Chemistry and Measurements: Study Notes

Chapter 2: Chemistry and Measurements

Introduction

This chapter introduces the fundamental concepts of measurement in chemistry, including the types of properties measured, units and systems of measurement, significant figures, accuracy and precision, and calculations involving conversions, density, and specific gravity.

Measurement Units

Qualitative vs. Quantitative Properties

• Qualitative properties are descriptive and do not involve numbers (e.g., color, texture).

• Quantitative properties are measured and expressed with numbers and units (e.g., mass, volume).

• Examples:

  • Qualitative: An apple is red, sandpaper is rough.

  • Quantitative: The mass of an apple is 150 grams.

Common Quantitative Properties

• Distance: How far apart two points are (measured in meters, centimeters, etc.).

• Volume: The amount of space an object occupies (measured in liters, milliliters, cubic centimeters, etc.).

• Mass: The amount of matter in an object (measured in grams, kilograms, etc.).

• Weight: The force exerted on an object by gravity (measured in newtons).

Measurement

Components of a Measurement

• A measurement requires both a number and a unit (e.g., 25.0 cm).

• Example: The predicted high temperature for today is 35°C.

Units of Measurement

Historical and Modern Units

• Early units were based on human body dimensions (e.g., the cubit).

• Problems arose due to lack of standardization (not all humans are the same size).

• Modern science uses standardized systems of measurement.

The Metric System and SI Units

• The metric system was developed in France during the French Revolution.

• Most nations, including the U.S., use the metric system for scientific measurements.

• The International System of Units (SI) is the modern form of the metric system.

SI Base Units

Base Quantity	Name	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Common Metric System Prefixes

Prefix	Symbol	Factor
kilo-	k	103
centi-	c	10-2
milli-	m	10-3
micro-	μ	10-6
nano-	n	10-9
pico-	p	10-12
mega-	M	106
giga-	G	109

Commonly Measured Values: Mass vs. Weight

• Mass: The amount of matter in an object. Measured with a balance.

• Weight: The force exerted by gravity on an object.

  • Formula: $\text{Weight} = \text{mass} \times \text{gravity}$

Temperature

Temperature Scales and Conversions

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

• Conversion formulas:

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

  • $K = ^\circ C + 273.15$

Uncertainty in Measurements

• All scientific measurements have some degree of uncertainty.

• Uncertainty arises from limitations in measurement tools and estimation of the last digit.

• The last reported digit is usually estimated and is considered significant.

• Significant figures are used to communicate the precision of a measurement.

Significant Figures (SFs)

Rules for Identifying Significant Figures

• All nonzero digits are significant.

• Zeros between nonzero digits are significant (e.g., 101, 1.0080000).

• Zeros to the right of a significant number and after a decimal point are significant (e.g., 0.10, 0.100000).

• Zeros to the left of a significant number are not significant (e.g., 0.01, 0.002502).

• In large numbers without a decimal, trailing zeros may not be significant unless specified (e.g., 1,250,000 may have 3, 4, 5, or 6 SFs depending on context).

• Use scientific notation to clarify significant figures (e.g., $1.25 \times 10^6$ has 3 SFs).

Significant Figures Table

Rule	Measured Number	Significant Figures
All nonzero digits are significant	4.56	3
Zeros between nonzero digits are significant	1003	4
Zeros to the left of a decimal are not significant	0.00456	3
Zeros to the right of a decimal and after a nonzero digit are significant	45.600	5
Exact numbers have infinite significant figures	1 dozen = 12	∞

Exact Numbers

• Counting numbers and defined quantities (e.g., 100 cm in 1 m) are considered exact and have infinite significant figures.

Significant Figures in Calculations

• Multiplication/Division: The result should have as many significant figures as the measurement with the fewest SFs.

• Addition/Subtraction: The result should have as many decimal places as the measurement with the fewest decimal places.

• Examples:

  • $0.03 \times 0.045/5.55 = 0.000243$ (rounded to 2 SFs)

  • $2.054 + 34.1 = 36.154$ (rounded to 1 decimal place: 36.2)

Precision and Accuracy

Definitions

• Precision: The agreement between repeated measurements (how close the measurements are to each other).

• Accuracy: The agreement of a measured value with the true or accepted value.

• Percent error formula:

  • $\text{Percent error} = \frac{\left| \text{measured value} - \text{true value} \right|}{\text{true value}} \times 100\%$

Visualizing Accuracy and Precision

• High accuracy, high precision: Measurements are close to the true value and to each other.

• High precision, low accuracy: Measurements are close to each other but not to the true value.

• Low precision, low accuracy: Measurements are neither close to each other nor to the true value.

Conversions

Unit Conversions in Chemistry

• Many chemistry problems require converting between units.

• Strategy:

  1. Identify the unit of the original measurement.

  2. Identify the unit of the final answer.

  3. Obtain conversion factors that relate the original measurement to the final answer.

  4. Arrange conversion factors to cancel units and perform the math.

• Conversion factors can be found in tables or stated in the problem.

Practice Problems (Examples)

• How many centimeters are in 7.5 inches? (1 in = 2.54 cm)

• If the average speed is 65 mph, how many kilometers away is a city 6.5 hours away? (1 km = 0.621 miles)

• How many fluid ounces are in a 4 L bottle? (1 gallon = 3.785 L, 1 qt = 2 pints, 1 pint = 16 fl. oz, 1 L = 1000 cm3)

Density

Definition and Formula

• Density relates the mass of an object to the volume it occupies.

• Formula:

  • $d = \frac{m}{V}$

  • Where d = density, m = mass, V = volume

• Units: g/cm3 (solids), g/mL (liquids), g/L (gases)

Practice Problem (Example)

• A cylindrical object with a radius of 4.02 cm and a height of 6 cm has a mass of 2.2 lbs. What is the density in g/cm3? (1 lb = 454 g)

Specific Gravity

Definition and Calculation

• Specific gravity is a comparison of the density of a substance to the density of water.

• Formula:

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

• Water usually has a density of 1 g/mL at standard conditions.

Practice Problem (Example)

• If a urine sample has a specific gravity of 1.039 and the normal range is 1.002 to 1.028, what is the density of the urine? What implications does this have for the sample?

Additional info: Some explanations and examples were expanded for clarity and completeness. All tables were reconstructed and some entries inferred for academic completeness.