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Introduction to Chemistry: Measurement & Problem Solving

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  • Measured vs. Exact Numbers
    Measured numbers are inexact and have uncertainty (e.g., 5.25 m). Exact numbers have no uncertainty and can be counted exactly (e.g., 24 students).
  • Uncertainty in Measurements
    Every measurement has some degree of uncertainty. The last digit is always uncertain, even with sensitive instruments.
  • Accuracy vs. Precision
    Accuracy is how close a measurement is to the true value. Precision is how close repeated measurements are to each other.
  • Mass Measurement
    Mass is the amount of matter in a substance, measured in grams (g) using a balance. Weight is the force of gravity on an object.
  • Volume Measurement
    Volume is the space occupied by a substance, measured in liters (L) or milliliters (mL). 1 mL = 1 cm\(^3\).
  • Graduated Cylinder Measurement
    Record volume at the meniscus, not the highest point. Uncertainty ranges from +0.1 mL to +0.5 mL.
  • Scientific Notation
    Expresses very large or small numbers as \(N \times 10^n\), where N is between 1 and 9, and n is an integer exponent.
  • Rules for Significant Figures
    All non-zero digits are significant. Zeros between non-zero digits and trailing zeros after a decimal are significant. Leading zeros are not significant.
  • Rounding with Significant Figures
    If the digit to drop is 5 or greater, round up the last significant figure. If less than 5, leave the last significant figure unchanged.
  • Addition & Subtraction with Sig Figs
    Result should have the same number of decimal places as the measurement with the fewest decimal places.
  • Multiplication & Division with Sig Figs
    Result should have the same number of significant figures as the measurement with the fewest significant figures.
  • Unit Conversion Factor
    A ratio of two equivalent quantities used to convert units, e.g., 1 foot = 12 inches.
  • Exact Equivalents
    Two units exactly equal to each other with infinite significant figures, e.g., 1 liter = 1000 milliliters.
  • Unit Analysis Problem Solving
    Carry units through calculations, cancel units properly, and check final units and significant figures.
  • Metric Prefixes
    Prefixes indicate powers of ten, e.g., kilo- (k) = 10\(^3\), milli- (m) = 10\(^{-3}\).
  • Density
    Density is mass per unit volume, \(d = \frac{mass}{volume}\). Water density is 1.00 g/mL.
  • Volume by Displacement
    Volume of an irregular solid is found by the difference in liquid volume before and after immersion.
  • Percent Concept
    Percent expresses a ratio as parts per 100: \(\frac{part}{whole} \times 100\).
  • Volume of a Rectangular Solid
    Volume = length × width × height. Units must be consistent.
  • Metric to English Conversion
    Conversions between metric and English units are not exact and require attention to significant figures.