Measurements and Problem Solving

Introduction to Measurements

Measurements are fundamental to chemistry, providing quantitative information about matter and its properties. Every measurement consists of a number (magnitude) and a unit, which defines the scale being used.

• Number: Indicates the magnitude of the measurement.

• Unit: Specifies the scale or standard used (e.g., meters, grams).

Units of Measurement

Chemistry uses several systems of units, but the SI (International System of Units) is the standard for scientific work.

• English Units: Used in everyday life in some countries (e.g., inches, pounds).

• Metric Units: Based on powers of ten, widely used globally.

• SI Units: Standardized units for scientific measurements.

SI Base Units

• Mass: kilogram (kg)

• Length: meter (m)

• Time: second (s)

• Temperature: kelvin (K)

• Amount of substance: mole (mol)

Temperature Scales

Temperature is a measure of the average kinetic energy of particles. It is used to predict the flow of heat, which always moves from warmer to cooler objects.

• Kelvin (K): The SI unit for temperature. Absolute zero (0 K) is the lowest possible temperature.

• Celsius (°C): Commonly used in science.

• Fahrenheit (°F): Used in some countries for everyday purposes.

Conversion formulas:

Metric Prefixes

Metric prefixes indicate multiples or fractions of base units, making it easier to express very large or small quantities.

• Tera (T):

• Giga (G):

• Mega (M):

• Kilo (k):

• Deci (d):

• Centi (c):

• Milli (m):

• Micro (μ):

• Nano (n):

• Pico (p):

• Femto (f):

Metric Conversions: Length, Mass, and Volume

Length (Meter)

• 1 km = 1000 m

• 1 m = 100 cm

• 1 m = 1000 mm

• 1 mm = 1000 μm

• 1 μm = 1000 nm

Mass (Gram)

• 1 kg = 1000 g

• 1 g = 1000 mg

• 1 mg = 1000 μg

• 1 μg = 1000 ng

Volume (Liter)

• 1 kL = 1000 L

• 1 L = 1000 mL

• 1 mL = 1000 μL

• 1 μL = 1000 nL

Volume Calculations

Volume is the amount of three-dimensional space occupied by a substance.

• Formula:

• 1 dm3 = 1 L

• 1 cm3 = 1 mL

Density

Density is a characteristic physical property of matter, defined as mass per unit volume. It is an intensive property, meaning it does not depend on the amount of substance.

• Formula:

• Units: g/mL or g/cm3

• Density is temperature dependent.

Significant Figures (Sig Figs)

Significant figures reflect the precision of a measurement. They are important for reporting and calculating scientific data accurately.

• Precision: Consistency of repeated measurements.

• Accuracy: Closeness to the true value.

• Uncertainty: The degree of doubt in a measurement.

Rules for Significant Figures

• All non-zero digits are significant.

• Trapped zeros (between non-zero digits) are significant.

• Leading zeros (before non-zero digits) are not significant.

• Trailing zeros are significant if a decimal point is present.

Examples of Significant Figures

• 100 m (1 sig fig)

• 100.0 m (4 sig figs)

• 100. m (3 sig figs)

• 1.0 x 102 m (2 sig figs)

• 0.003050 km (4 sig figs)

• 1 m = 1000 mm (definition, infinite sig figs)

Significant Figures in Calculations

• Multiplication/Division: Result is limited by the factor with the fewest sig figs.

• Addition/Subtraction: Result is limited by the least accurate measurement (fewest decimal places).

• Round only at the end of calculations.

Dimensional Analysis and Unit Conversions

Dimensional analysis (factor-label method) is a systematic way to convert between units using conversion factors.

• Equivalence statement: Shows the relationship between two units (e.g., 1 in = 2.54 cm).

• Conversion factor: Fraction used to cancel unwanted units and introduce desired units.

Steps for Unit Conversion

1. Identify the starting unit.

2. Identify the desired unit.

3. Find equivalence statements or conversion factors.

4. Multiply by conversion factors to cancel unwanted units.

Examples

• Convert 36.0 inches to centimeters.

• Convert 88 cm to meters.

• Convert 325 mg to g.

• Convert 900 ng to kg.

• Convert 256 kilobytes (kb) to megabytes (Mb).

• Convert 165 pounds to kg.

• Convert 26.2 miles to meters.

• Convert 5.0 g to ounces.

Units Raised to a Power

When converting units raised to a power (e.g., volume), apply the conversion factor to each dimension.

• Example: Calculate the volume in liters of a 305 in3 engine, given 1 in = 2.54 cm.

Density as a Conversion Factor

Density can be used to convert between mass and volume.

• Example: Acetone has a density of 0.7857 g/cm3. What is the mass of 28.56 mL of acetone?

• Example: What is the volume of 6.54 g of acetone?

Application Example

• Human fat has a density of 0.918 g/cm3. How much volume (in cm3) is gained by a person who gains 10.0 lbs of pure fat?

Problem Solving with Equations

Chemistry often requires solving for unknowns using equations and conversion factors.

• Example: What is the thickness of a 45.4 cm x 104.6 cm rectangular piece of cast iron (d = 7.76 g/cm3) that has a mass of 89.8 kg?

• Example: Find the radius (r) of an aluminum cylinder that is 2.00 cm long and has a mass of 12.4 g. Given dAl = 2.70 g/cm3 and .

Applied Unit Conversions in Medicine

• Example: An ibuprofen suspension for infants contains 100 mg / 5.0 mL. The recommended dose is 10 mg / kg of body weight. How many mL should be given to an infant weighing 18 lb? (1 kg = 2.2 lb)

Summary Table: Metric Prefixes

Summary Table: SI Base Units

Summary Table: Significant Figure Rules

Summary Table: Common Conversion Factors

Summary Table: Density Calculations

Summary Table: Volume Relationships

Summary Table: Temperature Conversions