemistry Mathematical Problems

Many chemistry problems require complex unit conversions, as they often involve quantities in various units that need to be compared or combined. Specifically, this applies to stoichiometry, gas laws, and concentration calculations. A strong understanding of how to convert units is invaluable.

In this exercise, we apply these conversion skills to a real-world scenario — calculating a car's fuel efficiency in different units. Although not a typical 'chemistry problem,' it relies on the same mathematical principles. The precise control over unit conversions is a fundamental skill that proves useful not only in academic tasks but also in real life, enabling us to make informed decisions about efficiency, consumption, and environmental impact based on numerical data from diverse sources.