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eqns.json
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{
"Quantum": {
"Energy - Wavelength Equation": {
"E": "c*h/lamb",
"h": "E*lamb/c",
"c": "E*lamb/h",
"lamb": "c*h/E"
},
"Heisenberg Uncertainty Equation": {
"dx": "0.0795774715459477*h/dp",
"dp": "0.0795774715459477*h/dx",
"h": "12.5663706143592*dp*dx"
},
"DeBroglie Equation": {
"lamb": "h/(m*v)",
"h": "lamb*m*v",
"m": "h/(lamb*v)",
"v": "h/(lamb*m)"
},
"Energy of an Electron at Particular Level": {
"E": "-Rh/n**2",
"Rh": "-E*n**2",
"n": "(-Rh/E)**0.5"
},
"Rydberg Equation - Wavelength": {
"lamb": "nf**2*ni**2/(Rh*(nf**2 - ni**2))",
"Rh": "nf**2*ni**2/(lamb*(nf**2 - ni**2))",
"ni": "-nf*(Rh*lamb/(Rh*lamb + nf**2)**0.5)",
"nf": "-ni*(Rh*lamb/(Rh*lamb - ni**2)**0.5)"
},
"Rydberg Equation - Energy": {
"E": "Rh/ni**2 - Rh/nf**2",
"Rh": "E*nf**2*ni**2/(nf**2 - ni**2)",
"ni": "nf*(Rh/(E*nf**2 + Rh)**0.5)",
"nf": "ni*(-Rh/(E*ni**2 - Rh)**0.5)"
}
},
"Gas Laws": {
"Ideal Gas Law - standard": {
"P": "R*T*n/V",
"V": "R*T*n/P",
"n": "P*V/(R*T)",
"R": "P*V/(T*n)",
"T": "P*V/(R*n)"
},
"Ideal Gas Law - Mass and Molar Mass": {
"P": "R*T*m/(M*V)",
"V": "R*T*m/(M*P)",
"m": "M*P*V/(R*T)",
"M": "R*T*m/(P*V)",
"R": "M*P*V/(T*m)",
"T": "M*P*V/(R*m)"
},
"Real Gas Law": {
"P": "n*(R*T*V**2 - V*a*n + a*b*n**2)/(V**2*(V - b*n))",
"V": "-(-3*a*n**2/P + (-P*b*n - R*T*n)**2/P**2)/(3*(sqrt(-4*(-3*a*n**2/P + (-P*b*n - R*T*n)**2/P**2)**3 + (-27*a*b*n**3/P - 9*a*n**2*(-P*b*n - R*T*n)/P**2 + 2*(-P*b*n - R*T*n)**3/P**3)**2)/2 - 27*a*b*n**3/(2*P) - 9*a*n**2*(-P*b*n - R*T*n)/(2*P**2) + (-P*b*n - R*T*n)**3/P**3)**(1/3)) - (sqrt(-4*(-3*a*n**2/P + (-P*b*n - R*T*n)**2/P**2)**3 + (-27*a*b*n**3/P - 9*a*n**2*(-P*b*n - R*T*n)/P**2 + 2*(-P*b*n - R*T*n)**3/P**3)**2)/2 - 27*a*b*n**3/(2*P) - 9*a*n**2*(-P*b*n - R*T*n)/(2*P**2) + (-P*b*n - R*T*n)**3/P**3)**(1/3)/3 - (-P*b*n - R*T*n)/(3*P)",
"n": "V/(3*b) - (V**2/b**2 - 3*(P*V**2*b + R*T*V**2)/(a*b))/(3*(-27*P*V**3/(2*a*b) - V**3/b**3 + 9*V*(P*V**2*b + R*T*V**2)/(2*a*b**2) + sqrt(-4*(V**2/b**2 - 3*(P*V**2*b + R*T*V**2)/(a*b))**3 + (-27*P*V**3/(a*b) - 2*V**3/b**3 + 9*V*(P*V**2*b + R*T*V**2)/(a*b**2))**2)/2)**(1/3)) - (-27*P*V**3/(2*a*b) - V**3/b**3 + 9*V*(P*V**2*b + R*T*V**2)/(2*a*b**2) + sqrt(-4*(V**2/b**2 - 3*(P*V**2*b + R*T*V**2)/(a*b))**3 + (-27*P*V**3/(a*b) - 2*V**3/b**3 + 9*V*(P*V**2*b + R*T*V**2)/(a*b**2))**2)/2)**(1/3)/3",
