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TX PACT: PHYSICAL SCIENCE: GRADES 6–12 CONSTANTS

Description Value

Ideal gas constant (R) 0.0821 L•atm/mol•K = 8.31 J/mol•K

4 4 Faraday constant (F) 9.65 × 10 C/mol e– = 9.65 × 10 J/V•mol e–

7 – 1 Rydberg constant (R) 1.097 × 10 m

– 34 –15 Planck's constant (h) 6.63 × 10 J•s = 4.14 × 10 eV•s

– 23 Boltzmann constant (kb) 1.38 × 10 J/K

– 18 Rydberg constant × Planck's constant × speed of 2.18 × 10 J light in a vacuum (Rhc)

Molal freezing point depression constant for water 1.86°C/m

(Kf)

Molal boiling point elevation constant for water (Kb) 0.51°C/m

∆ Heat of fusion of water ( Hfus) 334 J/g = 80 cal/g = 6.01 kJ/mol

∆ Heat of vaporization of water ( Hvap) 2260 J/g = 540 cal/g = 40.7 kJ/mol

Specific heat (s) of water (liquid) 4.184 J/g•K = 4.184 J/g•°C = 1.0 cal/g•°C

– 14 Dissociation constant of water (Kw) 1.0 × 10 at 25°C

Standard atmospheric pressure 1 atm = 760 mm Hg = 760 torr = 101.325 kPa

8 Speed of light in a vacuum (c) 3.00 × 10 m/s

1 calorie (cal) 4.184 J

1 watt (W) 1 J/s TX PACT: PHYSICAL SCIENCE: GRADES 6–12 CONSTANTS (continued)

Description Value

2 Acceleration of gravity on Earth (g) 9.80 m/s

–31 Electron rest mass (me) 9.11 × 10 kg

–27 Proton rest mass (mp) 1.67 × 10 kg

–19 Elementary charge (e) 1.60 × 10 C

9 2 2 Coulomb's constant (ke) 8.99 × 10 N•m /C

–11 2 2 Gravitational constant (G) 6.67 × 10 N•m /kg

µ π –7 Permeability of free space ( 0) 4 × 10 T•m/A

23 Avogadro's number (NA) 6.02 × 10 particles/mole

ρ 3 3 Density of water ( w) 1.00 × 10 kg/m

TX PACT: PHYSICAL SCIENCE: GRADES 6–12 FORMULAS

Description Formula

Gibbs free energy equation ∆G = ∆H – T∆S RT Nernst equation E = E° – ln Q nF  0.0257 V  E = E° –   ln Q at 298 K  n   0.0592 V  E = E° –   log Q at 298 K  n  Relationship between emf and free energy change ∆G° = –nFE° for reactants and products in their standard states   Energy change as an electron transitions between  1 1  ∆E = Rhc – energy states  2 2   ni nf  Henderson-Hasselbalch equation  [conjugate base]  pH = pKa + log    [acid]  Coulombs (C) C = amperes × seconds

Photon energy E = hν

Speed of light c = λν

2 Nuclear binding energy ∆E = c ∆m

Amount of heat (q) q = ms∆T

Root-mean-square speed 3RT u = rms M

Graham's law of diffusion r1 M2 = M r2 1 Pressure-volume work (at constant pressure) w = –P∆V

TX PACT: PHYSICAL SCIENCE: GRADES 6–12 FORMULAS (continued)

Mathematics Force and Motion

C = 2πr vf = vi + at

1 2 2 x = x + vt + at A = πr f i i 2

2 2 2 v – v = 2a(x – x ) SA = 4πr f i f i 2 v 4 3 ac = π r V = 3 r ΣF = ma F = –kx (a, b) denotes a vector with an x-component of a F ≤ µN and a y-component of b.

Gm 1m 2 F = r 2

1 2 θ = θ + ω t + αt f i i 2

ωf = ωi + αt v = rω a = rα ∑ mr r = cm ∑ m 2 I = Σ mr τ = r × F Στ = Iα P = ρgh

F = ρVg

A1v1 = A2v2

1 2 ρ ρ P + 2 v + gy = constant

TX PACT: PHYSICAL SCIENCE: GRADES 6–12 FORMULAS (continued)

Energy, Momentum, and Heat Transfer Electricity and Magnetism

W = Fd cos θ keq1 q2 F = 2 ΔW r P = Δt F E = 1 2 q0 KE = mv 2 PE = qV PE = mgh V = –Ed

1 2 keq PE = kx V = 2 r = m ρ p v R = A ∆p = F∆t V = IR ∆ α ∆ B = B0 T Σ R = Ri Q = mc∆T 1 1

R = ∑ Q = mL Ri ΔQ kA∆T = P = IV Δt d Q PV = nRT C = V 1 3 mv 2 = k T C = Σ C 2 2 b i 1 1 ∆E = Q – W = ∑ C Ci W = P∆V F = qv × B

= IB Th – Tc F × B e = Th μ I B = 0 2πr 1 2 KE = Iω μ NI 2 B = 0  L = r × p ∆φ εave = –EA ∆E tE L = Iω

φ = B⊥A Tk = 273 + Tc In questions on electricity and magnetism, the term current refers to "conventional current" and the use of the right-hand rule is assumed. TX PACT: PHYSICAL SCIENCE: GRADES 6–12 FORMULAS (continued)

Waves, Sound, and Light Modern Physics

2π E = hf T = A ω 2 2 E = γmc a = –ω x 1 x = A sin ωt γ = v 2 m 1− π E 2 T = 2 k c hf = φ + eV L π E T = 2 g ∆x∆p ≥ h v = f λ T ∆E∆t ≥ h v = μ h γRT p = v = λ M

2L = nλ, n is an integer

4L = nλ, n is odd θ θ n1 sin 1 = n2 sin 2 c n = A vE 1 1 1 = + f si s0 h s M = i = – i h0 s0 d sin θ = mλ

2 θ I = I0 cos

NOTES

Not all constants and formulas necessary are listed, nor are all constants and formulas listed used on this exam.

While attention has been paid to significant figures, no answer should be considered incorrect solely because of the number of significant figures.

In questions on electricity and magnetism, the term current refers to "conventional current" and the use of the right-hand rule is assumed.