Essentials: Units, Measurement, and Problem Solving – Study Notes

Essentials: Units, Measurement, and Problem Solving

Units of Measurement

Understanding units is fundamental in chemistry, as they provide a standard for expressing physical quantities. The International System of Units (SI) is the most widely used system in scientific work.

• Length: Meter (m)

• Mass: Kilogram (kg)

• Time: Second (s)

• Temperature: Kelvin (K)

• Amount of substance: Mole (mol)

• Electric current: Ampere (A)

• Luminous intensity: Candela (cd)

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

Temperature Scales

Temperature is measured in degrees Fahrenheit (°F), degrees Celsius (°C), and Kelvin (K). Converting between these scales is essential for laboratory work and scientific calculations.

• 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 and °F.

• $K = 100 + 273.15 = 373.15$

• $^\circ F = \frac{9}{5}(100) + 32 = 212$

Prefix Multipliers

Prefix multipliers are used to express units that are much larger or smaller than the base unit. They are essential for scientific notation and dimensional analysis.

Prefix	Symbol	Multiplier
giga	G	$10^9$
mega	M	$10^6$
kilo	k	$10^3$
deci	d	$10^{-1}$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	μ	$10^{-6}$
nano	n	$10^{-9}$

Example: Convert 5.0 g to mg: $5.0 \text{ g} \times \frac{1000 \text{ mg}}{1 \text{ g}} = 5000 \text{ mg}$

Derived Units: Volume

Volume is a derived unit calculated from length measurements. The SI unit for volume is the cubic meter (m³), but liters (L) and milliliters (mL) are commonly used in chemistry.

• $1 \text{ L} = 1000 \text{ mL}$

• $1 \text{ m}^3 = 1000 \text{ L}$

• $1 \text{ cm}^3 = 1 \text{ mL}$

Example: Calculate the volume of a cube with sides of 2 cm: $V = (2 \text{ cm})^3 = 8 \text{ cm}^3 = 8 \text{ mL}$

Reliability of Measurement

Reliability in measurement is assessed by accuracy and precision. 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: Consistency among repeated measurements

Example: If the true value is 7.12 g, and measurements are 7.10 g, 7.12 g, and 7.11 g, the measurements are both accurate and precise.

Significant Figures in Calculations

Significant figures indicate the precision of a measured or calculated quantity. The rules for determining significant figures are crucial for reporting scientific data.

• 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.

Calculations:

• Addition/Subtraction: Round to the least number of decimal places.

• Multiplication/Division: Round to the least number of significant figures.

Example: $3.905 \times 2.20 = 8.59$ (rounded to three significant figures)

Density

Density is the ratio of mass to volume and is used to characterize substances. The formula for density is:

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

Example: An object with a mass of 100 g and a volume of 25.0 mL has a density of $\frac{100 \text{ g}}{25.0 \text{ mL}} = 4.00 \text{ g/mL}$

Dimensional Analysis

Dimensional analysis is a method for converting between units using conversion factors. It is essential for solving problems in chemistry.

• Conversion factor: $\frac{\text{Desired Unit}}{\text{Given Unit}}$

Example: Convert 5.0 m to cm: $5.0 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 500 \text{ cm}$

Practice Problems

• Calculate the volume of 100 g of CCl4 with a density of 1.58 g/mL.

• Calculate the mass of acetone (density = 0.7857 g/mL) in 25.36 mL.

• Calculate the density of an irregular solid with a mass of 10.0 g and a volume displacement from 50.0 mL to 53.3 mL.

Additional info: These notes include foundational concepts and practice problems for mastering units, measurement, and problem solving in general chemistry.