In the United States, the emissions limit for carbon monoxide in motorcycle engine exhaust is 12.0 g of carbon monoxide per kilometer driven. What is this limit expressed in mg per mile with the correct number of significant figures?

Verified step by step guidance

1. Convert the emissions limit from grams to milligrams. Since 1 gram is equal to 1000 milligrams, multiply 12.0 g by 1000 to convert to mg.
2. Convert kilometers to miles. Use the conversion factor: 1 kilometer is approximately 0.621371 miles.
3. Divide the emissions limit in milligrams by the conversion factor to express the limit in mg per mile.
4. Ensure the final answer has the correct number of significant figures. The original value, 12.0 g, has three significant figures, so the final result should also have three significant figures.
5. Compile the result, ensuring all units are correctly labeled as mg per mile.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this question, we need to convert grams of carbon monoxide per kilometer to milligrams per mile. This involves using conversion factors, such as knowing that 1 gram equals 1000 milligrams and that 1 kilometer equals approximately 0.621371 miles.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. When performing calculations, especially conversions, it is essential to maintain the correct number of significant figures based on the precision of the given data. In this case, the emissions limit of 12.0 g/km has three significant figures, which will guide how we express the final answer.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another by multiplying by conversion factors. It ensures that units cancel appropriately, leading to the desired unit in the final answer. This method is particularly useful in chemistry for ensuring that calculations involving different units are accurate and consistent.