Problem 42 - Chemistry: The Central Science

Question

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) \(\mu \mathrm{m}\) to \(\mathrm{mm},(\mathrm{b}) \mathrm{ms}\) tons, \((\mathrm{c}) \mathrm{mi}\) to \(\mathrm{km},(\mathrm{d}) \mathrm{ft}^{3}\) to \(\mathrm{L}\).

Step-by-Step Solution

Answer

To convert the given units: a) Micrometers to Millimeters: Divide the length in micrometers by 1000: \(Length (mm) = Length (μm) / 1000\) b) Millisecond Tons to Tons (assuming short tons to metric tons): Multiply the mass in short tons by 0.907185: \(Mass (metric tons) = Mass (short tons) * 0.907185\) c) Miles to Kilometers: Multiply the length in miles by 1.60934: \(Length (km) = Length (mi) * 1.60934\) d) Cubic Feet to Liters: Multiply the volume in cubic feet by 28.3168: \(Volume (L) = Volume (ft³) * 28.3168\)

Step 1: Write down the conversion factor for length

The conversion factor for length from micrometers to millimeters is: 1 mm = 1000 μm

Step 2: Divide by the conversion factor

In order to convert from micrometers to millimeters, we need to divide the given length (in μm) by the conversion factor: Length (mm) = Length (μm) / 1000 #b) Conversion of Millisecond Tons (ms tons) to Tons (Assuming this means converting short tons to metric tons)#

Step 1: Write down the conversion factor for mass

The conversion factor for mass from short tons to metric tons is: 1 short ton = 0.907185 metric tons

Step 2: Multiply by the conversion factor

In order to convert from short tons to metric tons, we need to multiply the given mass (in short tons) by the conversion factor: Mass (metric tons) = Mass (short tons) * 0.907185 #c) Conversion from Miles (mi) to Kilometers (km)#

Step 1: Write down the conversion factor for length

The conversion factor for length from miles to kilometers is: 1 mi = 1.60934 km

Step 2: Multiply by the conversion factor

In order to convert from miles to kilometers, we need to multiply the given length (in miles) by the conversion factor: Length (km) = Length (mi) * 1.60934 #d) Conversion from Cubic Feet (ft³) to Liters (L)#

Step 1: Write down the conversion factor for volume

The conversion factor for volume from cubic feet to liters is: 1 ft³ = 28.3168 L

Step 2: Multiply by the conversion factor

In order to convert from cubic feet to liters, we need to multiply the given volume (in ft³) by the conversion factor: Volume (L) = Volume (ft³) * 28.3168

Key Concepts

Metric System

The metric system is a universal language for scientists and students alike. It is an international decimal system of weights and measures, used predominantly across the globe. What makes it particularly user-friendly is its systematic structure based on factors of ten.
This system includes units for length, mass, volume, and temperature, making it highly adaptable for various scientific fields. Some key features of the metric system include:

• Units of measurement are expressible in multiples of ten, which simplifies calculations.
• It's consistent and predictable, which minimizes confusion.
• Prefixes like kilo-, centi-, and milli- provide easy conversion between units.

When dealing with everyday measurements or scientific calculations, the metric system's logical framework provides clarity and precision. This is why it's often introduced early in educational settings around the world.

Conversion Factors

Conversion factors are essential tools in transitioning from one unit of measurement to another. They act as bridges that facilitate seamless conversions by making use of known equivalences between units.For example:

• To convert micrometers (\( \mu m \)) to millimeters (mm), the conversion factor is 1 mm = 1000 \( \mu m \).


• When switching from short tons to metric tons, we use the factor 1 short ton = 0.907185 metric tons.

Conversion factors simplify the often daunting task of unit conversion, particularly when dealing with different measurement systems. They ensure precision and accuracy in calculations, often using simple multiplication or division to effectuate conversions.Remembering key conversion factors can significantly streamline any conversion process, making them a vital component in any scientific or educational toolkit.

Volume Conversion

Volume conversion involves changing the measured amount of space an object or substance occupies from one unit to another. In many instances, you may need to convert between units such as cubic feet (\( ft^3 \)) and liters (L), since these are often used in different contexts.
In this case, the conversion factor is 1 \( ft^3 \) = 28.3168 L.
When converting volumes:

• Identify the conversion factor relevant to your units.
• Multiply the given value by the conversion factor if converting from a larger unit to a smaller unit (like from \( ft^3 \) to L).


• If converting the other direction, divide the value by the conversion factor.

Volume conversion is crucial in fields such as chemistry, physics, and engineering, where precise measurements are necessary. Understanding the mechanics of these conversions aids in achieving accuracy in scientific observations and calculations.

Length Conversion

Length conversion, much like volume and mass conversions, is about translating a measurement from one unit to another. It often comes into play when working within different measurement systems such as Imperial and Metric.For instance:

• To convert from miles (mi) to kilometers (km), you use the conversion factor 1 mi = 1.60934 km.


• Conversion from micrometers (\( \mu m \)) to millimeters (mm) uses the factor 1 mm = 1000 \( \mu m \).

Converting lengths accurately is essential in fields like architecture, geography, and transportation, where precise distance measurements are essential. Practicing these conversions helps build a solid foundation in handling various scientific and practical applications efficiently.