Adv/AP Chemistry Unit 1: Data Analysis, Measurement, and Matter

What is a conversion factor?

A ratio of equivalent measurements used to convert from one unit to another. For example, $(\frac{1 \text{ m}}{100 \text{ cm}})$ or $(\frac{100 \text{ cm}}{1 \text{ m}})$.

How many significant figures are in an exact conversion factor (e.g., $1 \text{ inch} = 2.54 \text{ cm})$?

Exact conversion factors have an infinite number of significant figures and do not limit the significant figures in a calculation.

How many centimeters are in $2.5 \text{ meters}$?

$$2.5 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 250 \text{ cm}$$

Convert $55 \text{ miles per hour}$ to $(\text{meters per second})$. ($1 \text{ mile} = 1609 \text{ m}$, $1 \text{ hour} = 3600 \text{ s})$

$$55 \frac{\text{miles}}{\text{hr}} \times \frac{1609 \text{ m}}{1 \text{ mile}} \times \frac{1 \text{ hr}}{3600 \text{ s}} \approx 25 \frac{\text{m}}{\text{s}}$$

What is the volume in $(\text{liters})$ of $500 \text{ mL}$?

$$500 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.500 \text{ L}$$

A car travels at $60 \frac{\text{km}}{\text{hr}}$. How far does it travel in $30 \text{ minutes}$ in $(\text{meters})$?

$$60 \frac{\text{km}}{\text{hr}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{60 \text{ min}} \times 30 \text{ min} = 30,000 \text{ m}$$

Convert $15 \text{ cubic feet}$ ($ft^3$) to $(\text{cubic meters})$ ($m^3$). ($1 \text{ ft} = 0.3048 \text{ m}$)

$$15 \text{ ft}^3 \times (\frac{0.3048 \text{ m}}{1 \text{ ft}})^3 = 15 \text{ ft}^3 \times \frac{(0.3048)^3 \text{ m}^3}{1 \text{ ft}^3} \approx 0.42 \text{ m}^3$$

If the density of a substance is $1.2 \frac{\text{g}}{\text{mL}}$, what is the mass of $25 \text{ mL}$ of the substance?

$$25 \text{ mL} \times 1.2 \frac{\text{g}}{\text{mL}} = 30 \text{ g}$$

How many nanometers are in $0.012 \text{ mm}$?

$$0.012 \text{ mm} \times \frac{1 \text{ m}}{1000 \text{ mm}} \times \frac{10^9 \text{ nm}}{1 \text{ m}} = 1.2 \times 10^4 \text{ nm}$$

Convert $2.5 \text{ days}$ into $(\text{seconds})$.

$$2.5 \text{ days} \times \frac{24 \text{ hr}}{1 \text{ day}} \times \frac{60 \text{ min}}{1 \text{ hr}} \times \frac{60 \text{ s}}{1 \text{ min}} = 216,000 \text{ s}$$

Define the SI base unit for mass.

The kilogram ($\text{kg}$).

Define the SI base unit for length.

The meter ($\text{m}$).

Define the SI base unit for time.

The second ($\text{s}$).

Define the SI base unit for temperature.

The Kelvin ($\text{K}$).

What is matter?

Anything that has mass and takes up space.

How is matter classified?

Matter can be classified into pure substances (elements and compounds) and mixtures (homogeneous and heterogeneous).

Define a pure substance.

A substance that has a fixed chemical composition and distinct properties. It cannot be separated into simpler substances by physical means.

What is an element? Provide an example.

A pure substance that cannot be broken down into simpler substances by chemical means. Examples: Oxygen ($\text{O}_2$), Gold ($\text{Au}$).

What is a compound? Provide an example.

A pure substance composed of two or more elements chemically combined in a fixed ratio. Examples: Water ($\text{H}<em>2\text{O}$), Carbon Dioxide ($\text{CO}</em>2$).

How do elements in a compound differ from a mixture of elements?

In a compound, elements are chemically bonded and lose their individual properties, forming a new substance with unique properties. In a mixture, elements retain their individual properties and are not chemically bonded.

What is a mixture?

A physical combination of two or more substances in which the identities of the individual substances are retained. They can be separated by physical means.

Define a homogeneous mixture. Provide an example.

A mixture that has a uniform composition and appearance throughout. Its components are indistinguishable even under a microscope. Also called a solution. Examples: Saltwater, air.

Define a heterogeneous mixture. Provide an example.

A mixture that does not have a uniform composition and appearance. Its components are visibly distinct or exist in different phases. Examples: Sand and water, salad.

What are the three common states of matter?

Solid, Liquid, Gas.

Describe the characteristics of solids, liquids, and gases.