"R": "P*V/(T*n) - P*b/T + a*n/(T*V) - a*b*n**2/(T*V**2)",
"T": "P*V/(R*n) - P*b/R + a*n/(R*V) - a*b*n**2/(R*V**2)",
"a": "V**2*(-P*V + P*b*n + R*T*n)/(n**2*(V - b*n))",
"b": "V*(P*V**2 - R*T*V*n + a*n**2)/(n*(P*V**2 + a*n**2))"
},
"Grahams Law": {
"r1": "sqrt(M2)*r2/sqrt(M1)",
"r2": "sqrt(M1)*r1/sqrt(M2)",
"M1": "M2*r2**2/r1**2",
"M2": "M1*r1**2/r2**2"
},
"RMS Particle Velocity": {
"v": "(3)**0.5*(R*T/M)**0.5",
"R": "M*v**2/(3*T)",
"T": "M*v**2/(3*R)",
"M": "3*R*T/v**2"
},
"Kinetic Energy Equation": {
"KE": "0.5*m*v**2",
"m": "2.0*KE/v**2",
"v": "-1.4142135623731*(KE/m)**0.5"
}
},
"Thermodynamics": {
"Entropy for an Isothermal Rxn - Changing Pressure": {
"P1": "P2*exp(H*(T1 - T2)/(R*T1*T2))",
"P2": "P1*exp(-H*(T1 - T2)/(R*T1*T2))",
"H": "-R*T1*T2*log(P2/P1)/(T1 - T2)",
"R": "H*(-T1 + T2)/(T1*T2*log(P2/P1))",
"T1": "H*T2/(H + R*T2*log(P2/P1))",
"T2": "H*T1/(H - R*T1*log(P2/P1))"
},
"Entropy for an Isothermal Rxn - Changing Volume": {
"S": "R*n*log(V2/V1)",
"n": "S/(R*log(V2/V1))",
"R": "S/(n*log(V2/V1))",
"V2": "V1*exp(S/(R*n))",
"V1": "V2*exp(-S/(R*n))"
},
"Entropy for an Isobaric Rxn - Changing Temp": {
"S": "c*m*log(T2/T1)",
"m": "S/(c*log(T2/T1))",
"c": "S/(m*log(T2/T1))",
"T2": "T1*exp(S/(c*m))",
"T1": "T2*exp(-S/(c*m))"
},
"Entropy from Microstates": {
"S": "kb*log(states)",
"kb": "S/log(states)",
"states": "exp(S/kb)"
},
"Gibb's Free Energy - Rxn Quotient": {
"G": "G_not + R*T*log(Q)",
"G_not": "G - R*T*log(Q)",
"R": "(G - G_not)/(T*log(Q))",
"T": "(G - G_not)/(R*log(Q))",
"Q": "exp((G - G_not)/(R*T))"
},
"Gibb's Free Energy - Keq Constant": {
"G_0": "-R*T*log(K)",
"R": "-G_0/(T*log(K))",
"T": "-G_0/(R*log(K))",
"K": "exp(-G_0/(R*T))"
},
"Gibb's Free Energy - Quotient vs Keq": {
"G": "R*T*(-log(Keq) + log(Q))",
"R": "-G/(T*(log(Keq) - log(Q)))",
"T": "-G/(R*(log(Keq) - log(Q)))",
"Q": "Keq*exp(G/(R*T))",
"Keq": "Q*exp(-G/(R*T))"
},
"Gibb's Free Energy - Enthalpy and Entropy": {
"G": "H - S*T",
"H": "G + S*T",
"T": "(-G + H)/S",
"S": "(-G + H)/T"
},
"Calorimetry - Heat from Temp Change": {
"q": "c*m*(Tf - Ti)",
"m": "q/(c*(Tf - Ti))",
"c": "q/(m*(Tf - Ti))",
"Ti": "Tf - q/(c*m)",
"Tf": "Ti + q/(c*m)"
