Essentials: Units, Measurement, and Problem Solving

Essentials: Units, Measurement, and Problem Solving

Units of Measurement

Understanding and using the correct units is fundamental in chemistry. The International System of Units (SI) is the standard system used in scientific measurements.

• Length: measured in meters (m)

• Mass: measured in kilograms (kg)

• Time: measured in seconds (s)

• Temperature: measured in kelvin (K)

• Amount of substance: measured in moles (mol)

• Electric current: measured in amperes (A)

• Luminous intensity: measured in candelas (cd)

Temperature Scales

Temperature can be measured in degrees Celsius (°C), Fahrenheit (°F), or Kelvin (K). The Kelvin scale is the SI unit for temperature and is commonly used in scientific contexts.

• Celsius to Kelvin: $K = ^\circ C + 273.15$

• Celsius to Fahrenheit: $^\circ F = \frac{9}{5}(^\circ C) + 32$

• Fahrenheit to Celsius: $^\circ C = \frac{5}{9}(^\circ F - 32)$

Example: Convert 100°C to K: $100 + 273.15 = 373.15\ K$

Prefix Multipliers

Prefix multipliers are used to express very large or very small quantities. They are attached to SI units to indicate multiples or fractions of units.

Prefix	Symbol	Multiplier
kilo	k	$10^3$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	\mu	$10^{-6}$
nano	n	$10^{-9}$
pico	p	$10^{-12}$
mega	M	$10^6$
giga	G	$10^9$

Dimensional Analysis

Dimensional analysis is a method used to convert one unit to another using conversion factors. It is essential for solving problems involving measurements.

• Conversion factor: A ratio that expresses how many of one unit are equal to another unit.

• Example: $1\ \text{cm} = 0.01\ \text{m}$, so $\frac{1\ \text{cm}}{0.01\ \text{m}}$ is a conversion factor.

Derived Units: Volume

Volume is a derived unit calculated from length measurements. The SI unit for volume is the cubic meter ($m^3$), but liters (L) and milliliters (mL) are commonly used in chemistry.

• $1\ \text{L} = 1000\ \text{mL} = 1000\ \text{cm}^3$

• $1\ \text{mL} = 1\ \text{cm}^3$

Reliability of Measurement

Measurements in chemistry must be both accurate and precise. Accuracy refers to how close a measurement is to the true value, while precision refers to how reproducible measurements are.

• Accuracy: Closeness to the true value.

• Precision: Closeness of repeated measurements to each other.

Example: If a true value is 7.62 g and measurements are 7.58 g, 7.59 g, and 7.60 g, the measurements are precise but not accurate.

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. The rules for determining the number of significant figures are:

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros after a decimal point are significant.

Example: 0.00450 has three significant figures.

Addition and Subtraction

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

• Example: $1.895 + 2.08 = 3.98$ (rounded to two decimal places)

Multiplication and Division

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

• Example: $3.05 \times 2.2 = 6.7$ (rounded to two significant figures)

Density

Density is the ratio of mass to volume. It is an important property for identifying substances and is calculated using the formula:

$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Units: Commonly expressed in $\text{g/cm}^3$ or $\text{g/mL}$ for solids and liquids.

• Example: If an object has a mass of 100 g and a volume of 25.0 mL, its density is $\frac{100\ \text{g}}{25.0\ \text{mL}} = 4.00\ \text{g/mL}$

Practice Problems

• Convert between temperature scales using the provided equations.

• Use prefix multipliers to convert between units (e.g., mg to g, nm to m).

• Determine the number of significant figures in a given measurement.

• Calculate density given mass and volume, or solve for mass or volume given density and one other variable.

Additional info: These notes are based on introductory material for General Chemistry, focusing on measurement, units, and problem-solving skills essential for laboratory and theoretical work.