Matter, Measurement, and Mass Relationships in Chemistry: Study Notes

Chapter 1: Chemistry – Matter & Measurement

1. Prefixes and Units in Measurement

Understanding the metric system and SI prefixes is essential for accurate scientific measurement and communication. Prefixes indicate the magnitude of a unit and are used to express very large or very small quantities.

• Prefix Table:

Prefix	Symbol	Multiplier	Exponent	Example of Use
mega	M	1,000,000	106	megawatt (MW)
kilo	k	1,000	103	kilogram (kg)
centi	c	0.01	10-2	centimeter (cm)
milli	m	0.001	10-3	milliliter (mL)
micro	μ	0.000001	10-6	micrometer (μm)
nano	n	0.000000001	10-9	nanometer (nm)
pico	p	0.000000000001	10-12	picogram (pg)
femto	f	0.000000000000001	10-15	femtometer (fm)

• Base SI Units: distance (meter, m), mass (kilogram, kg), time (second, s), temperature (kelvin, K)

2. Derived Units (Compound Units)

Derived units are combinations of base units used to express other physical quantities.

• Velocity: meters per second (m/s)

• Acceleration: meters per second squared (m/s2)

• Force: newton (N) = kg·m/s2

• Pressure: pascal (Pa) = N/m2

• Energy: joule (J) = N·m = kg·m2/s2

• Density: kilogram per cubic meter (kg/m3)

• Volume: cubic meter (m3) or liter (L)

Common Conversion: 1 mL = 1 cm3

3. Working with Conversions and Prefixes

Unit conversions are essential for solving problems in chemistry. Always use conversion factors and dimensional analysis to ensure units cancel appropriately.

• Example: To convert 0.000001 m to nm, use the conversion factor $1~\text{nm} = 1 \times 10^{-9}~\text{m}$.

• Key Conversion: 1 inch = 2.54 cm (exact)

4. Significant Figures: Uncertainty in Measured Numbers

Significant figures (sig figs) reflect the precision of a measurement. The last digit in a measurement is always estimated and thus uncertain.

• Rules for Counting Significant Figures:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Trailing zeros after a decimal point are significant.

  • Leading zeros are not significant.

  • Exact numbers (from counting or definitions) have infinite significant figures.

• Example: 0.00470 has 3 significant figures; 1200 has 2 (unless specified otherwise).

5. Mathematics with Significant Figures

When performing calculations, the number of significant figures in the result depends on the operation:

• Multiplication/Division: The result should have as many significant figures as the measurement with the least number of significant figures.

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

Example:

• $2.34 \times 1.0 = 2.3$ (2 sig figs)

• $12.11 + 18.0 = 30.1$ (1 decimal place)

Note: Do not round intermediate steps; round only the final answer.

6. Accuracy vs. Precision

Accuracy and precision are two important concepts in measurement:

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

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

• Systematic Error: Consistent, repeatable error associated with faulty equipment or bias.

• Random Error: Error that varies unpredictably from one measurement to another.

Example: If a scale always reads 0.5 g too high, it is precise but not accurate.

7. Problems Using Dimensional Analysis

Dimensional analysis (factor-label method) is a systematic approach to problem-solving that uses conversion factors to move from one unit to another.

• Example: Calculating the total mass of mercury in a lake given its concentration and the lake's volume.

• Steps:

  1. List all given information and units.

  2. Set up a "road map" of conversions.

  3. Multiply by conversion factors so units cancel appropriately.

Chapter 3: Mass Relationships in Chemical Reactions

8. Counting Atoms by Weighing (Molar Mass)

Atoms are extremely small, so chemists count them by weighing large numbers of them. The concept of the mole allows us to relate mass to number of particles.

• Example: If a pencil weighs 6.5 g and a bundle of 100,000 pencils weighs 27,950 g, you can determine the number of pencils by dividing the total mass by the mass of one pencil.

9. Molar Mass and the Mole

The mole is the SI unit for amount of substance. One mole contains Avogadro's number ($6.022 \times 10^{23}$) of entities (atoms, molecules, etc.).

• Molar Mass (M): The mass of one mole of a substance, usually in grams per mole (g/mol).

• Relative Scale: Molar masses are based on the mass of $^{12}$C, which is defined as exactly 12 g/mol.

Example: The molar mass of $^{12}$C is 12.00 g/mol; $^{1}$H is 1.008 g/mol.

10. Molar Masses Listed on the Periodic Table

The molar mass of each element on the periodic table is a weighted average of the masses of its naturally occurring isotopes.

• Example using Silicon:

Isotope	Abundance (%)	g/mol (amu)
$^{28}$Si	92.21	27.977
$^{29}$Si	4.70	28.976
$^{30}$Si	3.09	29.974

• Weighted Average Formula:

$\text{Average atomic mass} = \sum (\text{fractional abundance} \times \text{isotopic mass})$

11. Formula Mass and Moles of Compounds

The formula mass (or molecular mass) of a compound is the sum of the atomic masses of all atoms in its chemical formula.

• Example: The formula mass of COCl2 is the sum of the masses of 1 C, 1 O, and 2 Cl atoms.

• Calculating Moles: Use the formula $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

12. Mass Percent in a Compound and as a Conversion

Mass percent expresses the mass of an element in a compound as a percentage of the total mass.

• Formula: $\text{Mass percent} = \frac{\text{mass of element in 1 mol of compound}}{\text{mass of 1 mol of compound}} \times 100$

• Application: Used in chemical analysis, jewelry, and engineering to determine composition.

13. Calculating Percent Composition for a Compound

Percent composition is calculated for each element in a compound.

• Example: For ammonium nitrate (NH4NO3), calculate the percent N, O, and H using their molar masses.

14. Empirical Formulas

The empirical formula gives the simplest whole-number ratio of atoms in a compound.

• Example: Benzene (C6H6) has the empirical formula CH.

• Calculation: Divide the moles of each element by the smallest number of moles to get the ratio.

15. Calculating Empirical & Molecular Formula: Experimental Data

Experimental data can be used to determine the empirical and molecular formulas of compounds.

• Example: If a compound is 60.0% C, 4.5% H, and the rest O, and its molar mass is between 110–200 g/mol, use the percent composition to find the empirical formula, then compare the empirical formula mass to the molar mass to find the molecular formula.

• Combustion Analysis: Used to determine the empirical formula of hydrocarbons by measuring the amounts of CO2 and H2O produced.

General Steps:

1. Convert mass percentages to grams (assume 100 g sample).

2. Convert grams to moles for each element.

3. Divide by the smallest number of moles to get the simplest ratio.

4. If necessary, multiply to get whole numbers.

Additional info: These notes cover foundational concepts in measurement, significant figures, dimensional analysis, and mass relationships, which are essential for success in General Chemistry. Practice problems and real-world examples are included to reinforce understanding.