Honors Chemistry Unit 2 Review: Scientific Measures & Calculations

Key Concepts and Definitions

• Matter anything that has mass and takes up space
  • Classified as pure substances (elements or compounds) or mixtures (homogeneous or heterogeneous)
• Mass fundamental property of matter representing the amount of substance
• Weight force exerted on an object due to gravity
• Volume amount of three-dimensional space occupied by an object or substance
  • Can be measured in cubic units (cm³, m³) or liters (L, mL)
• Density ratio of an object's mass to its volume, calculated as $density = \frac{mass}{volume}$
• Temperature measure of the average kinetic energy of particles in a substance
  • Commonly measured in Celsius (°C), Fahrenheit (°F), or Kelvin (K)
• Precision degree to which repeated measurements under the same conditions yield the same results
• Accuracy degree to which a measured value agrees with the true or accepted value

Units of Measurement

• SI (International System of Units) standardized system of measurement used in science
  • Based on seven base units (meter, kilogram, second, ampere, kelvin, mole, candela)
• Metric system decimal-based system of measurement used in most countries
  • Prefixes (kilo-, centi-, milli-, micro-) used to indicate multiples or fractions of base units
• Length measured in meters (m) or its multiples and submultiples (km, cm, mm)
• Mass measured in kilograms (kg) or its multiples and submultiples (g, mg, μg)
• Volume measured in liters (L) or its submultiples (mL, μL)
• Time measured in seconds (s), minutes (min), or hours (h)
• Temperature measured in degrees Celsius (°C) or Kelvin (K)
  • Kelvin is the SI unit for temperature, with 0 K representing absolute zero

Significant Figures

• Significant figures (sig figs) digits in a measured or calculated value that are known with certainty plus one estimated digit
  • Determine the precision and uncertainty of a measurement or calculation
• Counting significant figures non-zero digits, zeros between non-zero digits, and trailing zeros in numbers with decimal points are significant
  • Leading zeros and trailing zeros in numbers without decimal points are not significant
• Rules for calculations with significant figures
  • Addition and subtraction round the answer to the least precise measurement (fewest decimal places)
  • Multiplication and division round the answer to the least number of significant figures in any of the values used
• Exact numbers (counted values or defined constants) have an infinite number of significant figures and do not affect the sig figs in a calculation

Scientific Notation

• Scientific notation concise way to express very large or very small numbers as a product of a number between 1 and 10 and a power of 10
  • Useful for calculations involving measurements that vary greatly in magnitude
• Format $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer
  • $a$ is called the significand or mantissa, and $n$ is the exponent or power of 10
• To convert a number to scientific notation move the decimal point to obtain a number between 1 and 10, then multiply by the appropriate power of 10
  • If the decimal point moves to the left, the exponent is positive; if it moves to the right, the exponent is negative
• Rules for calculations with numbers in scientific notation
  • Addition and subtraction numbers must have the same exponent (adjust as needed), then add or subtract the significands
  • Multiplication multiply the significands and add the exponents
  • Division divide the significands and subtract the exponents

Dimensional Analysis and Unit Conversion

• Dimensional analysis problem-solving method that uses the units of measurement to guide the solution
  • Involves setting up a series of fractions (conversion factors) that cancel out unwanted units and yield the desired unit
• Conversion factor ratio of equivalent quantities expressed in different units, derived from a known relationship or equality
  • Can be used to convert between units within the same system (metric or English) or between different systems
• Steps for dimensional analysis
  1. Identify the given quantity and the desired unit
  2. Write the given quantity as a fraction, with the given unit in the denominator
  3. Multiply by one or more conversion factors to cancel out the unwanted units and obtain the desired unit
  4. Perform the calculation and round the answer to the appropriate number of significant figures
• Common metric-metric conversion factors
  • Length $1 \text{ km} = 1000 \text{ m}$, $1 \text{ m} = 100 \text{ cm}$, $1 \text{ cm} = 10 \text{ mm}$
  • Mass $1 \text{ kg} = 1000 \text{ g}$, $1 \text{ g} = 1000 \text{ mg}$, $1 \text{ mg} = 1000 \text{ μg}$
  • Volume $1 \text{ L} = 1000 \text{ mL}$, $1 \text{ mL} = 1 \text{ cm³}$
• Common metric-English conversion factors
  • Length $1 \text{ in} = 2.54 \text{ cm}$, $1 \text{ ft} = 30.48 \text{ cm}$, $1 \text{ mi} = 1.609 \text{ km}$
  • Mass $1 \text{ lb} = 453.6 \text{ g}$, $1 \text{ oz} = 28.35 \text{ g}$
  • Volume $1 \text{ gal} = 3.785 \text{ L}$, $1 \text{ qt} = 0.9464 \text{ L}$, $1 \text{ fl oz} = 29.57 \text{ mL}$

Accuracy vs. Precision

• Accuracy closeness of a measured value to the true or accepted value
  • Affected by systematic errors (consistent bias in the measurement process)
• Precision closeness of agreement among a set of repeated measurements
  • Affected by random errors (unpredictable fluctuations in the measurement process)
• High accuracy and high precision measurements are close to the true value and to each other
• High accuracy but low precision measurements are clustered around the true value but not close to each other
• Low accuracy but high precision measurements are close to each other but not to the true value
• Low accuracy and low precision measurements are neither close to the true value nor to each other
• Improve accuracy by calibrating instruments, using proper techniques, and minimizing systematic errors
• Improve precision by using consistent methods, controlling environmental factors, and increasing the number of measurements

Error Analysis and Uncertainty

• Error difference between the measured or calculated value and the true or accepted value
  • Expressed as absolute error (actual difference) or relative error (percentage difference)
• Absolute error $\text{absolute error} = \text{measured value} - \text{true value}$
• Relative error $\text{relative error} = \frac{\text{absolute error}}{\text{true value}} \times 100\%$
• Types of errors
  • Systematic errors consistent bias in the measurement process, causing measured values to be consistently higher or lower than the true value
  • Random errors unpredictable fluctuations in the measurement process, causing measured values to be sometimes higher and sometimes lower than the true value
• Uncertainty range of values within which the true value is expected to lie, based on the precision of the measurement
  • Expressed as a ± value after the measured value, indicating the maximum expected absolute error
• Propagation of uncertainty calculating the uncertainty in a result based on the uncertainties of the input measurements
  • For addition and subtraction, add the absolute uncertainties
  • For multiplication and division, add the relative uncertainties

Practical Applications in Chemistry

• Stoichiometry calculation of the quantities of reactants and products in a chemical reaction based on the balanced equation
  • Requires accurate measurements of mass, volume, and concentration, and proper use of dimensional analysis
• Preparation of solutions mixing a solute (solid, liquid, or gas) with a solvent to achieve a desired concentration
  • Requires precise measurements of mass or volume, and proper use of units and conversion factors
• Titration quantitative analysis technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration
  • Requires accurate measurements of volume, proper use of glassware (burette, pipette), and identification of the endpoint (color change)
• Gravimetric analysis quantitative analysis technique used to determine the mass or concentration of a substance by measuring the mass of a precipitate formed in a reaction
  • Requires precise measurements of mass, proper filtration and drying techniques, and calculation of the theoretical yield
• Calorimetry measurement of the heat absorbed or released during a physical or chemical process
  • Requires accurate measurements of mass, temperature change, and the specific heat capacity of the substances involved
• Gas laws relationships between the pressure, volume, temperature, and amount of a gas under various conditions
  • Requires precise measurements of pressure, volume, and temperature, and proper use of the ideal gas equation ($PV = nRT$)