Problem 91 - Chemistry A Molecular Approach

Question

Perform each unit conversion. MISSED THIS? Read Section 1.8; Watch \(K C V 1.8,\) IWE 1.8 a. \(27.8 \mathrm{~L}\) to \(\mathrm{cm}^{3}\) b. \(1898 \mathrm{mg}\) to \(\mathrm{kg}\) c. \(198 \mathrm{~km}\) to \(\mathrm{cm}\)

Step-by-Step Solution

Answer

\(27.8 \mathrm{L} = 27800 \mathrm{cm}^3, \quad 1898 \mathrm{mg} = 0.001898 \mathrm{kg}, \quad 198 \mathrm{km} = 19800000 \mathrm{cm}\)

Step 1: Convert Liters to Cubic Centimeters

To convert liters to cubic centimeters, remember that 1 liter is equivalent to 1,000 cubic centimeters. Multiply the number of liters by 1,000. Calculation: \(27.8 \mathrm{~L} \times 1000 = 27800 \mathrm{~cm}^3\)

Step 2: Convert Milligrams to Kilograms

To convert milligrams to kilograms, know that 1 kilogram is equivalent to 1,000,000 milligrams. Divide the number of milligrams by 1,000,000. Calculation: \(1898 \mathrm{mg} \times \frac{1}{1000000} = 0.001898 \mathrm{kg}\)

Step 3: Convert Kilometers to Centimeters

To convert kilometers to centimeters, remember that 1 kilometer is equivalent to 100,000 centimeters. Multiply the number of kilometers by 100,000. Calculation: \(198 \mathrm{~km} \times 100000 = 19800000 \mathrm{cm}\)

Key Concepts

Converting Liters to Cubic Centimeters in Chemistry

When working with volume measurements in chemistry, it's common to convert liters to cubic centimeters to align with the desired units for a particular task or experiment. One liter is defined as the volume of one kilogram of water at maximum density under standard pressure, which is also equivalent to 1,000 cubic centimeters (cm³) due to the conversion factor between these units. Therefore, to convert liters to cm³, you simply multiply the number of liters by 1,000.

Let's apply this conversion to an example:If we need to convert 27.8 liters to cubic centimeters, we do the calculation as follows:\[\begin{equation}27.8\, \text{L} \times 1000 = 27800\, \text{cm}^3\end{equation}\]This calculation shows that 27.8 liters of a substance would occupy 27,800 cubic centimeters of space. Understanding this conversion is fundamental when measuring liquids in smaller containers or working with reactions where precision in volume is crucial.

Transitioning Between Milligrams and Kilograms

When chemists work with mass, they might need to convert from a smaller unit like milligrams (mg) to a larger unit such as kilograms (kg) to report the mass of substances in a more convenient or understandable size. The metric system simplifies this transition with a straightforward conversion factor: there are 1,000,000 milligrams in one kilogram. To convert milligrams to kilograms, you divide the number of milligrams by 1,000,000.

For instance, if we convert 1898 mg to kilograms, the calculation would be:\[\begin{equation}1898\, \text{mg} \div 1000000 = 0.001898\, \text{kg}\end{equation}\]This tells us that 1898 mg of a substance is equivalent to 0.001898 kilograms, which could be important when recording the mass of active ingredients in medication or chemicals in a precise scientific formulation.

Converting Kilometers to Centimeters

Conversion between kilometers and centimeters may be required in a variety of scientific contexts, especially when measurements taken on a large scale need to be translated into a more practical unit for laboratory use or data analysis. Since one kilometer is equivalent to 100,000 centimeters, you multiply the number of kilometers by 100,000 to perform this conversion.

For an exercise converting 198 kilometers to centimeters, the calculation process would be straightforward:\[\begin{equation}198\, \text{km} \times 100000 = 19800000\, \text{cm}\end{equation}\]This conversion shows the relativity of scale in measurements. While 198 km can represent a considerable distance between two cities, when converted into centimeters, it provides a much larger figure that can be useful for detailed engineering plans, mapping, or scientific calculations where the centimeter is the standard unit of measurement.