Chapter 1: Measuring Matter – Foundations of GOB Chemistry

Measuring Matter

Introduction

This chapter introduces the fundamental concepts and measurements used in chemistry, focusing on the properties of matter, units of measurement, and calculations essential for understanding chemical substances and their behavior. These concepts are foundational for students in General, Organic, and Biological (GOB) Chemistry.

Classifying Matter

Pure Substances and Mixtures

• Pure Substance: A material with a constant composition. Examples include elements (e.g., O2, Fe) and compounds (e.g., H2O, NaCl).

• Mixture: A physical blend of two or more substances. Mixtures can be:

  • Homogeneous: Uniform composition throughout (e.g., salt water).

  • Heterogeneous: Non-uniform composition (e.g., salad, sand in water).

Elements, Compounds, and the Periodic Table

• Element: A substance that cannot be broken down into simpler substances by chemical means.

• Compound: A substance composed of two or more elements chemically combined in fixed proportions.

• The Periodic Table organizes elements by increasing atomic number and groups elements with similar properties into columns (groups) and rows (periods).

Quantifying Matter: Percent and Ratios

Percent Calculations

Percentages are used to compare parts of a whole, especially in solutions and mixtures.

• Percent (%) is defined as the part per hundred:

$\text{Percent} (\%) = \frac{\text{part}}{\text{whole}} \times 100$

• To convert a fraction to a percent, divide the numerator by the denominator, multiply by 100, and add the percent sign.

• To convert a decimal to a percent, multiply by 100 and add the percent sign.

Example Calculations

• Problem: A solution of water and hydrochloric acid is 24% HCl by mass. What mass of HCl is in 15.5 g of solution?

• Solution: $15.5\,\text{g solution} \times \frac{24\,\text{g HCl}}{100\,\text{g solution}} = 3.7\,\text{g HCl}$

• Problem: In CO2, what percent of the total mass is carbon? (C = 12 g, O = 32 g)

• Solution: $\frac{12\,\text{g}}{12\,\text{g} + 32\,\text{g}} \times 100 = 27\%$

The "Stuff" of Chemistry: Mass, Volume, and Density

Mass

• Mass is a measure of the amount of material in an object, typically measured in grams (g).

• Weight is the force of gravity on an object; it can vary with location, but mass remains constant.

Volume

• Volume is the three-dimensional space occupied by matter.

• Common units: milliliter (mL), cubic centimeter (cm3 or cc), and liter (L).

• 1 mL = 1 cm3 = 1 cc

• Volumes are measured with graduated cylinders, pipets, or calibrated syringes.

Density

• Density (d) is the ratio of mass (m) to volume (V):

$d = \frac{m}{V}$

• For water at 4°C, $d = 1.00\,\text{g/mL}$

• Density is constant for a substance at a given temperature and can be used as a conversion factor.

Specific Gravity

• Specific gravity is the ratio of the density of a sample to the density of water:

$\text{Specific gravity} = \frac{\text{density of sample}}{\text{density of water}}$

• Specific gravity is unitless.

• Measured with a hydrometer in clinical and laboratory settings.

Example Problem

• Problem: Sugar has a density of 1.29 g/mL. What is the mass of 2.50 teaspoons of sugar (1 tsp = 4.93 mL)?

• Solution: $2.50\,\text{tsp} \times \frac{4.93\,\text{mL}}{1\,\text{tsp}} \times \frac{1.29\,\text{g}}{1\,\text{mL}} = 15.9\,\text{g}$

States of Matter

Solids, Liquids, and Gases

• Solid: Particles are closely packed in an orderly arrangement; definite shape and volume.

• Liquid: Particles are less orderly, move freely; definite volume but takes the shape of its container.

• Gas: Particles are far apart, move rapidly; no definite shape or volume, fills the container.

Property	Solid	Liquid	Gas
Shape	Definite	Adopts shape of container	Adopts shape of container
Volume	Definite	Definite	Fills container
Particle Arrangement	Closely packed, fixed	Loosely packed, random	Far apart, random
Compressibility	Very low	Low	High

Temperature and Energy

Temperature Scales

• Temperature measures the hotness or coldness of a substance.

• Common scales: Fahrenheit (°F), Celsius (°C), Kelvin (K).

• Kelvin is the SI unit for temperature.

$K = ^\circ C + 273$

$^\circ C = ( ^\circ F - 32 ) \times \frac{5}{9}$

$^\circ F = ( ^\circ C \times \frac{9}{5} ) + 32$

• Normal body temperature: 98.6°F or 37.0°C.

• Hyperthermia: >40°C (104°F); Hypothermia: <35°C (95°F).

Energy and Units

• Energy is the capacity to do work or produce heat.

• Potential energy is stored energy; kinetic energy is energy of motion.

• Law of Conservation of Energy: Energy is neither created nor destroyed.

• SI unit: joule (J); 1 calorie (cal) = 4.184 J.

• 1 Calorie (Cal, used in nutrition) = 1000 calories = 4184 J.

Specific Heat

• Specific heat (SH) is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C.

$\text{Specific heat} = \frac{\text{heat}}{\text{grams} \times \Delta T}$

• Water has a high specific heat; metals have low specific heat.

Measurement in Chemistry

Accuracy and Precision

• Accuracy: How close a measurement is to the true value.

• Precision: How close repeated measurements are to each other.

• Best practice: Take multiple measurements to ensure both accuracy and precision.

Units and Conversions

• Chemists use SI (metric) units, but must also be familiar with U.S. customary units.

• Common conversions: 1 dL = 100 mL; 1 kg = 2.205 lbs.

• Dimensional analysis is used to convert between units and calculate dosages.

Dimensional Analysis for Dosage Calculations

1. Determine the units for the final answer.

2. Identify the given information.

3. Find conversion factors to cancel unwanted units.

4. Set up the equation so all units cancel except the desired unit.

Example Problem

• Problem: Prescription for acetaminophen is 7.5 mg per kg body weight. If a patient weighs 42 kg, what is the dose?

• Solution: $42\,\text{kg} \times \frac{7.5\,\text{mg}}{1\,\text{kg}} = 315\,\text{mg}$

Applications in Health and Nutrition

Percent in Health and Nutrition

• Percent Active Ingredient: Medications may contain binders; percent active ingredient is important for dosing.

• Percent of Adult Dose: Children often receive a percent of the adult dose based on body weight.

• Percent Daily Value (%DV): Nutrition labels show the percent of daily dietary requirements provided by a serving.

Summary Table: States of Matter

State	Shape	Volume	Particle Arrangement	Compressibility
Solid	Definite	Definite	Closely packed, fixed	Very low
Liquid	Adopts container	Definite	Loosely packed, random	Low
Gas	Adopts container	Fills container	Far apart, random	High

Additional info: Some context and examples were inferred and expanded for clarity and completeness, especially in the areas of percent calculations, dimensional analysis, and the properties of matter.