MCAT Physics Equations and Constants

Gravity

• Gravitational Force:
  • Equation: $F_{grav} = mg$
  • Where:
    • $m$ = mass
    • $g$ = acceleration due to gravity
• Gravitational Acceleration:
  • Equation: $g = G \frac{M}{r^2}$
  • Common Approximation for Earth:
  • $g_{earth} \approx 10 \ m/s^2$

Kinematics

• Basic Equations of Motion:
  • Velocity:
  • Equation: $v = v_0 + at$
  • Displacement:
  • Equation: $x = v_0xt$
  • Horizontal Component:
  • Equation: $v<em>{x} = v</em>{0x}$
  • Vertical Component with Gravity:
  • Equation: $v<em>{y} = v</em>{0y} - gt$
  • Where:
    • $g$ = acceleration due to gravity
  • For an object in free fall:
  • Equation: $y = v_{0y}t - \frac{1}{2} gt^2$
  • Acceleration:
  • Equation: $a_{y} = -g$

Work, Energy, and Power

• Work Done by a Force:
  • Equation: $W = Fd \cos\theta$
• Kinetic Energy:
  • Equation: $KE = \frac{1}{2} mv^2$
• Work-Energy Theorem:
  • Equation: $W_{net} = \Delta KE$
• Power:
  • Equation: $P = \frac{W}{t} = Fv$
• Gravitational Potential Energy:
  • Equation: $PE_{grav} = mgh$
• Total Mechanical Energy:
  • Equation: $E = KE + PE$

Circular Motion

• Centripetal Acceleration:
  • Equation: $a_{c} = \frac{v^2}{r}$
• Centripetal Force:
  • Equation: $F<em>{c} = ma</em>{c} = m \frac{v^2}{r}$
• Torque:
  • Equation: $\tau = rF\sin\theta$

Friction

• Static Friction:
  • Equation: $F<em>{f, static} < \mu</em>{s} F_{N}$
• Kinetic Friction:
  • Equation: $F<em>{f, kinetic} = \mu</em>{k} F_{N}$

Fluids

• Density:
  • Equation: $\rho = \frac{mass}{volume}$
• Pascal’s Law:
• Continuity Equation:
  • Equation: $A<em>{1}v</em>{1} = A<em>{2}v</em>{2}$
• Archimedes’ Principle:
• Buoyant Force:
  • Equation: $F<em>{buoyant} = \rho</em>{fluid} V_{submerged} g$
• Flow Rate:
  • Equation: $Q = Av$

MCAT Chemistry Equations and Constants

General Chemistry

pH and pOH

• pH:
  • Equation: $pH = -\log[H^+]$
• pOH:
  • Equation: $pOH = -\log[OH^-]$
• Relationship:
  • Equation: $K_w = [H^+][OH^-] = 1 \times 10^{-14}$ at 25°C
  • $pH + pOH = 14$

Ideal Gas Law

• Equation: $PV = nRT$
• STP (Standard Temperature and Pressure):
  • $T = 0°C = 273 K$
  • $P = 1 atm = 760 torr = 760 mmHg$

Electrochemistry

• Faraday's Constant:
  • $F = 96,000 \, C/mol$
• Dilution Equation:
  • $M<em>1V</em>1 = M<em>2V</em>2$
• Thermodynamics:
  • Heat:
  • Equation: $q = mc\Delta T$
  • Molar Heat of Fusion/Vaporization:
  • $q = n\Delta H_{fusion/vaporization}$

Thermodynamics

• First Law:
  • Equation: $\Delta E = Q - W$
• Gibbs Free Energy:
  • Equation: $\Delta G = \Delta H - T\Delta S$
  • Standard Gibbs Free Energy:
  • Equation: $\Delta G^\circ = -RT \ln K$

Rate Laws and Equilibrium

• Rate Law:
  • Equation: $Rate = k[A]^a[B]^b…$
• Reaction Quotient:
  • Equation: $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• Equilibrium Constant:
  • Equation: $K_{eq} = \frac{products}{reactants}$ at equilibrium

Thermochemistry

• Enthalpy Change of Reaction:
  • Equation: $\Delta H^\circ<em>{rxn} = \Sigma n\Delta H^\circ</em>f, products - \Sigma n\Delta H^\circ_f, reactants$

Acids and Bases

• Ionization Constants:
  • $K<em>a$ and $K</em>b$
  • Relationship:
  • $K<em>w = K</em>a \cdot K_b$
  • Henderson-Hasselbalch Equation:
  • Equation: $pH = pK_a + \log [A^-]/[HA]$

Stoichiometry and Gases

• Molarity:
  • Equation: $M = \frac{moles}{L}$
• Mole Fraction:
  • Equation: $X<em>a = \frac{moles</em>{a}}{total \, moles}$

Additional Equations

• Capacitance:
  • $C = \frac{Q}{V}$
• Thermodynamic Equations:
  • $\Delta G = -nFE_{cell}$
  • Arrhenius Equation:
  • $k = Ae^{-\frac{E_a}{RT}}$