General Chemistry I: Separation of Mixtures, Energy, Units, Conversion Factors, and Significant Figures

Separation of Mixtures

Introduction to Mixture Separation

Mixtures are combinations of two or more substances that retain their individual properties. They can be separated into their components based on differences in physical and chemical properties.

• Physical properties include solubility, boiling point, and particle size.

• Chemical properties may also be exploited in some separation techniques.

Filtration

Filtration is a method used to separate a solid from a liquid in a heterogeneous mixture.

• The mixture is poured through a filter (such as filter paper).

• The liquid passes through the pores of the filter, while the solid remains on the filter.

Example: Separating sand from water using filter paper.

Separation by Solubility

Substances with different solubility can be separated using a suitable solvent.

• A mixture of sand (SiO2) and salt (NaCl) can be separated by adding water.

• SiO2 is insoluble in water, while NaCl is soluble.

• After stirring and filtering, the sand remains on the filter and the salt is dissolved in the filtrate.

Example: Dissolving a mixture of sand and salt in water, then filtering to separate the sand.

Separation by Boiling Point (Distillation and Evaporation)

Substances with different boiling points can be separated by distillation or evaporation.

• Distillation involves heating a solution to boil off the more volatile component, which is then condensed and collected.

• Evaporation removes the solvent, leaving the solute behind.

Example: Separating salt from water by heating the solution until the water evaporates, leaving salt behind.

Sublimation

Some substances can undergo sublimation, which is the direct conversion from solid to gas upon heating.

• NH4Cl (ammonium chloride) sublimes at temperatures above 500°C, while NaCl does not sublime below 800°C.

• Heating a mixture of NH4Cl and NaCl between 500–800°C will cause NH4Cl to sublime, leaving NaCl behind.

Distillation of Homogeneous Mixtures

Homogeneous mixtures of liquids can be separated by distillation based on differences in volatility (boiling points).

• For example, methanol (CH3OH, boiling point 64.7°C) and water (boiling point 100°C) can be separated by distillation.

• The more volatile methanol boils off first and can be condensed and collected separately from water.

Energy in Physical and Chemical Changes

Definition and Forms of Energy

Energy is the capacity to do work or transfer heat. It is not considered a form of matter, but it is involved in all physical and chemical changes.

• Kinetic energy is the energy of motion, dependent on mass and speed: $E_{kinetic} = \frac{1}{2}mv^2$

• Potential energy is stored energy due to position or composition (e.g., chemical bonds).

Example: Water at the top of a hill has high potential energy, which is converted to kinetic energy as it flows down.

Law of Conservation of Energy

The total energy of an isolated system remains constant. Energy can be transformed from one form to another, but it cannot be created or destroyed.

• Example: Chemical energy in gasoline is converted to kinetic energy and heat in a car engine.

Units of Measurement

SI Base Units

Scientific measurements use the International System of Units (SI), which is based on the metric system.

Physical Quantity	Name of Unit	Abbreviation
Mass	Kilogram	kg
Length	Meter	m
Time	Second	s
Temperature	Kelvin	K
Amount of substance	Mole	mol
Electric current	Ampere	A
Luminous intensity	Candela	cd

Metric Prefixes

Prefixes are used to indicate decimal fractions or multiples of units.

Prefix	Abbreviation	Factor	Example
giga	G	$10^9$	1 gigameter (Gm) = $1 \times 10^9$ m
mega	M	$10^6$	1 megameter (Mm) = $1 \times 10^6$ m
kilo	k	$10^3$	1 kilometer (km) = $1 \times 10^3$ m
centi	c	$10^{-2}$	1 centimeter (cm) = $1 \times 10^{-2}$ m
milli	m	$10^{-3}$	1 millimeter (mm) = $1 \times 10^{-3}$ m
micro	μ	$10^{-6}$	1 micrometer (μm) = $1 \times 10^{-6}$ m
nano	n	$10^{-9}$	1 nanometer (nm) = $1 \times 10^{-9}$ m
pico	p	$10^{-12}$	1 picometer (pm) = $1 \times 10^{-12}$ m

Scientific Notation

Scientific notation expresses very large or very small numbers in the form $N \times 10^n$, where $1 \leq N < 10$ and $n$ is an integer.

• Example: $1,200,000 = 1.2 \times 10^6$

• Example: $0.00034 = 3.4 \times 10^{-4}$

Unit Analysis and Conversion Factors

Conversion Factors

To convert a value from one unit to another, multiply by a conversion factor that relates the two units.

• General formula: $\text{Given unit} \times \frac{\text{Desired unit}}{\text{Given unit}} = \text{Desired unit}$

• Example: To convert 5 m to mm: $5 \text{ m} \times \frac{1000 \text{ mm}}{1 \text{ m}} = 5000 \text{ mm}$

Dimensional Analysis with Powers

When converting squared or cubed units, the entire conversion factor must be raised to the appropriate power.

• Example: $1 \text{ mm} = 10^{-3} \text{ m}$, so $1 \text{ mm}^2 = (10^{-3} \text{ m})^2 = 10^{-6} \text{ m}^2$

Precision, Accuracy, and Significant Figures

Precision vs. Accuracy

• Precision refers to how close repeated measurements are to each other.

• Accuracy refers to how close a measurement is to the true or accepted value.

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one estimated digit. The number of significant figures reflects the precision of the measurement.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant (e.g., 304.8 has 4 sig figs).

• Leading zeros are not significant (e.g., 0.00034 has 2 sig figs).

• Trailing zeros are significant only if there is a decimal point (e.g., 3.400 has 4 sig figs).

• Exact numbers (e.g., 12 eggs) have an infinite number of significant figures.

Rules for Calculations

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

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

Example (Multiplication): $1.052 \times 12.054 \times 0.53 = 6.7$ (rounded to 2 sig figs)

Example (Addition): $2.0034 + 3.20 = 5.20$ (rounded to 2 decimal places)

Temperature

Temperature Scales

• Celsius (°C): Based on the properties of water; 0°C is the freezing point, 100°C is the boiling point.

• Kelvin (K): The SI unit of temperature; absolute zero (0 K) is the lowest possible temperature.

• Fahrenheit (°F): Not commonly used in scientific measurements.

Conversion formulas:

• $K = °C + 273.15$

• $°F = \frac{9}{5}(°C) + 32$

• $°C = \frac{5}{9}(°F - 32)$

Volume and Density

Volume

Volume is the amount of space occupied by a substance. Common units are the liter (L) and milliliter (mL).

• 1 L = 1 dm3

• 1 mL = 1 cm3

Density

Density is a physical property defined as mass per unit volume:

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

• Common units: g/cm3 or g/mL

• Density is an intensive property (independent of sample size).

• Example: Gold has a density of 19.3 g/cm3; if a nugget has a mass of 22.5 g and a volume of 2.38 cm3, its density is $\frac{22.5\,g}{2.38\,cm^3} = 9.45\,g/cm^3$.