MCAT Physics, Chemistry, and Constants Study Guide

MCAT Equations and Constants - Detailed Study Notes

1. Physics Equations

1.1. Gravity

• Gravitational Force:
  • $F_{grav} = mg$
  • Definition: The force exerted by gravity on an object is equal to the mass of the object multiplied by the acceleration due to gravity.

1.2. Kinematics

• Basic Kinematic Equations:
  • Velocity:
  • $v = v_0 + at$
  • Definition: The final velocity of an object is equal to its initial velocity plus the product of acceleration and time.
  • Position:
  • $x = v_{0x}t + \frac{1}{2}at^2$
  • Definition: The position is given by the initial horizontal velocity multiplied by time plus half the acceleration multiplied by time squared.
  • Horizontal and Vertical Components:
  • $v<em>{x} = v</em>{0x}$
  • $a_x = 0$
  • $v<em>{y} = v</em>{0y} - gt$
  • Displacement:
  • $y = v_{0y}t - \frac{1}{2}gt^2$
  • Definition: The vertical displacement is given by initial vertical velocity multiplied by time minus half the acceleration due to gravity multiplied by time squared.

1.3. Forces on Inclines

• Forces on an Inclined Plane:
  • Static Friction:
  • F{f, ext{static}} < bcs F_N
  • Forces due to Gravity:
  • $F_{g, parallel} = mg ext{sin}( heta)$
  • $F_{g, perpendicular} = mg ext{cos}( heta)$

1.4. Centripetal Force and Motion

• Centripetal Acceleration and Force:
  • Centripetal Acceleration:
  • $a_c = \frac{v^2}{r}$
  • Centripetal Force:
  • $F<em>c = ma</em>c = m\frac{v^2}{r}$

1.5. Thermodynamics and Energy

• Work and Energy:
  • Work:
  • $W = Fd ext{cos}( heta)$
  • Kinetic Energy:
  • $KE = \frac{1}{2}mv^2$
  • Total Mechanical Energy:
  • $E = KE + PE$
  • Power:
  • $P = \frac{W}{t} = Fv$
  • Gravitational Potential Energy:
  • $PE_{grav} = mgh$

1.6. Fluid Dynamics

• Basic Fluid Dynamics:
  • Fluid Density:
  • 
    ho = rac{mass}{volume}
  • Pascal’s Law:
  • $P<em>1 = P</em>2$
  • Continuity Equation:
  • $A<em>1v</em>1 = A<em>2v</em>2$

1.7. Miscellaneous Equations

• Work in Thermodynamics:
  • $W = P riangle V$
• Heat Capacity:
  • $Q = C riangle T$
• Specific Heat:
  • $Q = mc riangle T$
• Flow Rate:
  • $Q = Av$

2. Electricity and Magnetism Equations

2.1. Ohm's Law

• Voltage, Current and Resistance:
  • $V = IR$
  • Power in Electricity:
  • $P = IV = I^2R = \frac{Q}{t}V$

2.2. Electrostatics

• Coulomb’s Law:
  • $F<em>E = k\frac{|q</em>1q_2|}{r^2}$
• Electric Field:
  • For a Point Charge:
  • $E = \frac{F}{q} = k\frac{q}{r^2}$

2.3. Circuits

• Series Resistors:
• $R<em>{Total} = R</em>1 + R_2 + …$
• Parallel Resistors:
• $\frac{1}{R<em>{Total}} = \frac{1}{R</em>1} + \frac{1}{R_2} + …$

2.4. Capacitance

• Capacitors:
  • Series Capacitors:
  • $\frac{1}{C<em>{Total}} = \frac{1}{C</em>1} + \frac{1}{C_2} + …$
  • Parallel Capacitors:
  • $C<em>{Total} = C</em>1 + C_2 + …$

2.5. Magnetism

• Magnetic Force:
  • $F_M = qvB ext{sin}( heta)$
  • Induced Electric Field:
  • $E = \frac{F_M}{q}$

2.6. Waves and Oscillations

• Velocity of Waves:
  • $v = f ext{λ}$

3. Chemistry Equations

3.1. Acids and Bases

• pH and pOH:
  • $pH = - ext{log}[H^+]$
  • $pOH = - ext{log}[OH^-]$
  • $K_w = [H^+][OH^-] = 1 imes 10^{-14}$ at 25°C

3.2. Ideal Gas Law and Stoichiometry

• Ideal Gas Law:
  • $PV = nRT$
• Dalton’s Law of Partial Pressures:
  • $P<em>{total} = ext{Σ}P</em>i$

3.3. Thermodynamics

• First Law of Thermodynamics:
  • $riangle E = Q - W$

3.4. Electrochemistry

• Faraday’s Constant:
  • $F = 96,000 ext{C/mol}$
• Gibbs Free Energy:
  • $riangle G = riangle H - T riangle S$
  • Standard Free Energy Change:
  • $riangle G^ heta = -RT ext{ln}K$

3.5. Rates of Reaction

• Rate Law:
  • $ext{Rate} = k[A]^a[B]^b$

3.6. Reaction Quotient and Equilibrium

• Equilibrium Constant:
  • $K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• Reaction Quotient:
  • $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

4. Definitions

4.1. Formal Charge

• Calculation:
  • FC = ext{# valence electrons} - ext{# bonds} - ext{# lone pair electrons}

4.2. Specific Gravity

• Definition:
  • $SG = \frac{ ext{Density of substance}}{ ext{Density of water}}$

4.3. Henderson-Hasselbalch Equation

• Equation:
  • $pH = pK_a + ext{log}\frac{[A^-]}{[HA]}$