Key Concepts for Exam Preparation

SI Prefixes

  • Milli- and Mega- represent:
    • Milli-: 10−310^{-3}
    • Mega-: 10610^{6}

Conversions Between Units

  • Micrograms to Kilograms:

    • Conversion of 65.3 kg to micrograms:
    • 1kg=106mg1 kg = 10^6 mg
    • 65.3kg=65.3×106mg=6.53×107mg65.3 kg = 65.3 \times 10^{6} mg = 6.53 \times 10^{7} mg

  • Microliters to Centiliters:

    • Volume of 35 microliters in centiliters:
    • 1mL=1000μL1 mL = 1000 \mu L and 1cL=10mL1 cL = 10 mL
    • 35μL=35×10−3cL=3.5×10−4cL35 \mu L = 35 \times 10^{-3} cL = 3.5 \times 10^{-4} cL

  • Inches to Centimeters:

    • Conversion of 15 inches to centimeters:
    • 1in=2.54cm1 in = 2.54 cm
    • 15in=15×2.54=38.1cm15 in = 15 \times 2.54 = 38.1 cm (Approximately 38 cm)

Density Conversion

  • Density of Mercury:
    • Given: 13.6g/cm313.6 g/cm^3
    • To convert to pounds per cubic inch:
    • 1lb=454g1 lb = 454 g
    • Convert:
      1. 1cm3=(1/2.54)3in31 cm^3 = (1/2.54)^3 in^3
      2. Dlb/in3=13.6g/cm3×(1lb/454g)×(2.543cm3/in3)D_{lb/in^3} = 13.6 g/cm^3 \times (1 lb/454 g) \times (2.54^3 cm^3/in^3)

Significant Figures

  • For the expression:
    • (13.7+0.027)/8.221(13.7 + 0.027) / 8.221
    • Answer choice for significant figures:
    • Minimum significant figures = 3 (due to 0.027)

Volume Calculation

  • Volume of a Smartphone:
    • Dimensions: 4.9 in (height), 2.3 in (width), 8.0 mm (depth)
    • Convert dimensions to centimeters:
    • 4.9in=12.446cm4.9 in = 12.446 cm
    • 2.3in=5.842cm2.3 in = 5.842 cm
    • 8.0mm=0.8cm8.0 mm = 0.8 cm
    • Volume calculation:
    • Volume=height×width×depth=12.446×5.842×0.8=58.078cm3Volume = height \times width \times depth = 12.446 \times 5.842 \times 0.8 = 58.078 cm^3

Atoms, Moles, and Isotopes

  • Atoms in Moles:

    • Atoms in 7.12 mol of Au:
    • 7.12mol×6.022×1023atoms/mol=4.29×1024atoms7.12 mol \times 6.022 \times 10^{23} atoms/mol = 4.29 \times 10^{24} atoms

  • Moles from Atoms:

    • Given 8.73×1025atoms8.73 \times 10^{25} atoms of boron, B:
    • Moles = 8.73×1025 atoms/6.022×1023 atoms/mol=145moles8.73 \times 10^{25} \text{ atoms} / 6.022 \times 10^{23} \text{ atoms/mol} = 145 moles

Atomic Structure

  • Chlorine Isotope:

    • Chlorine-37:
    • 17 protons (p), 17 electrons (e), 20 neutrons (n)

  • Lithium Percent Abundance:

    • Lithium atomic mass = 6.9412 amu
    • For isotopes 6Li and 7Li:
    • Percent abundance of 6Li can be calculated using weighted averages.

Electromagnetic Radiation

  • Frequency and Wavelength:

    • For 532nm532 nm:
    • c=λfc = \lambda f, where c=3.00×108m/sc = 3.00 \times 10^{8} m/s;
    • Frequency can be calculated as f=cλ=3.00×108532×10−9f = \frac{c}{\lambda} = \frac{3.00 \times 10^{8}}{532 \times 10^{-9}}.

  • Energy of Photons:

    • E=hfE = hf, where h=6.63×10−34J sh = 6.63 \times 10^{-34} J \, s
    • E associated with 486nm486 nm can be found by converting to joules.

Quantum Mechanics

  • de Broglie Wavelength:

    • λ=hmv\lambda = \frac{h}{mv} for proton with mass 1.673×10−24g1.673 \times 10^{-24}g moving at 1000m/s1000 m/s.

  • Quantum Numbers:

    • Incorrect quantum number set, such as (n=4, l=3), is not valid since l must always be less than n.

Electron Configurations

  • Ground-State Configurations:
    • Identify elements by their electron configurations and how they correspond to atomic structure.