01 Chemical Foundations and Measurement

Measurements and SI Units

A Measurement is meaningful only when it includes both a number and a unit. For example, $12.4\,\mathrm{g}$ identifies a mass and its unit. The International System of Units (SI) provides standard units; common examples include length in meters, mass in grams or kilograms, time in seconds, temperature in kelvins or degrees Celsius, amount of substance in moles, and volume in liters or cubic meters.

Prefixes express powers of ten. For example:

Leave a space between a number and its unit symbol, as in $25\,\mathrm{mL}$. Unit symbols are not pluralized. Temperature conversions use an offset:

No measuring instrument provides unlimited precision. When reading a graduated scale, record all certain digits and one estimated digit. Reported digits describe the measurement’s precision; they do not make the value exact.

Takeaway: Pair every measurement with a unit, and report only the precision supported by the instrument.

Significant Figures and Rounding

Significant figures are the meaningful digits in a measured value. Use these rules to identify them:

• Nonzero digits are significant: $347$ has three significant figures.

• Zeros between nonzero digits are significant: $1002$ has four.

• Leading zeros are not significant: $0.0045$ has two.

• Trailing zeros after a decimal point are significant: $2.300$ has four.

• Trailing zeros in a whole number without a decimal point can be ambiguous. Scientific notation clarifies the intended precision: $1.0\times10^2$ has two significant figures, while $1.00\times10^2$ has three.

For calculations, the operation determines how to round:

• Multiplication and division: Round to the same number of significant figures as the input with the fewest. For example, $4.56\times1.4=6.384$, which is reported as $6.4$.

• Addition and subtraction: Round to the least precise decimal place among the inputs. For example, $12.11+0.3=12.41$, which is reported as $12.4$.

Counted items and defined conversion relationships are exact, so they do not limit significant figures. For instance, $60\,\mathrm{s}=1\,\mathrm{min}$ is exact. Keep extra digits during intermediate steps and round the final answer once to avoid unnecessary rounding error.

Takeaway: Use significant figures to match a calculated result to the precision of the measured inputs.

Converting Units with Dimensional Analysis

Dimensional analysis (also called the factor-label method) converts units using ratios of equal quantities. Because each conversion factor equals one, multiplying by it changes the units without changing the quantity. Arrange the factors so the original units cancel and the desired unit remains.

To convert $3.50\,\mathrm{h}$ to seconds:

Hours and minutes cancel, leaving seconds. Since the conversion relationships are exact, the answer retains the three significant figures in the starting measurement.

Dimensional analysis also checks equations: units on both sides must be consistent. Density is mass divided by volume, so it can have units such as $\frac{\mathrm{g}}{\mathrm{mL}}$ or $\frac{\mathrm{kg}}{\mathrm{m^3}}$.

Takeaway: Set up conversion factors so unwanted units cancel; check that equations have consistent units.

Matter: Substances and Mixtures

Matter is anything that has mass and occupies space. It can be classified as a pure substance or a mixture.

A Pure substance has a definite composition. An element, such as copper, contains one kind of element. A compound, such as water, contains elements chemically combined in a fixed proportion.

A Mixture contains substances physically combined in variable proportions. A homogeneous mixture, such as salt water, is uniform throughout. A heterogeneous mixture, such as oil and water, is not uniform throughout.

Mass and weight are related but different. Mass measures the amount of matter and is reported in units such as grams or kilograms. Weight is the force of gravity on that mass.

Takeaway: A substance has a definite composition; a mixture combines substances physically in variable proportions.

Properties, Changes, and Sample Size

A Physical property can be observed or measured without changing a substance’s chemical identity. Examples include color, density, melting point, and electrical conductivity. A physical change alters form or state without changing chemical identity: melting ice produces liquid water, while crushing a crystal changes its size and shape.

A chemical property describes a substance’s ability to undergo a change that forms different substances. Flammability and the tendency to react with oxygen are examples. A Chemical change produces substances with new chemical identities. Iron rusting forms iron oxides, and burning wood produces substances such as carbon dioxide and water.

Properties can also be classified by whether they depend on sample size:

• Intensive properties do not depend on the amount of sample; examples include temperature, density, and color.

• Extensive properties depend on the amount of sample; examples include mass and volume.

A practical test is to divide a uniform sample into smaller portions. Each portion retains the sample’s density, but has less mass and volume.

Takeaway: Physical changes preserve chemical identity, while chemical changes create substances with new identities. Intensive properties remain the same for portions of a uniform sample; extensive properties vary with sample amount.