MCAT EQUATION

Average Speed Equation

Δx/Δt (Units m/s)

Average Velocity

Δd/Δt (units m/s)

Acceleration

Δv/Δt (units m/s²)

Newtons 2nd Law

F(net)=ma ( Units 1 N= 1 kg*m/s²)

Static Friction

𝐹(f,max)= 𝜇(s)*F(Normal) (Units 1 N= 1 kg*m/s²)

Kinetic Friction

𝐹(f,max)= 𝜇(k)*F(Normal) (Units 1 N= 1 kg*m/s²)

Force of gravity acting perpendicular to an inclined plane

m*g*cosθ (Units 1N= 1 kg*m/s²)

Forces of gravity acting parallel to an inclined plane

m*g*sinθ (Units 1N= 1 kg*m/s²)

Torque

𝜏=𝑟*𝐹*sinθ (Units N*m)

Work

W=F*d*cos θ (Units 1 J= N*m)

Work (Pressure-Vol. Curve)

W=PΔV (W=-PΔV) (Units J)

Mechanical Advantage

MA=F(out)/F(in)

Mechanical Advantage

MA=F(out)/F(in)

Power

P=W/t =ΔE/t (Units 1 watt(W)=J/s)

Power

P=Fv (Units W)

Change in internal energy of a system

ΔU= Q-w

Kinetic Energy

KE=1/2mv² (Units J)

Work-Kinetic Energy Theorem

W(net)= ΔKE= K(f)-K(i) (Units J)

Gravitational Potential Energy

U=m*g*h (Units J)

Elastic Potential Energy

U=1/2*k*x² (Units J)

Hooke’s Law

F= -k*x (Units N)

Frequency of wave

f=1/T (Units 1/s= Hz)

Speed of a wave

v=f*λ (Units m/s)

Density

ρ = m/V (Units g/cm³)

Specific Gravity

ρ(object)/ρ(water)

Buoyant Force

F(B)=m*g= ρ(fluid)*V*g (V=4/3*pi*r³; V=4r³) (Units N)

Pascal’s Law

F1/A1= F2/A2 (Force/Area)

Hydrostatic Pressure

P= P(0)+ρgz (P=P(atm)+pgh)

Poiseuille’s Law

Q=𝜋*r^4*Δ𝑃/ 8ηL (Q=flow rate; r=radius; P= Pressure; η=viscosity; L=Length)

Continuity Equation

A1v1=A2v2

Bernoulli’s Equation

P1+1/2ρv²(1)+ρgh(1)= P(2)… (Pressure Energy+ KE+PE) (Decrease Pressure when fluid speeds up)

Absolute Temp.

K= C+ 273

Pressure

P=F/A ((Force/Area))

Ideal Gas Law

PV=nRT (R=0.821; T= Temp in Kelvin; n=moles)

Boyle’s Law

P1V1=P2V2

Charles’ Law

V1/T1=V2/T2 (AT CONSTANT PRESSURE)

AVOGADRO’S LAW

n1/V1=n2/V2

Average Kinetic Energy of a Gas Particle

KEavg=3/2k(B)T (k(B)= 1.4×10-23) (Units J)

Heat capacity at constant volume for an ideal monoatomic gas

C(p)= 5/2nR (Units J/K)

Heat capacity at constant pressure for an ideal monoatomic gas

C(p)=5/2nR (Units J/K)

Van der Waals equation of state

P=(nRT/V-nb)-(n2a/V²)

Dalton’s Law of Partial Pressure

P(A)=X(A)P(r); P=P(A)+P(B)+P(C)

Heat Transferred

q=mcΔT (Units 1 cal/g*K=4.184 J/g*K

Standard Heat of Reaction

ΔH(f,prod.)- ΔH(f,reac.)

Standard Heat of Reaction

ΔH(bonds broken)- ΔH (bonds formed)

Change in Gibbs Free Energy

ΔG=ΔH-TΔS (Units kJ/mol)

Linear Expansion (solids)

ΔL=aLΔT

Volumetric Expansion (S & L)

ΔV= BVΔT

Sound Level

B=10log (I/I(0)) (Units dB)

Sound Level

B(f)=B(i)+10log (I(f)/I(i)) (Units dB)

Intensity

I=P/A (units W/m²)

Doppler Effect

f’=f v+-v(d)/ v+-v(s) (Units Hz)

Waves in Open Pipes

λ=2L/n; f=v/λ= nv/2L

Waves in Closed Pipes

λ =4L/n; f=v/λ= nv/4L

Speed of Light

C=fλ (c=3.0×10^8) (Units m/s)

Energy of Photon

E=hf; E=hc/λ (h=6.626×10^-34) (Units m/s)

Law of Reflection

θ1= θ2

Index of Refraction

n=c/v. (c=3×10^8)

Snell’s Law

n1sinθ1=n2sinθ2

Critical Angle

θ(c)= sin^-1 (n2/n1)

Optics Equation

1/f=1/o+1/i=2/r

Magnification

m=-i/o

Lens Power

P=1/f (Units Diopters)

Focal Length of Lenses in a Series

1/f=1/f1+1/f2+1/f3+…+1/f(n)

Power of Lenses in a Series

P=P1+P2+P3+…+P(n) (Units Diopters)

Magnification for a system of lenses

m=m1*m2*m3

Coulomb’s Law

F(e)=k*q1*q2/r² (k=9×10^9 N*m²/C²) (Units N)

Electric Field

E=F(e)/q= KQ/r² (N/C or V/m)

Electric Potential Energy

U=kQq/r (Units J)

Electric Potential

V=U/q= kQ/r (Units 1V=1 J/C)

Intensity of Uniform Electric Field

V/d (Units V/m)

Voltage (Potential Difference)

ΔV=V(b)-V(a)= W(ab)/q (Units Volts)

Power

V*I (Unit W)

Power

V²/R (Units W)

Power

I²R (Units W)

Current

I=Q/t (Unit 1A= 1 C/s)

Ohm’s Law

V=IR

Resistors in Series

R(s)+R1+R2+R3+… (Units Ω)

Resistors in Parallel

1/R(total)=1/R1+1/R2+1/R3 (Units Ω)

Resistivity

ρ=R*A/L (Units Ohm-meter (Ω*m)

Capacitance

C=Q/V= e(o)(A/d) (Unit 1F=1 C/V)

Energy of a Charged Capacitor

U=Q²/C= ½QΔV= ½C(ΔV)²

Capacitors in Series

1/C(s)=1/C1+1/C2+1/C3 (Units F)

Capacitors in Parallel

C(p)=C1+C2+C3 (Units F)

Magnetic Force

F(B)=qvBsinθ (Unit 1 T=1 N*s/m*C)

Lorentz Force

F=qE+qvBsinθ

Max Number of Electrons in a Shell

2n²

Kinetic Energy of a Photoeletron

hf-Φ (Units eV)

Formal Charge

FC=V-NB-1/2B

Dipole Moment

p=q*d (Units C*m)

Specific Rotation

[a]= a(obs.)/x*l (Units Degrees)

Electrodeposition Equation

Mol M= It/nF

Cell Potential

Cell pot.=red pot-ox pot

Rate Law

Rate=k[A]^x * [B]^y

Arrhenius Equation

k=Ae^-E(a)/RT (Increase Temp Increase k (cause exponent gets more +)

Law of Mass Action

Keq=[C]^c*[D]^d/ [A]^a*[B]^b

Wave Number

1/ λ (Units cm^-1)

Autoionization of water

Kw=[H3O+][OH-]=10^-14

pH

-log[H+]