Chemistry Notes

Dimensional analysis involves converting units using conversion factors.
Given Unit: A number with a single unit is chosen as the starting point.
- Example: Converting 16 dollars to another currency, or determining feet in 13 miles starts with "13 miles" as the given.
Railroad Tracks: Conversion factors are placed in the middle, visualized as railroad tracks.

Two types:
- Equalities: Use an equal sign (e.g., x = y, 60 \text{ ounces} = 1 \text{ pound}, 10^{-2} \text{ meters} = 1 \text{ centimeter}).
- Ratios: Expressed as fractions (e.g., miles per hour, dollars per pound).
Setting up Conversion: The given unit is placed on the bottom to cancel out, with the corresponding number from the conversion factor.
- The new unit appears on top with its number.
- Once a unit is crossed out, it's not used again.
- Conversion factors are added until the desired unit is reached.
Example: Converting gallons to liters.
- Set up the number in the upper left corner.
- Place the bottom unit to match and cancel the given unit.
- The new unit is on top.
- Multiply the numbers on top and divide by the numbers on the bottom.
- Only multiplication and division are used in dimensional analysis.

Always consider significant figures in the final answer.
Example: If the given number has two significant figures, the answer must also have two.
Scientific notation is acceptable but not required.
Be aware of calculator outputs and how to convert between different formats (e.g., standard notation and scientific notation) for multiple-choice exams.

Sometimes, multiple conversion factors are needed.
Example: Converting kilograms to pounds requires converting kilograms to grams first, then grams to pounds.
Road Map Analogy: Plan the conversion steps before starting.

Given: Conversion factor between grams and pounds.
Need to know: Conversion factor between grams and kilograms (1 \text{ kilogram} = 1000 \text{ grams}).
Two-Step Method:
1. Kilograms to grams.
2. Grams to pounds.
Example: Convert 100 kilograms to pounds.
- 100 \text{ kg} \times \frac{1000 \text{ g}}{1 \text{ kg}} \times \frac{1 \text{ lb}}{453.6 \text{ g}}
Round the final answer to four significant figures.

Given: 1 fortnight = 2 weeks.
Convert fortnight to weeks to days to hours.
Example: Convert 1 fortnight to hours.
- 1 \text{ fortnight} \times \frac{2 \text{ weeks}}{1 \text{ fortnight}} \times \frac{7 \text{ days}}{1 \text{ week}} \times \frac{24 \text{ hours}}{1 \text{ day}}
If the problem does not specify significant figures, leave the number as is.

Convert 15 miles to micrometers.
Conversion Factors:
- 1 \text{ inch} = 2.54 \text{ cm}
- 5280 \text{ feet} = 1 \text{ mile}
Multi-Step Conversion:
1. Miles to feet.
2. Feet to inches.
3. Inches to centimeters.
4. Centimeters to meters (using the definition of "centi").
5. Meters to micrometers (using the definition of "micro").
If given a prefix conversion factor, use the base unit as an intermediate step.
Example:
- 15 \text{ miles} \times \frac{5280 \text{ feet}}{1 \text{ mile}} \times \frac{12 \text{ inches}}{1 \text{ foot}} \times \frac{2.54 \text{ cm}}{1 \text{ inch}} \times \frac{1 \text{ m}}{100 \text{ cm}} \times \frac{1 \mu \text{m}}{1 \times 10^{-6} \text{ m}}
Micrometers are used to measure cell sizes.

Energy: The ability to do work.
Types of Energy:
- Heat
- Electrical
- Mechanical
Body as a Complex Machine:
- Heart pumping (mechanical).
- Sweating (heat).
- Brain signals (electrical).

Classification: Categorizing matter by physical properties.
Two Major Types of Physical Properties:
- Intensive Values: Do not depend on the amount of substance.
- Examples: Number of states in the USA (50), gravity (9.81 \frac{m}{s^2}), fingers on a hand (5), eyes on a human (2).
- Extensive Values: Depend on the amount of substance.
- Examples: Color of a liquid (Sprite, coffee), color depending on conditions or additives.

Color, shape, physical state (solid, liquid, gas).
Solid: Definite shape and definite volume.
Liquid: Definite volume but indefinite shape (takes the shape of the container).
Gas: Indefinite shape and indefinite volume.
Other physical properties: Strength, smell, color, melting point, boiling point.
Key: The substance remains the same after a physical property is observed.

Alter the physical substance but do not change the substance itself.
Examples: Freezing water (ice is still water), boiling water (steam is still water).

Solid to liquid: Melting.
Liquid to solid: Freezing.
Liquid to gas: Vaporization (evaporation).
Gas to liquid: Condensation.
Solid to gas: Sublimation (rare, occurs in pressurized or cold conditions).
- Remembered as: solid sublimes to gas (s in the beginning)
Gas to solid: Deposition.
- Remembered as: gas is depocited (s in the end)
Example exam Question: What is the temperature a liquid changes in to a gas is called?
- Answer: Vaporization

Density: Mass divided by volume (D = \frac{M}{V}).
- Important Equation: D = \frac{M}{V}
Units:
- Mass: Grams (g).
- Volume:
- Liquids: Milliliters (mL).
- Solids: Cubic centimeters (cm³).
- 1 \text{ mL} = 1 \text{ cm}^3
Density: Grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³).
Emphasis: Always use the correct units for density calculations.
Trick Questions: Be aware of incorrect units (e.g., mL/g) in multiple-choice questions.

Calculating Density: Using the equation D = \frac{M}{V}, where M is mass and V is volume.
- Example Problem 1: The sample has a mass of 322 grams, the volume has 250ml. What is the final answer with two sig figs?
- Answer: 1.3 \frac{g}{mL}
Finding Mass: If given density and volume, rearrange the equation to solve for mass (M = D \times V).
- Example Problem 2: What is the equation to find mass for density and volume?
- Answer: M = D \times V
Intrinsic Properties: Do not count intrinsic properties or equalities in your significant figure count only go by what the given values have.

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