},
"Calorimetry - Heat from Enthalpy": {
"q": "H*n",
"n": "q/H",
"H": "q/n"
},
"Hess's Law - Heats of Formation": {
"H_rxn": "-Hf_A*moles_a - Hf_B*moles_b + Hf_C*moles_c + Hf_D*moles_d",
"moles_a": "(-H_rxn - Hf_B*moles_b + Hf_C*moles_c + Hf_D*moles_d)/Hf_A",
"Hf_A": "(-H_rxn - Hf_B*moles_b + Hf_C*moles_c + Hf_D*moles_d)/moles_a",
"moles_b": "(-H_rxn - Hf_A*moles_a + Hf_C*moles_c + Hf_D*moles_d)/Hf_B",
"Hf_B": "(-H_rxn - Hf_A*moles_a + Hf_C*moles_c + Hf_D*moles_d)/moles_b",
"moles_c": "(H_rxn + Hf_A*moles_a + Hf_B*moles_b - Hf_D*moles_d)/Hf_C",
"Hf_C": "(H_rxn + Hf_A*moles_a + Hf_B*moles_b - Hf_D*moles_d)/moles_c",
"moles_d": "(H_rxn + Hf_A*moles_a + Hf_B*moles_b - Hf_C*moles_c)/Hf_D",
"Hf_D": "(H_rxn + Hf_A*moles_a + Hf_B*moles_b - Hf_C*moles_c)/moles_d"
}
},
"Equilibrium & Solutions": {
"Dilution Equation": {
"ci": "cf*vf/vi",
"vi": "cf*vf/ci",
"cf": "ci*vi/vf",
"vf": "ci*vi/cf"
},
"Keq of a Reaction: aA + bB <--> cC + dD": {
"A": "(B**(-b)*C**c*D**d/Keq)**(1/a)",
"B": "(A**(-a)*C**c*D**d/Keq)**(1/b)",
"C": "(A**a*B**b*D**(-d)*Keq)**(1/c)",
"D": "(A**a*B**b*C**(-c)*Keq)**(1/d)",
"a": "log(B**(-b)*C**c*D**d/Keq)/log(A)",
"b": "log(A**(-a)*C**c*D**d/Keq)/log(B)",
"c": "log(A**a*B**b*D**(-d)*Keq)/log(C)",
"d": "log(A**a*B**b*C**(-c)*Keq)/log(D)",
"Keq": "A**(-a)*B**(-b)*C**c*D**d"
},
"Kp - Kc Conversation": {
"Kp": "Kc*(R*T)**n",
"Kc": "Kp*(R*T)**(-n)",
"R": "(Kp/Kc)**(1/n)/T",
"T": "(Kp/Kc)**(1/n)/R",
"n": "log(Kp/Kc)/log(R*T)"
},
"Molar Solubility in Water for AB --> aA + bB": {
"a": "exp(LambertW(molar_sol*log(Ksp*(b*molar_sol)**(-b))))/molar_sol",
"b": "exp(LambertW(molar_sol*log(Ksp*(a*molar_sol)**(-a))))/molar_sol",
"Ksp": "(a*molar_sol)**a*(b*molar_sol)**b",
"molar_sol": "(Ksp*a**(-a)*b**(-b))**(1/(a + b))"
},
"Van't Hoff Equation - Single Keq": {
"Keq": "exp((-H + S*T)/(R*T))",
"H": "T*(-R*log(Keq) + S)",
"R": "(-H + S*T)/(T*log(Keq))",
"T": "-H/(R*log(Keq) - S)",
"S": "H/T + R*log(Keq)"
},
"Van't Hoff Equation - Two Keq": {
"K2": "K1*exp(-H*(T1 - T2)/(R*T1*T2))",
"K1": "K2*exp(H*(T1 - T2)/(R*T1*T2))",
"H": "-R*T1*T2*log(K2/K1)/(T1 - T2)",
"R": "H*(-T1 + T2)/(T1*T2*log(K2/K1))",
"T2": "H*T1/(H - R*T1*log(K2/K1))",
"T1": "H*T2/(H + R*T2*log(K2/K1))"
},
"Henderson Hasselbach - pKa": {
"pH": "pKa + log(B/A)/log(10)",
