Chap 2

Title Slide

Chemistry Concepts and Critical Thinking 8th Edition Lecture Presentation: Chapter 2 - The Metric System Authors: Charles H. Corwin, John Singer, Jackson College

Introduction to the Metric System

The English system, initially used for commerce and daily life primarily in the British Empire, proved cumbersome and inconsistent for scientific applications. In response, a French committee devised a universal measuring system in the late 18th century, leading to the adoption of the metric system. The metric system is praised for its simplicity as it offers a single base unit for each measurement category, facilitating ease of use and conversion between units.

Metric System Basic Units

Table 2.1 presents key basic units employed within the metric system, which includes:

• Physical Quantity: Length

  • Basic Unit: Meter

  • Symbol: m

• Physical Quantity: Mass

  • Basic Unit: Gram

  • Symbol: g

• Physical Quantity: Volume

  • Basic Unit: Liter

  • Symbol: L

• Physical Quantity: Time

  • Basic Unit: Second

  • Symbol: s

Note: The U.S. Metric Association prefers the spellings "meter" and "liter," while other regions may opt for "metre" and "litre."

Original Metric Unit Definitions

Definitions of fundamental metric units were historically grounded in natural phenomena:

• Meter defined as 1/10,000,000 of the distance from the North Pole to the equator, rooted in a geodetic measurement.

• Kilogram (1000 grams) is defined as the mass of a cube of water measuring 0.1 m on each side (the specific definition has shifted to a physical constant).

• Liter equates to the volume of one kilogram of water at 4 °C, reflecting the density of water at that temperature.

Metric Prefixes

Common prefixes in the metric system are essential for understanding various measurements:

• Kilo- (10^3)

• Hecto- (10^2)

• Deka- (10^1)

• Deci- (10^-1)

• Centi- (10^-2)

• Milli- (10^-3)

• Micro- (10^-6)

• Nano- (10^-9)These prefixes modify the base unit to indicate multiples or fractions, significantly enhancing clarity in measurement notation.

Metric Symbols

Understanding how metric units are abbreviated is crucial for science:

• Kilometer = km

• Milligram = mg

• Microliter = mL

• Nanosecond = ns

Critical Thinking: International System of Units (SI)

The SI metric system, developed in 1960, is a decimal-based system that standardizes measurements worldwide. Prefixes associated with SI units, such as kilo (k) for thousand or milli (m) for one-thousandth, simplify calculations and conversions. For instance:

• 1 kilometer = 1000 meters (1 km = 1000 m)

• 1 millimeter = 1/1000 of a meter, aiding in precision and uniformity across scientific disciplines.

Metric Conversion Factors

Unit equations articulate relationships among equal quantities, which serve as helpful reference points for conversions:

• Example: 1 kilometer = 1000 meters (1 km = 1000 m)

• Example: 1 centimeter = 1/100 of a meter, or 0.01 m.

Unit Factors

A unit conversion factor is a ratio of two equivalent quantities, crucial for changing measurements between different units without altering the physical quantity itself:

• Example: From the unit equation 1 m = 100 cm:

  • Conversion factors can be expressed as:
    1 m/100 cm or 100 cm/1 m

Metric–Metric Conversions

Unit analysis, also known as dimensional analysis or the factor-label method, is vital for accurately solving scientific problems involving measurement conversions. This technique helps ensure that the final results maintain the correct units of measure.

Applying the Unit Analysis Method

Steps for unit analysis include:

1. Write down the unit required in the answer.

2. Write the given value related to the answer.

3. Apply unit factors to facilitate conversion of the given unit to the required unit without losing significant figures.

Metric–Metric Conversion Problem

Example: To calculate the mass of a 325 mg aspirin tablet in grams:

1. Identify the unit needed (grams).

2. Given: 325 mg.

3. Apply the conversion (1000 mg = 1 g):325 mg × (1 g/1000 mg) = 0.325 g.

Two Metric–Metric Conversions

Example: To convert 125 deciliters of blood plasma to milliliters:

1. Convert dL to L, then to mL using appropriate factors: 125 dL × (1 L/10 dL) × (1000 mL/1 L) = 12,500 mL.

Depth of Conversion Method

In complex conversions, the best approach is to first convert to the base metric unit, avoiding prefixes. This strategy allows the use of unit factors to convert and ensure accuracy by rounding to significant figures where necessary.

Mass Conversion Example

Example: To convert the mass of Earth’s moon (7.35 × 10^22 kg) to nanograms:

1. Use the calculation steps:7.35 × 10^22 kg × (1000 g/1 kg) × (1 × 10^6 ng/1 g) = 7.35 × 10^31 ng.

Metric–English Conversions

The persistence of the English system, particularly in the U.S., necessitates the application of conversion practices when interacting with the metric system, especially in scientific and medical contexts.

English-Metric Equivalents

Table 2.3 outlines common conversions that are widely applied in practice:

• 1 in. = 2.54 cm

• 1 lb = 454 g

• 1 qt = 946 mL

• 1 sec = 1 s

Example Conversion

Example: To convert the length of 120 yards to meters:120 yd × (0.914 m/1 yd) = 110 m, demonstrating practical applications of unit conversion.

Fl Oz to mL Conversion

Example: Convert a 64.0 fl oz carton of milk to milliliters:64.0 fl oz × (1 qt/32 fl oz) × (946 mL/1 qt) = 1890 mL.

Marathon Distance Conversion

Example: The marathon distance of 26.2 miles is a commonly calculated conversion in athletic statistics.

