MCAT Physics Formulas 2

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  1. Standing waves - one end fixed and one end free
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    • n=1, 3, 5, ...
    • L = string or pipe length
    • fixed end is a node, open/free end is antinode
  2. Beat frequency - alternating increases and decreases in intensity
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    • Pitch correlates with frequency
    • 2 waves with constant A and different f interfere
  3. Doppler Effect
    Image Upload 3  OR Image Upload 4

    • Apparent frequency of the source is increased (apparent wavelength is decreased) as source approaches observer, and the opposite as the source leaves
    • Because pitch correlates with f, apparent pitch also increased as source approaches and decreased as it leaves
  4. Angular frequencies of a mass on a spring or a pendulum
    • Whack 'em: Image Upload 5 on a spring
    • Wiggle: Image Upload 6 on a pendulum
  5. Simple Harmonic motion (mass on a spring, pendulum, planetary orbit viewed from the side, e- movement in alternating current)
    • Hooke's Law: Image Upload 7
    • ⇒acceleration is proportional and oppositely directed to displacement
    • Image Upload 8 ⇒ acceleration is proportional to frequency squared
  6. Wave velocity is medium dependent
    • positively correlates with tension, bulk modulus, pressure (gas) & temperature (gas)
    • negatively correlates with density and μ (mass per unit length)
  7. Coulomb's law: electric force, F, as a function of Boltzmann's constant, k
    • Image Upload 9
    • Image Upload 10
    • Q's are charges and r is center-center distance
    • F is repulsive if both charges positive or negative
    • F is attractive if one charge positive and the other is negative
  8. Electric field due to a point charge, q, at a distance, r
    Image Upload 11

    E is a vector that points away from positive toward negative charge
  9. Electric potential energy stored between the interaction between two point charges
    Image Upload 12
  10. Electric potential, Voltage, due to a point charge
    Image Upload 13 in Volts (V) or J/C
  11. Force in a constant electric field
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    F is in the same direction as E if q is positive and in the opposite direction is q is negative
  12. Electric potential, Voltage, in a constant electric field
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  13. Energy gained by a charge, q, in a constant electric field, E.
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    • Energy gained is force times distance traveled through the field
    • Potential is the energy per unit charge
  14. Force,F, on a charge,q, moving through a magnetic field,B, with a velocity, v.
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    Magnitude of the force is expressed in terms of the angle, θ, between velocity and the magnetic field
  15. Ohm's law (electronic circuits) to relate electric potential (V) with the current (I) and the resistance (R) of the device through which it flows.
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  16. Resistance of a wire
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    • ρ is resistivity (experimentally determined for a given substance, units are Ω·m), L is Length of the wire, & A is the cross-sectional area of the wire
    • R is measured in Ohms, Ω
  17. Electric Power, P
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  18. Root Mean Square (RMS) voltage and current in alternating current (AC) circuits
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    • Where V0 and I0 are peak values
    • Thus average power in AC circuits:
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  19. Total resistance in a circuit with resistors in series.
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  20. Effective resistance in a circuit with resistors in parallel.
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  21. Capacitance, C, of a capacitor
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    Charge per voltage
  22. Effective capacitance of capacitors in series
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  23. Effective capacitance of capacitors in parallel
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  24. Electric energy stored by a capacitor
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    • Electric energy stored is given in terms of the capacitance, C, and the potential difference between the conductors, V.
    • Remember in a constant electric field:
    • Image Upload 31
  25. Electromagnetic wave speed in a vacuum, c
    Image Upload 32

