Please Help me with this question. Reactor theory and reaction kinetics. Later t

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Please Help me with this question.

Reactor theory and reaction kinetics. Later this semester, we'll study disinfection of drinking water. One powerful disinfectant is ozone (O_3). A problem with ozone is that it decomposes relatively quickly in water, the effectiveness of ozone as a disinfectant depends partly on how fast it decomposes. Therefore, many researchers have investigated the kinetics of ozone decomposition in water. It has commonly been observed that the decomposition of ozone follows second-order kinetics. That is, the rate of ozone decomposition is given by r = k_2 [O_3]^2

Explanation / Answer

a.

molar mass of O3 is 48 g/mol

0.004 g/L / 48 g/mol = 1/12000 mol/L = Co

0.04 g/L / 48 g/mol = 1/1200000 mol/L =C

For a second order reaction

1/[C] = kt + 1/[Co]

1200000 L/mol = 14 L/(mol.s) x t   + 12000 L/mol

t = (1200000 -12000)/14 = 84857 s

b.

In a Plug-Flow Reactor PFR, for a second order reaction

kCoT = Co/C - 1

T = 30 min = 1800 s

14L/mol.s x (1/12000 mol/L) x 1800 = (1/12000 mol/L) / C - 1

2.1 + 1 = (1/12000 mol/L) / C

37200 = 1/C

C = 1/37200 mol/L

C = 1/37200 mol/L x 48 g/mol = 1.29 x 10-3 g/L = 1.3 mg/L that is higher than 1 mg/L

Answer: Yes. The ozone concentration will remains higher than 1 mg/L

c

Q C1 = Vxreaction rate + QCout

Detention time T = V/Q

Reaction rate = kC2out

C1 = TkC2out + Cout

d.

TkC2out + Cout – C1 = 0

Cout = +/_ ……

Solve for Cout the second order equation and keep the positive solution.

e. Use the given values in the equation from d.

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