Problem 54 - Chemistry: The Central Science in SI Units, Global Edition

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) \(\mathrm{km} / \mathrm{hr}\) to \(\mathrm{m} / \mathrm{s}\) (b) \(\mathrm{mL}\) to \(\mu \mathrm{L}(\mathbf{c}) \mathrm{ps}\) to \(\mathrm{s}(\mathbf{d}) \mathrm{m}^{3}\) to gal.

Step-by-Step Solution

Answer

To convert (a) km/hr to m/s, multiply the value by \( \frac{5}{18} \). (b) To convert mL to µL, multiply the value by 1000. (c) To convert ps to s, multiply the value by \(\frac{1}{10^{12}}\). (d) To convert m³ to gal, multiply the value by 264.172.

Step 1: (a) Converting kilometers per hour to meters per second

First, we need to convert kilometers to meters as there are 1000 meters in 1 kilometer. Next, we'll need to convert hours to seconds, since there are 3600 seconds in an hour. The conversion factor for this problem can be found as follows: \[\frac{\text{1 km}}{\text{1 hr}} =\frac{1000\text{ m}}{3600\text{ s}} \Rightarrow \frac{\text{km}}{\text{hr}} = \frac{5}{18} \frac{\text{m}}{\text{s}}\] To convert a given value in km/hr to m/s, multiply it by the conversion factor (5/18).

Step 2: (b) Converting milliliters to microliters

To perform this conversion, we need to know that there are 1000 microliters (µL) in 1 milliliter (mL). Therefore, the conversion factor for this problem is: \[\frac{\text{1 mL}}{\text{1}} =\frac{1000\text{ µL}}{\text{1}} \Rightarrow \frac{\text{mL}}{\text{1}} = \frac{\text{1000 µL}}{\text{1}}\] To convert a given value in mL to µL, multiply it by 1000.

Step 3: (c) Converting picoseconds to seconds

To convert picoseconds (ps) to seconds (s), we need to know that 1 second equals 10^12 picoseconds. The conversion factor for this problem is: \[\frac{\text{1 s}}{10^{12}\text{ ps}} \Rightarrow \frac{\text{s}}{\text{ps}} = \frac{1}{10^{12}}\] To convert a given value in picoseconds to seconds, multiply it by the conversion factor (1/10^12).

Step 4: (d) Converting cubic meters to gallons

To convert cubic meters (m³) to gallons (gal), we need to know the conversion factor, which is 264.172 gallons per cubic meter. The conversion factor for this problem is: \[\frac{\text{1 m}^{3}}{\text{1}} =\frac{264.172\text{ gal}}{\text{1}} \Rightarrow \frac{\text{m}^{3}}{\text{1}} = \frac{264.172\text{ gal}}{\text{1}}\] To convert a given value in cubic meters to gallons, multiply it by the conversion factor (264.172).

Key Concepts

Understanding Metric Units

Metric units are part of a standardized system used worldwide to measure length, volume, weight, and other quantities. This system is preferred in scientific and many everyday applications because of its simplicity and ease of use. The basic units include meters for length, liters for volume, and grams for mass, among others.
These units are based on powers of ten, which makes conversions straightforward.
For example:

• 1 meter (m) equals 100 centimeters (cm).
• 1 liter (L) equals 1000 milliliters (mL).
• 1 kilogram (kg) equals 1000 grams (g).

Using these relations helps in making quick conversions without needing complex calculations. Understanding these units is crucial, especially in sciences where precise measurements are essential.

The Role of Conversion Factors

Conversion factors are essential tools that allow us to change one unit into another. These factors are derived from the relationships between different units. For instance, to change from kilometers per hour to meters per second, you can use the conversion factor derived through known measurements:

• 1 kilometer equals 1000 meters.
• 1 hour equals 3600 seconds.

Thus, the conversion factor becomes \(\frac{5}{18}\), useful for converting speeds from \(\text{km/hr}\) to \(\text{m/s}\).
To apply a conversion factor, multiply the value you want to convert by the factor. This method ensures accurate and quick conversions and is used in a broad range of scientific and analytical tasks.

Differentiating Measurement Units

Measurement units are fundamental to compare and comprehend different physical quantities. They provide a basis for comparison and measurement. Without these units, quantifying aspects like temperature or distance would be impossible.
There are various systems of measurement units, but metric units are commonly used internationally due to their decimal-based structure. Measurement units can vary widely:

• Length can be measured in kilometers, meters, centimeters, etc.
• Volume is often measured in liters, milliliters, or cubic meters.
• Time is typically measured in seconds, minutes, and hours.

Understanding these units and being able to convert them using proper conversion factors is a pivotal element in both academic and practical, real-world scenarios.

Exploring SI Units

The International System of Units (SI) is the modern form of the metric system and the most widely used measurement system. It is designed to ensure uniformity and consistency in measurements worldwide. SI units include seven base units, such as meters for length, kilograms for mass, and seconds for time.
Beyond these, derived units are used for other measurements like speed, force, and energy. For instance, speed is measured in meters per second, while force is in newtons.
The consistency provided by SI units makes it easier for scientists and engineers to share and compare data. It's critical for students to familiarize themselves with both base and derived SI units as they advance in scientific studies.