Question

Perform the following conversions. a) \(0.674 \mathrm{~kL}\) to milliliters b) \(2.81 \times 10^{12} \mathrm{~mm}\) to kilometers c) \(94.5 \mathrm{~kg}\) to milligrams

Short answer

a) 674,000 mL; b) 2.81 x 10^6 km; c) 94,500,000 mg.

Step-by-step solution

Understand the Units

First, identify the units involved in each conversion. For part a, the units are kiloliters and milliliters. For part b, the units are millimeters and kilometers. For part c, the units are kilograms and milligrams.

Conversion Factors

Determine the appropriate conversion factors for each unit pair: - 1 kiloliter (kL) is equivalent to 1,000,000 milliliters (mL). - 1 kilometer (km) is equivalent to 1,000,000 millimeters (mm). - 1 kilogram (kg) is equivalent to 1,000,000 milligrams (mg).

Convert Kiloliters to Milliliters

For part a, convert 0.674 kL to milliliters:Use the conversion factor, \[ \text{Value in mL} = 0.674 ext{ kL} \times 1,000,000 \text{ mL/kL} = 674,000 \text{ mL} \]

Convert Millimeters to Kilometers

For part b, convert \(2.81 \times 10^{12} \text{ mm}\) to kilometers:Use the conversion factor,\[ \text{Value in km} = \frac{2.81 \times 10^{12} \text{ mm}}{1,000,000 \text{ mm/km}} = 2.81 \times 10^6 \text{ km} \]

Convert Kilograms to Milligrams

For part c, convert 94.5 kg to milligrams:Use the conversion factor,\[ \text{Value in mg} = 94.5 \text{ kg} \times 1,000,000 \text{ mg/kg} = 94,500,000 \text{ mg} \]

Key concepts

Metric System

The Metric System is a standardized system of measurement used globally, particularly in scientific contexts. It is decimal-based, meaning it operates on powers of ten, which makes it simpler to convert between units. The metric system uses a series of prefixes to denote different scales:

• Kilo- means one thousand times the base unit. For example, 1 kilometer (km) is 1,000 meters (m).
• Milli- signifies one-thousandth of the base unit. So, 1 millimeter (mm) is 0.001 meters.
• Centi- refers to one-hundredth of the base unit, such as 1 centimeter (cm) being 0.01 meters.

Knowing the metric prefixes aids in understanding how to manipulate and convert units within the system. For example, converting from kiloliters to milliliters involves moving through several scales (kilo to milli), while conversions like millimeters to kilometers require moving from milli to kilo. This consistency is one of the main advantages of the metric system. Utilize this systematic approach to achieve accurate measurements in scientific calculations, especially in subjects like Chemistry.

Conversion Factors

Conversion factors are essential to performing accurate unit conversions. They serve as a multiplier that relates one unit to another. For example, to translate kiloliters into milliliters, you utilize the conversion factor of 1 kL = 1,000,000 mL. Here’s how to effectively apply conversion factors:

• Identify the known and the desired units in your conversion.
• Determine the appropriate conversion factor between these units.
• Multiply the original quantity by this factor if converting to a larger unit, or divide if converting to a smaller unit.

In the exercise, when converting 2.81 x 10¹² mm to kilometers, you apply a conversion factor of 1 km = 1,000,000 mm: divide the original number of millimeters by 1,000,000 to get kilometers. Consistency and precision with conversion factors are fundamental in calculations, particularly in Chemistry, where accurate measurements are crucial for experiments and computations.

Chemistry Calculations

Chemistry often requires precise measurements and conversions, as matter's properties and interactions are nuanced and complex. In Chemistry, understanding the quantitative aspects starts with mastering unit conversions—transforming units like kilograms into milligrams to facilitate calculations involving molar mass, concentration, and reaction rates.

• Conversions are critical when calculating concentrations for solutions or comparing molecular weights of reactants and products.
• Accurate unit conversions ensure that the resulting values are applicable in practical and theoretical Chemistry scenarios.
• They also help align units for equations and formulas, allowing chemists to predict the outcomes of reactions accurately.

In practical terms, when converting 94.5 kg to milligrams, the logic involves applying a conversion factor of 1 kg = 1,000,000 mg. This results in 94,500,000 mg, ensuring you can precisely compute with these units in any chemical equation. Mastery of conversions aids chemists in maintaining accuracy and consistency across their work.