Measurement and Problem Solving in General Chemistry (Chapter 2 Study Notes)

Measurement and Problem Solving

Introduction

Measurement and problem solving are foundational skills in general chemistry. Understanding units, measurement systems, and conversion techniques is essential for accurate scientific calculations and communication.

Systems of Units

Overview of Measurement Systems

• English System: Used primarily in the USA. Common units include inches, yards, and pounds.

• Metric System: Used in most of the world. Common units include centimeters, meters, and kilograms.

• International System of Units (SI System): Based on the metric system and used universally in science for consistency and precision.

SI Base Units

The SI system defines seven base units from which all other units are derived. The most relevant for general chemistry are:

Quantity	Unit	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Amount of substance	mole	mol
Electric current	ampere	A
Luminous intensity	candela	cd
Temperature	kelvin	K

Mass and Weight

Definitions and Differences

• Mass: A measure of the quantity of matter in an object. The SI base unit is the kilogram (kg).

• Weight: A measure of the gravitational pull on an object’s mass. Weight depends on gravity, while mass does not.

Key Equation:

$1\,\text{kg} = 1000\,\text{g} = 10^3\,\text{g}$

• An object with a mass of 22.0 lb weighs 22.0 lb on Earth but only 3.7 lb on the Moon. The mass remains the same, but the weight changes due to gravity.

SI Prefix Multipliers

Purpose and Common Prefixes

SI prefixes are used to express multiples or fractions of base units, making it easier to handle very large or very small measurements.

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

Example: $1000\,\text{m} = 1\,\text{km}$; $0.001\,\text{m} = 1\,\text{mm}$

Length, Volume, and Derived Units

Length

• The SI base unit for length is the meter (m).

• Common conversions: $1\,\text{in.} = 2.54\,\text{cm}$ (exact)

Volume

• Volume is a derived unit: $\text{Volume} = (\text{length})^3$

• SI unit for volume is the cubic meter (m3).

• Common laboratory units: liter (L) and milliliter (mL)

Key Equations:

$1\,\text{L} = 1\,\text{dm}^3$

$1\,\text{mL} = 1\,\text{cm}^3$

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

Unit Conversions and Dimensional Analysis

Conversion Factors

• To convert between units, use a conversion factor (a ratio equal to 1 that relates two units).

• Always write numbers with their units and treat units algebraically.

• Conversion factors can be inverted depending on the direction of the conversion.

General Formula:

$\text{Given quantity} \times \text{Conversion factor} = \text{Desired quantity}$

Example: To convert 14.6 in. to cm:

• Relationship: $1\,\text{in.} = 2.54\,\text{cm}$

• Conversion: $14.6\,\text{in.} \times \frac{2.54\,\text{cm}}{1\,\text{in.}} = 37.1\,\text{cm}$

Multistep Unit Conversions

• Some problems require multiple conversion steps (e.g., cm to in. to ft).

• Set up a solution map to plan the sequence of conversions.

Example: Convert 68 cm to feet:

• Step 1: $68\,\text{cm} \times \frac{1\,\text{in.}}{2.54\,\text{cm}} = 26.77\,\text{in.}$

• Step 2: $26.77\,\text{in.} \times \frac{1\,\text{ft}}{12\,\text{in.}} = 2.23\,\text{ft}$

Polyatomic Ions

Common Polyatomic Ions

Polyatomic ions are ions composed of two or more atoms covalently bonded, carrying a net charge. They are important in naming and understanding chemical compounds.

Formula	Name
CO32−	carbonate
HCO3−	bicarbonate (or hydrogen carbonate)
NO3−	nitrate
SO42−	sulfate
NH4+	ammonium
OH−	hydroxide
PO43−	phosphate
ClO4−	perchlorate
CrO42−	chromate
MnO4−	permanganate
NO2−	nitrite
SO32−	sulfite
HPO42−	hydrogen phosphate
CN−	cyanide

Practice and Application

Sample Problems

• Convert 7.8 lb to kg: $7.8\,\text{lb} \times \frac{1\,\text{kg}}{2.205\,\text{lb}} = 3.54\,\text{kg}$

• How many grams are in $1.48 \times 10^6$ μg? $1.48 \times 10^6\,\mu\text{g} \times \frac{1\,\text{g}}{10^6\,\mu\text{g}} = 1.48\,\text{g}$

• Convert 2.0 gal to cm3: $2.0\,\text{gal} \times \frac{3.785\,\text{L}}{1\,\text{gal}} \times \frac{1000\,\text{mL}}{1\,\text{L}} \times \frac{1\,\text{cm}^3}{1\,\text{mL}} = 7570\,\text{cm}^3$

Tips for Success

• Always include units in calculations.

• Use dimensional analysis to ensure units cancel appropriately.

• Check significant figures and use exact numbers where appropriate (e.g., 1 in. = 2.54 cm is exact).