"pKa": "pH - log(B/A)/log(10)",
"B": "A*exp((pH - pKa)*log(10))",
"A": "B*exp(-(pH - pKa)*log(10))"
},
"Henderson Hasselbach - pKb": {
"pOH": "pKb + log(A/B)/log(10)",
"pKb": "pOH - log(A/B)/log(10)",
"A": "B*exp(-(pKb - pOH)*log(10))",
"B": "A*exp((pKb - pOH)*log(10))"
}
},
"Kinetics": {
"Average Rate of a Reactant": {
"r": "(A1 - A2)/(t1 - t2)",
"t2": "(-A1 + A2 + r*t1)/r",
"t1": "(A1 - A2 + r*t2)/r",
"A2": "A1 - r*t1 + r*t2",
"A1": "A2 + r*t1 - r*t2"
},
"Order of Reactant from Initial Rates": {
"order": "log(r2/r1)/log(conc2/conc1)",
"r2": "r1*exp(order*log(conc2/conc1))",
"r1": "r2*exp(-order*log(conc2/conc1))",
"conc2": "conc1*exp(log(r2/r1)/order)",
"conc1": "conc2*exp(-log(r2/r1)/order)"
},
"Main Rate Law": {
"r": "A**m*B**n*k",
"k": "A**(-m)*B**(-n)*r",
"A": "(B**(-n)*r/k)**(1/m)",
"m": "log(B**(-n)*r/k)/log(A)",
"B": "(A**(-m)*r/k)**(1/n)",
"n": "log(A**(-m)*r/k)/log(B)"
},
"0th Order Integrated Rate Law": {
"At": "Ao - k*t",
"k": "(Ao - At)/t",
"t": "(Ao - At)/k",
"Ao": "At + k*t"
},
"1st Order Integrated Rate Law": {
"At": "Ao*exp(-k*t)",
"k": "(log(Ao) - log(At))/t",
"t": "(log(Ao) - log(At))/k",
"Ao": "At*exp(k*t)"
},
"2nd Order Integrated Rate Law": {
"At": "Ao/(Ao*k*t + 1)",
"k": "(Ao - At)/(Ao*At*t)",
"t": "(Ao - At)/(Ao*At*k)",
"Ao": "-At/(At*k*t - 1)"
},
"Arrhenius Equation": {
"k": "A*exp(-Ea/(R*T))",
"A": "k*exp(Ea/(R*T))",
"Ea": "R*T*(log(A) - log(k))",
"R": "Ea/(T*(log(A) - log(k)))",
"T": "Ea/(R*(log(A) - log(k)))"
},
"Rate Constant from changing Temp": {
"ki": "kf*exp(-Ea*(Tf - Ti)/(R*Tf*Ti))",
"kf": "ki*exp(Ea*(Tf - Ti)/(R*Tf*Ti))",
"Ea": "R*Tf*Ti*log(kf/ki)/(Tf - Ti)",
"R": "Ea*(Tf - Ti)/(Tf*Ti*log(kf/ki))",
"Ti": "Ea*Tf/(Ea + R*Tf*log(kf/ki))",
"Tf": "Ea*Ti/(Ea - R*Ti*log(kf/ki))"
}
},
"Electrochemistry": {
"Nernst Equation": {
"Ecell": "Ecell_0 - R*T*log(Q)/(F*n)",
"Ecell_0": "Ecell + R*T*log(Q)/(F*n)",
"R": "F*n*(-Ecell + Ecell_0)/(T*log(Q))",
"T": "F*n*(-Ecell + Ecell_0)/(R*log(Q))",
"n": "-R*T*log(Q)/(F*(Ecell - Ecell_0))",
"F": "-R*T*log(Q)/(n*(Ecell - Ecell_0))",
"Q": "exp(-F*n*(Ecell - Ecell_0)/(R*T))"
},
"Electroplating Relationship": {
"n_atom": "I*t/(F*n_elec)",
"n_elec": "I*t/(F*n_atom)",
"I": "F*n_atom*n_elec/t",
"t": "F*n_atom*n_elec/I",
"F": "I*t/(n_atom*n_elec)"
}
}
}