Chemical Tools: Experimentation and Measurement – Study Notes

Chapter 1: Chemical Tools – Experimentation and Measurement

Section 1.1: The Scientific Method

The scientific method is a systematic approach used by scientists to understand natural phenomena. It involves making observations, forming hypotheses, conducting experiments, and developing theories or models.

• Observations: Gathering data from natural phenomena or measured events.

• Hypothesis: A tentative explanation that can be tested by experiments. It must be falsifiable.

• Experiment: A procedure to test the hypothesis, involving variables and controls.

• Model (Theory): A conceptual explanation that accounts for observations and experimental results. Theories can be used to make further predictions.

• Further Experiment: Used to test predictions based on the model or theory.

Note: If a hypothesis is not supported by experimental results, it must be revised or rejected.

Section 1.2: Experimentation and Measurement

Scientific measurements require standardized units. The International System of Units (SI) is the standard system used in science.

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

All other units are derived from these fundamental units.

Section 1.3, 1.4: Measurement of Length and Mass

Mass is the amount of matter in an object, while weight measures the force with which gravity pulls on an object.

• SI unit of mass: kilogram (kg)

• SI unit of length: meter (m)

Common SI-English equivalent quantities:

Quantity	SI to English Equivalent	English to SI Equivalent
Length	1 km = 0.6214 mile	1 mile = 1.609 km
	1 m = 39.37 inches	1 inch = 2.54 cm (exact)
Volume	1 L = 1.057 qt	1 qt = 0.9464 L
	1 mL = 1.057 x 10-3 qt	1 fl oz = 29.57 mL
Mass	1 kg = 2.205 lb	1 lb = 453.6 g
	1 g = 0.03527 oz	1 oz = 28.35 g

Section 1.5: Temperature and Its Measurement

Temperature is a measure of the average kinetic energy of particles. The three common temperature scales are Celsius (°C), Fahrenheit (°F), and Kelvin (K).

• Celsius to Kelvin: $K = ^\circ C + 273.15$

• Celsius to Fahrenheit: $^\circ F = \frac{9}{5}(^\circ C) + 32$

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

Section 1.7: Density

Density is a measure of how much mass is contained in a specific volume. It is an intensive property, meaning it does not depend on the amount of substance.

• Formula: $\text{density} = \frac{\text{mass}}{\text{volume}}$

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

• Density is temperature dependent and must be reported with the temperature of measurement.

• Density of water at 3.98°C: 1.0000 g/mL

Section 1.6: Derived Units – Volume and Its Measurement

Derived units are combinations of SI base units. Volume, speed, acceleration, and energy are examples of derived quantities.

Quantity	Definition	Derived Unit (Name)
Area	Length × length	m2
Volume	Area × length	m3
Speed	Distance per unit time	m/s
Acceleration	Change in speed per unit time	m/s2
Density	Mass per unit volume	kg/m3
Energy	Force times distance	kg·m2/s2 (joule, J)

Section 1.8: Derived Units – Energy and Its Measurement

Energy is the capacity to do work or supply heat. It can be classified as kinetic or potential energy.

• Kinetic Energy (EK): Energy due to motion.

• Potential Energy (EP): Stored energy.

Formulas:

• Kinetic Energy: $E_K = \frac{1}{2}mv^2$

• 1 joule (J) = 1 kg·m2/s2

• 1 cal = 4.184 J (exact)

• 1 Cal (nutritional) = 1000 cal = 1 kcal = 4.184 kJ

Section 1.7 (cont.): Densities of Some Common Materials

Substance	Density (g/cm3)
Ice (0°C)	0.917
Water (3.98°C)	1.000
Gold	19.32
Helium (25°C, 1.00 atm)	0.000164
Air (25°C)	0.001185
Human fat	0.94
Human muscle	1.06
Cork	0.22-0.26
Balsa wood	0.12
Earth	5.54

Section 1.9: Precision, Accuracy, and Error

Measurement quality is described by precision and accuracy:

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

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

• Systematic error: Consistent deviation in one direction (can be corrected by calibration).

• Random error: Unpredictable variations (cannot be corrected by calibration).

Example: If three students measure the density of water and get values close to each other but far from the true value, their measurements are precise but not accurate.

Section 1.9: Accuracy, Precision, and Significant Figures in Measurement

Significant figures reflect the precision of a measured value. The number of significant figures in a result depends on the precision of the measurement.

Measurement #	Bathroom Scale	Lab Balance	Analytical Balance
1	0.1 kg	54.4 g	54.441 g
2	0.2 kg	54.5 g	54.444 g
3	0.1 kg	54.4 g	54.447 g
Average	0.1 kg	54.4 g	54.444 g

Interpretation: Analytical balance gives both high precision and high accuracy.

Section 1.9: Rules for Significant Figures

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros are significant only if there is a decimal point.

• Use exponential notation to avoid ambiguity.

Exact numbers (e.g., counting numbers, defined conversion factors) have infinite significant figures.

Section 1.9: Significant Figures – Uncertainty in Measurement

• All digits known with certainty plus one estimated digit are significant.

• Uncertainty is usually ±1 in the last digit.

Exponential Notation: Used to express very large or small numbers. For example, 1,000,000 = $1 \times 10^6$.

Section 1.9: Calculations with Significant Figures

• Addition/Subtraction: The answer cannot have more digits after the decimal point than the number with the fewest decimal places.

• Multiplication/Division: The answer cannot have more significant figures than the value with the fewest significant figures.

Example: $2.976 \div 0.07246 = 41.1$ (rounded to 3 significant figures)

Section 1.10: Rounding

• If the digit to be dropped is less than 5, leave the preceding digit unchanged.

• If the digit to be dropped is 5 or greater, increase the preceding digit by 1.

• If the digit to be dropped is exactly 5, round to the nearest even number.

Section 1.11: Chemical Problem Solving

All measured quantities consist of a number and a unit. Units can be manipulated mathematically like numbers.

• Units can be multiplied and divided to solve problems.

• Always include units in calculations to ensure correct results.

Example: $\frac{350\ \text{mi}}{7\ \text{h}} = 50\ \text{mi/h}$

Conversion Factors

A conversion factor expresses the equivalence of a measurement in two different units. It is used to convert from one unit to another by multiplying so that units cancel appropriately.

• Example: 10 dimes = 1 dollar gives the conversion factors $\frac{10\ \text{dimes}}{1\ \text{dollar}}$ or $\frac{1\ \text{dollar}}{10\ \text{dimes}}$.

• Set up the conversion so that all units cancel except those required for the answer.

Sample Problem: Convert 37 yards to inches.

Practice Problems

1. Convert 626 g to mg.

2. Convert 22.4 oz (fluid) to mL.

3. Convert 2.45 ounces to g.

Additional info: For all conversions, use appropriate conversion factors and significant figures as discussed above.