    *same as any wave
  26. Snell's Law: relating refractive indices, angle of incidence, and angle of refraction with respect to the perpendicular of the interface
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  27. Total internal reflection and the critical angle, θc
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    Only applies if n1>n2 and light is traveling in medium 1
  28. Index of refraction, n for a given medium
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    • c is speed of light in a vacuum
    • v is the speed of light in that medium
    • nair is about 1
    • nwater = 1.3
    • nglass = 1.5
  29. Energy, E, of one photon and Planck's constant, h
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    Energy is dependent on its frequency
  30. The lens equation and positive negative determinations for focal length, object distance, and image distance
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    • focal length, f, is positive for converging and negative for diverging lenses
    • object distance, do, is positive if it is on the side of the lens from which light is coming and negative if on the opposite side
    • image distance, di, is positive if it is on the opposite side of the lens from which the light is coming and negative if on the same side
    • This also applies to mirrors but remember that light comes from the same side of a mirror as the observer and the opposite side of a lens.
  31. Focal length of a spherical mirror
    Image Upload 38

    r is the radius of curvature
  32. Lateral magnification, m, for a lens or mirror
    • Image Upload 39
    • For an upright image, magnification is positive and for an inverted image, m is negative.
    • Images and focal lengths are positive, real, & inverted on the same side as the observer.
  33. Power of a lens, P, in diopters (m-1)
    Image Upload 40

    Power is inversely proportional to the focal length, f
  34. General nature of diffraction
    • If a wave passes through an opening smaller or the same size as wavelength, it will bend (spread out).
    • Smaller opening --> more diffraction
  35. Aufbau Principle
    • Orbitals fill lowest energy to highest
    • 1s
    • 2s 2p
    • 3s 3p 3d
    • 4s 4p 4d 4f
    • 5s 5p 5d 5f
    • 6s 6p 6d 6f
  36. Hund's rule
    • single electrons enter each orbital of equal energy before a second electron of opposite spin enters any orbital and spin remains parallel if possible
    • Ex. Nitrogen:
    • N= 1s (↑↓) 2s (↑↓) 2px(↑) 2py(↑) 2pz(↑)
  37. Pauli Exclusion Principle
    no two electrons in an atom can have the same set of four quantum numbers, each orbital of specific quantum numbers (n,l,m) can hold at most two electrons with opposite spins (ms=-1/2 for one and +1/2 for the other)
  38. Heisenberg Uncertainty Principle
    position and momentum of a particle cannot both be exactly known at the same time
  39. Chemistry: Quantum numbers
    • Principal, n = shell level (higher n means increased size and energy)
    • Azimuthal, l = subshell (s, p, d, & f); l=0 means subshell s (for each new shell, n, l=n-1)
    • Magnetic, ml = precise orbital numbered -l to +l (for n=1; l=0 and m=0; for n=3, l=2 and m=-2, -1, 0, +1, or +2, 5 orbitals)
    • Electron spin, ms = -1/2 or +1/2 (unpaired electrons in same shell have parallel spins, paired electrons in same orbital have opposite spins)
  40. Ideal Gas Law (include Boyle's, Charles's, & Avogadro's Laws)
    Image Upload 41

    • Boyle's Law: Image Upload 42
    • Charles's Law: Image Upload 43
    • Avogadro's Law: Image Upload 44
    • Also (no one's) Law: Image Upload 45
    • Universal Gas Constant: Image Upload 46
  41. Standard Molar Volume of an Ideal Gas at STP
    • 22.4L/mol
    • Image Upload 47

    Standard Conditions: 25oC and 1atm
  42. Partial Pressure of a Gas in a mixture
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    Image Upload 49
  43. Dalton's Law: Total Pressure of a mixture of gasses
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  44. Average Kinetic Energy of one mole of gas (or liquid) molecules
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  45. Graham's Law: average rms velocities of two gasses in a mixture
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  46. Effusion rates of 2 gasses in a mixture through a pinhole
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    M represents molecular weights
  47. Van der Waal's Equation: behavior of a Real Gas
    Image Upload 54

    Where a relates to the strength of intermolecular interactions and b is the volume of one mole of the gas
  48. General (qualitative) characteristics of a Real gas compared with an Ideal gas
    Image Upload 55 because of the volume of the gas molecules

