Theoretical Test
Theoretical Test Theoretical Test
Constants and useful formulasGas constant R = 8.314 J K -1 mol -1Faraday constant F = 96485 C mol -1Use as standard pressure: p = 1.013·10 5 PaUse as standard temperature: T = 25°C = 298.15 KAvogadro’s number N A = 6.022·10 23 mol -1Planck constant h = 6.626·10 -34 J sSpeed of light c = 3.00·10 8 m s -1∆G = ∆H - T∆S∆G = - nFE∆G 0 = - RT·lnK ∆G = ∆G 0 + RT·lnQ with Q =product ofproduct ofc(products)c(reactands)∆H(T 1 ) = ∆H 0 + (T 1 - 298.15 K)·C p(C p = constant)E− aArrhenius equation k = A · eR ⋅ TIdeal gas lawpV = nRTNernst equation E = E 0 RT c+ ⋅ lnnF coxredBeer- Lambert LawA = log PP 0= ε·c·dV(cylinder) = πr 2 hA(sphere) = 4πr 2V(sphere) = 34 πr31 J = 1 N m 1 N = 1 kg m s -2 1 Pa = 1 N m -21 W = 1 A V = 1 J s -1 1 C = 1 A s
1. Avogadro's number (5pts)Spherical water droplets are dispersed in argon gas. At 27 o C, each droplet is1.0 micrometer in diameter and undergoes collisions with argon. Assume thatinter-droplet collisions do not occur. The root-mean-square speed of thesedroplets was determined to be 0.50 cm/s at 27 o C. The density of a water dropletis 1.0 g/cm 3 .1-1. Calculate the average kinetic energy (mv 2 /2) of this droplet at 27 o C. Thevolume of a sphere is given by (4/3) π r 3 where r is the radius.If the temperature is changed, then droplet size and speed of the droplet willalso change. The average kinetic energy of a droplet between 0 o C and 100 o Cas a function of temperature is found to be linear. Assume that it remains linearbelow 0 o C.0At thermal equlibrium, the average kinetic energy is the same irrespective ofparticle masses (equipartition theorem).The specific heat capacity, at constant volume, of argon (atomic weight, 40)gas is 0.31 J g -1 K -1 .1-2. Calculate Avogadro's number without using the ideal gas law, the gasconstant, Boltzmann’s constant).1
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Constants and useful formulasGas constant R = 8.314 J K -1 mol -1Faraday constant F = 96485 C mol -1Use as standard pressure: p = 1.013·10 5 PaUse as standard temperature: T = 25°C = 298.15 KAvogadro’s number N A = 6.022·10 23 mol -1Planck constant h = 6.626·10 -34 J sSpeed of light c = 3.00·10 8 m s -1∆G = ∆H - T∆S∆G = - nFE∆G 0 = - RT·lnK ∆G = ∆G 0 + RT·lnQ with Q =product ofproduct ofc(products)c(reactands)∆H(T 1 ) = ∆H 0 + (T 1 - 298.15 K)·C p(C p = constant)E− aArrhenius equation k = A · eR ⋅ TIdeal gas lawpV = nRTNernst equation E = E 0 RT c+ ⋅ lnnF coxredBeer- Lambert LawA = log PP 0= ε·c·dV(cylinder) = πr 2 hA(sphere) = 4πr 2V(sphere) = 34 πr31 J = 1 N m 1 N = 1 kg m s -2 1 Pa = 1 N m -21 W = 1 A V = 1 J s -1 1 C = 1 A s
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