4. Thermal Activation (Chapter 1. Problem 19, modified). A certain chemical oxid

Question

4. Thermal Activation (Chapter 1. Problem 19, modified). A certain chemical oxidation process (e.g., SiO2) has an activation energy of 2 eV atom has an activation energy of 2 eV atom, (a) Consider the material exposed to pure oxygen gas at a pressure of 1 atm. at 27 °C. Estimate how many oxygen molecules per unit volume will have energies in excess of 2 eV? (Assume Maxwell- Boltzmann distribution) (6 marks) (b) If the temperature is 900 °C, estimate the number of oxygen molecules with energies more than 2 cV·(2 marks) (c) Keep the temperature at 900 °C, and double the pressure of oxygen gas, estimate the number of oxygen molcculcs with cncrgics morc than 2 cV. (2 marks)

Explanation / Answer

activation energy of an atom

EA= (2 eV/atom) x (1.602 x 10^-19 J/eV)

= 3.204 x 10^-19 J/atom

Part a

Pressure P = 1 atm = 101325 Pa

Temperature T = 27°C + 273 = 300 K

Calculate the number of molecules of O2 in a unit volume

From the ideal gas equation

PV = (moles/Avogadro number) x RT

Moles = (6.022 x 10^23 x 101325) / (8.314 x 300)

n = 2.445 x 10^25 molecules/m3

In excess of 2 eV energy (E > EA)

Estimation of concentration of molecules

(nA / n) = exp ( - EA /kB T)

nA = 2.445 x 10^25 x exp(-3.204 x 10^-19/1.381 x 10^-23 x 300)

nA = 6.34 x 10^-9 molecules /m3

Part b

Temperature T = 900°C +273 = 1173 K

Calculate the number of molecules of O2 in a unit volume

From the ideal gas equation

PV = (moles/Avogadro number) x RT

Moles = (6.022 x 10^23 x 101325) / (8.314 x 1173)

n = 6.254 x 10^24 molecules/m3

In excess of 2 eV energy (E > EA)

Estimation of concentration of molecules

(nA / n) = exp ( - EA /kB T)

nA = 6.254 x 10^24 x exp(-3.204 x 10^-19/1.381 x 10^-23 x 1173)

nA = 1.61 x 10^16 molecules /m3

Part c

On doubling the pressure means

Pressure = 2P

Number of molecules /m3 will be double

Number of O2 molecules /m3 with energy more than 2 eV will be double.

nA = 2 x 1.61 x 10^16

= 3.22 x 10^16 molecules /m3

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