    Image Upload 56 because of attractive intermolecular forces
  49. Types of Solids and descriptions of each
    • Molecular solid: molecules held in place by dispersion forces, dipole interactions, and/or hydrogen bonds
    • Metallic Solid: atoms held in place by delocalized bonding
    • Network Solid: contains an array of covalent bonds linking every atom to its neighbors
    • Ionic Solid: Contains cations and anions attracted to one another by coloumbic interactions (charge forces)
  50. Intermolecular Forces: Hydrogen Bonding
    Involves the lone pair of electrons on an electronegative atom of one molecule and a polar bond to hydrogen in another molecule, generally confined to molecules that contain O, N, and F atoms
  51. Intermolecular Forces: Dipole Interactions
    Describe the attraction between the negatively charged end of a polar molecule and the positively charged ends of neighboring polar molecules
  52. Intermolecular Forces: Dispersion Forces or London Dispersion Forces
    Attraction between the negatively charged electron cloud of one molecule and the positively charged nuclei of neighboring molecules
  53. Rate law of an elementary chemical reaction: dependence of reaction rate on [reactants]

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    *If reaction is not elementary replace orders with α,β, etc and determine orders experimentally: Image Upload 59
  54. Arrhenius equation for temperature dependence of reaction rate constant, k
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    • z is the number of collisions, p is the fraction of collisions occurring in the correct orientation, and e is the fraction of collisions containing sufficient energy to carry out the reaction (higher Ea means lower reaction rate, higher temperature means higher reaction rate)
  55. The law of mass action: forward and reverse reaction rates are equal at equilibrium so, for the following elementary reaction:
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    *This applies to non-elementary reactions as well.
  56. Reaction quotient, Q, for a non-equilibrium state predicts which direction a reaction will proceed.
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    • Q=K @ equilibrium
    • Q>K then reverse reaction predominates
    • Q<K then forward reaction predominates
  57. Le Chatelier's principle regarding a reaction at equilibrium that is stressed in one of three ways:
    • 1) addition or removal of a reactant or product
    • 2) changing the pressure of the system
    • 3) heating or cooling the system
  58. Ionic Bonding and the Electrostatic Forces between Ions
    Image Upload 64

    • Image Upload 65 (energy given off when ions in gas phase come together to form a crystal, largest for smallest ions)
    • Electrostatic Force: Image Upload 66
  59. Molarity; Molality; Mole fraction (χ); mass percent; parts per million
    • Molarity, M = moles solute/volume solution
    • Molality, m = moles solute/kg solvent
    • mole fraction, χ = moles solute/total moles
    • mass percent = mass solute/total mass of solution * 100%
    • parts per million, ppm = mass solute/total mass of solution * 106
  60. Colligative properties, Raoult's law or distillation
    • Vapor pressure lowering: Image Upload 67 (mole fraction of A * vapor pressure of pure A)
    • Freezing point depression: Image Upload 68 (K is a constant for the solvent and m is molality of the solution)
    • Boiling point elevation: Image Upload 69 (K is a constant for the solvent and m is molality)
    • Osmotic pressure: Image Upload 70 (II is osmotic pressure, number of moles over volume of solution is c, molarity, R is the gas constant and T is absolute temperature)
  61. Henry's Law: Solubility of Gas in a Liquid
    • is directly proportional to the partial pressure of the gas above the liquid
    • Think: CO2 leaves soda after pressure is released.
    • Mathematically: Image Upload 71 (p is partial pressure, c is concentration of gas in liquid and k is a constant)
  62. Thermo-chemistry State Variables
    • Conditions that must be specified to establish the state of a system
    • Pressure (P)
    • volume (V)
    • Temperature (T)
    • amounts of substances (n)
  63. Standard Enthalpy of Formation
    • Enthalpy change accompanying the formation of one mole of a chemical substance from pure elements in their most stable forms under standard conditions
    • Symbol: Image Upload 72
  64. Hess's Law of heat summation
    The enthalpy change for any overall process is equal to the sum of enthalpy changes for any set of steps that leads from the reactants to the products (ΔH is path independent)
  65. Enthalpy (definition and equation)
    • A thermodynamic quantity whose change equals the heat flow at constant pressure
    • Image Upload 73
  66. Henderson Hasselbalch Equation for calculating the pH of solutions of weak acids (or bases)
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  67. Relate Equilibrium and ΔG
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Card Set
MCAT Physics Formulas 2
The rest of the MCAT formulas, they wouldn't all fit in one card set.
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