Compound Units

When working with measurements that involve ratios of units, such as speed limits expressed in miles per hour, it is essential to convert individual components leveraging unit factors:

• Convert miles to meters, then hours to seconds to maintain the integrity of the measurement.

Speed Conversion Example

Example: To convert the speed of 105 km/h to m/s: 105 km/h × (1000 m/1 km) × (1 h/3600 s) = 29.2 m/s.

Critical Thinking: Measurement Importance

Precision in measurement is critical, underscored by historical instances such as a NASA mishap that resulted from the use of mixed units, illustrating the real-world implications of unit consistency.

Percent Concept

The definition of percent expresses a part of a whole as a ratio per 100 parts, which is widely used in statistics, finance, and various sciences. The formula for calculating percent is introduced as essential knowledge in these disciplines.

Calculating Percentages

Example with bronze: Calculate the percent of copper in an alloy as follows: (79.2 g / (79.2 g + 10.8 g)) × 100% = 88.0%. This example emphasizes its applicability in material science.

Percent Unit Factors

Percent is expressed as parts per 100, which provides a direct conversion path, illustrating: Example: 25% = 25/100, reinforcing the necessity of understanding percentages in various contexts.

Unit Factor Calculation Example

The calculation of density for a specific sample illustrates principles of direct measurement:Mass of iron in a sample can be illustrated as: (92 g × (4.70 g iron / 100 g sample)).

Volume Calculation

The formula for volume calculation is defined as follows:Volume = Length × Width × Thickness; ensuring all dimensions are expressed in the same units.

Volume of Solids, Liquids, and Gases

The definition of a liter is correlated with the volume of a cube measuring 10 cm on each side, translating to 1000 cm³, which is a fundamental volume measurement in both solid and liquid contexts.

Volume Conversion

A liter is equivalently defined as 1000 cm³ or 1000 mL; hence 1 cm³ = 1 mL allows for straightforward conversions between volume units.

Volume Displacement Conversion Example

Example: Cylinder volume calculated in cubic inches could be converted (cm³ to in³) using conversion factors that relate inch measurements back to centimeters.

Volume by Displacement Concept

The technique to measure the volume of irregularly shaped solids or gases via water displacement is emphasized in laboratory settings, demonstrating its significance in practical chemistry.

Solid Volume Measurement

An example of volume measurement using water displacement can demonstrate how practical approaches yield accurate volumes for solids.

Gas Volume Measurement

Gas volumes derived from chemical reactions can be calculated through water displacement techniques, illustrating real-world applications in reacting substances.

Density Concept

Density, defined as mass divided by volume, serves as a fundamental property in science, affecting the buoyancy and behavior of substances.

Density Units

Density is often expressed in various scientific units according to the state of matter:

• Liquids: g/mL

• Solids: g/cm³

• Gases: g/LUnderstanding these distinctions aids in accurately describing material properties.

Densities of Common Substances

Table summarizing densities of selected solids, liquids, and gases offers a quick reference for comparative studies in materials science and physics.

Estimating Density

The comparison of objects' densities assists in predicting behaviors such as whether an object will float or sink when placed in a fluid, which is foundational in various scientific fields.

Calculating Density Example

Example: Calculate the density of a platinum nugget using the appropriate formula and measurements to demonstrate practical application of the density concept.

Density as Unit Factor

Using density in conversions provides a bridge in calculating other properties: Example with acid mass derived from volume indicates the integrated nature of chemical calculations.

Temperature Definition

Temperature is defined as a measure of the average kinetic energy of particles within a substance; the three main scales utilized are:

• Fahrenheit

• Celsius

• Kelvin (absolute).Each scale has distinct uses and conversion methods, impacting many scientific disciplines.

Temperature Scales

The water freezing and boiling points across the Fahrenheit, Celsius, and Kelvin scales are essential reference points, aiding in scientific discussions and calculations.

Temperature Conversion Formulas

Essential formulas for converting between Celsius and Fahrenheit provide crucial knowledge for students and professionals working with thermal dynamics.

Temperature Scale Solving

Modified equations for converting °F to °C are important to understand the relationship between these two commonly used temperature scales.

Celsius to Kelvin Conversion

The equation for converting Celsius to Kelvin (K = °C + 273.15) is essential for scientific measurements involving thermodynamic calculations.

Body Temperature Calculation

The calculation of human body temperature from Fahrenheit to Celsius and Kelvin demonstrates practical applications of temperature conversions in health sciences.

The Heat Concept

Heat is defined as the total energy measured in joules (J) or calories (cal), distinguishing it from temperature and influencing many physical processes.

Heat vs. Temperature

This section clarifies the distinction between heat as total energy and temperature as a measure of the average energy, helping clarify common misconceptions.

Specific Heat

Specific heat is defined as the amount of heat required to raise the temperature of 1 gram of a substance by 1°C, which is crucial in thermodynamics and materials science.

Chapter Summary: Metric System

Basic units are defined: grams (mass), liters (volume), meters (distance). Modifications through prefixes enable scaling and enhance the flexibility of measurement results.

Chapter Summary: Quantities

Unit equations and factors presented for equivalency reinforce the foundation of conversion practices.

Chapter Summary: Volume Measurement

Volume can be calculated through the formula: Volume = length × width × thickness, alongside measurement by water displacement as a reliable method in practical applications.

Chapter Summary: Energy Measurement

Temperature relates directly to the measure of average energy; specific heat indicates the energy necessary for temperature change, bridging the understanding between heat and temperature throughout scientific disciplines.