MCAT Physics Formulas 2

• n=1, 3, 5, ...
• L = string or pipe length
• fixed end is a node, open/free end is antinode

• Pitch correlates with frequency
• 2 waves with constant A and different f interfere

  OR

• 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

• Whack 'em: on a spring
• Wiggle: on a pendulum

• Hooke's Law:
• ⇒acceleration is proportional and oppositely directed to displacement
• ⇒ acceleration is proportional to frequency squared

• positively correlates with tension, bulk modulus, pressure (gas) & temperature (gas)
• negatively correlates with density and μ (mass per unit length)

• 
• 
• 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

E is a vector that points away from positive toward negative charge

in Volts (V) or J/C

F is in the same direction as E if q is positive and in the opposite direction is q is negative

• Energy gained is force times distance traveled through the field
• Potential is the energy per unit charge

Magnitude of the force is expressed in terms of the angle, θ, between velocity and the magnetic field

• 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

• Where V₀ and I₀ are peak values
• Thus average power in AC circuits:
• 

Charge per voltage

• 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:
• 

*same as any wave

Only applies if n₁>n₂ and light is traveling in medium 1

• c is speed of light in a vacuum
• v is the speed of light in that medium
• n_air is about 1
• n_water = 1.3
• n_glass = 1.5

Energy is dependent on its frequency

• focal length, f, is positive for converging and negative for diverging lenses
• object distance, d_o, 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, d_i, 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.

r is the radius of curvature

• 
• 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.

Power is inversely proportional to the focal length, f

• If a wave passes through an opening smaller or the same size as wavelength, it will bend (spread out).
• Smaller opening --> more diffraction

• Orbitals fill lowest energy to highest
• 1s
• 2s 2p
• 3s 3p 3d
• 4s 4p 4d 4f
• 5s 5p 5d 5f
• 6s 6p 6d 6f

• 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 (↑↓) 2p_x(↑) 2p_y(↑) 2p_z(↑)

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 (m_s=-1/2 for one and +1/2 for the other)

position and momentum of a particle cannot both be exactly known at the same time

• 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, m_l = 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, m_s = -1/2 or +1/2 (unpaired electrons in same shell have parallel spins, paired electrons in same orbital have opposite spins)

• Boyle's Law: 
• Charles's Law:
• Avogadro's Law:
• Also (no one's) Law:
• Universal Gas Constant:

• 22.4L/mol
• 

Standard Conditions: 25^oC and 1atm

M represents molecular weights

Where a relates to the strength of intermolecular interactions and b is the volume of one mole of the gas

because of the volume of the gas molecules

because of attractive intermolecular forces

• 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)

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

Describe the attraction between the negatively charged end of a polar molecule and the positively charged ends of neighboring polar molecules

Attraction between the negatively charged electron cloud of one molecule and the positively charged nuclei of neighboring molecules

*If reaction is not elementary replace orders with α,β, etc and determine orders experimentally:

• 
• 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)

*This applies to non-elementary reactions as well.

• Q=K @ equilibrium
• Q>K then reverse reaction predominates
• Q<K then forward reaction predominates

• 1) addition or removal of a reactant or product
• 2) changing the pressure of the system
• 3) heating or cooling the system

• (energy given off when ions in gas phase come together to form a crystal, largest for smallest ions)
• Electrostatic Force:

• 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

• Vapor pressure lowering: (mole fraction of A * vapor pressure of pure A)
• Freezing point depression: (K is a constant for the solvent and m is molality of the solution)
• Boiling point elevation: (K is a constant for the solvent and m is molality)
• Osmotic pressure: (II is osmotic pressure, number of moles over volume of solution is c, molarity, R is the gas constant and T is absolute temperature)

• is directly proportional to the partial pressure of the gas above the liquid
• Think: CO₂ leaves soda after pressure is released.
• Mathematically: (p is partial pressure, c is concentration of gas in liquid and k is a constant)

• Conditions that must be specified to establish the state of a system
• Pressure (P)
• volume (V)
• Temperature (T)
• amounts of substances (n)

• Enthalpy change accompanying the formation of one mole of a chemical substance from pure elements in their most stable forms under standard conditions
• Symbol:

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)

• A thermodynamic quantity whose change equals the heat flow at constant pressure
•