• Solid: Definite shape and volume; particles tightly packed, vibrate in fixed positions.
• Liquid: Indefinite shape, definite volume; particles close but can move past each other.
• Gas: Indefinite shape and volume; particles far apart, move randomly and rapidly.

What is a physical property? Provide an example.

A characteristic of a substance that can be observed or measured without changing the substance's chemical identity. Examples: melting point, boiling point, density, color, hardness.

What is a chemical property? Provide an example.

A characteristic that describes how a substance reacts or changes into a new substance. Examples: flammability, reactivity with acid, ability to rust.

What is a physical change? Provide an example.

A change in the form or appearance of a substance, but not its chemical composition. No new substance is formed. Examples: melting ice, dissolving sugar in water, cutting paper.

What is a chemical change? Provide an example.

A change that results in the formation of one or more new substances with different chemical compositions and properties. Examples: burning wood, rusting iron, cooking an egg.

How can mixtures be separated?

By physical means such as filtration, distillation, decantation, evaporation, or chromatography.

How can compounds be separated?

By chemical means, which involve breaking chemical bonds (e.g., electrolysis for water).

Classify: sugar as an element, compound, or mixture.

Compound.

Rule for counting non-zero digits in sig figs.

All non-zero digits are always significant. Ex: $45.87 \text{ g}$ has $4$ sig figs.

Rule for counting zeros between non-zero digits.

Zeros between non-zero digits are significant. Ex: $1005 \text{ kg}$ has $4$ sig figs.

Rule for counting leading zeros.

Leading zeros (zeros before non-zero digits) are never significant. They are placeholders. Ex: $0.0025 \text{ m}$ has $2$ sig figs.

Rule for counting trailing zeros with a decimal point.

Trailing zeros (zeros at the end) are significant if the number contains a decimal point. Ex: $12.00 \text{ g}$ has $4$ sig figs.

Rule for counting trailing zeros without a decimal point.

Trailing zeros without a decimal point are generally ambiguous and assumed to be not significant unless otherwise specified. Ex: $1200 \text{ m}$ has $2$ sig figs (unless context says otherwise). To make them significant, write in scientific notation: $1.20 \times 10^3 \text{ m}$ (3 sig figs).

How many significant figures are in $3.400$?

$4$ significant figures.

How many significant figures are in $0.0050$?

$2$ significant figures.

How many significant figures are in $2050$ (no decimal)?

$3$ significant figures (assuming trailing zeros without a decimal are not significant).

Rule for sig figs in addition/subtraction.

The result must have the same number of decimal places as the measurement with the fewest decimal places.

Rule for sig figs in multiplication/division.

The result must have the same number of significant figures as the measurement with the fewest significant figures.

Calculate $2.5 \text{ cm} + 0.35 \text{ cm} + 1.255 \text{ cm}$ with correct sig figs.

$2.5 \text{ cm}$ (1 dec. place) $+ 0.35 \text{ cm}$ (2 dec. places) $+ 1.255 \text{ cm}$ (3 dec. places) $= 4.105 \text{ cm}$. Rounded to 1 decimal place: $4.1 \text{ cm}$.

Calculate $5.23 \text{ g} \times 1.2 \frac{\text{cm}}{\text{g}}$ with correct sig figs.

$5.23 \text{ g}$ (3 sig figs) $\times 1.2 \frac{\text{cm}}{\text{g}}$ (2 sig figs) $= 6.276 \text{ cm}$. Rounded to 2 sig figs: $6.3 \text{ cm}$.

Define Accuracy.

How close a measurement or calculation is to the true or accepted value.

Define Precision.

How close multiple measurements or calculations are to each other (reproducibility).

If a dartboard has all darts clustered tightly in one corner, what does this indicate about accuracy and precision?

High precision (darts are close to each other) but low accuracy (they are far from the bullseye).

What is random error?

Error that arises from uncontrolled and unpredictable factors, causing measurements to vary randomly around the true value. It affects precision.

What is systematic error?

Error that consistently biases measurements in one direction (always too high or always too low) due to flaws in equipment or experimental design. It affects accuracy.

How is percent error calculated?

$$(Percentage~Error) = (\frac{| \text{experimental value} - \text{accepted value} |}{\text{accepted value}} \times 100\%)$$

Express $0.000000567 \text{ m}$ in scientific notation.

$$5.67 \times 10^{-7} \text{ m}$$

What is density? Write its formula.

A physical property defined as mass per unit volume. $(Density) = (\frac{Mass}{Volume})$.

A block has a mass of $25.0 \text{ g}$ and a volume of $10.0 \text{ cm}^3$. What is its density?

$(Density) = (\frac{25.0 \text{ g}}{10.0 \text{ cm}^3}) = 2.50 \frac{\text{g}}{cm^3}$ (3 sig figs due to division rule).