a) Given the following data from a batch reactor experiment, determine if the re
ID: 531106 • Letter: A
Question
a) Given the following data from a batch reactor experiment, determine if the reaction is 0^th, 1^st, or 2^nd order, and what the reaction rate constant k is (with appropriate units). Show your work', or what you did to determine the order (Excel tables are fine, label the columns clearly, include r^2). b) Use your answer to solve for the volume of CSTR required to degrade the material from 50 to 5 mg/L, given an influent flowrate of 500 m^3/d (one only inflow and outflow; you can use the solved equations from class and just plug in).Explanation / Answer
the realtion between order and rate (-r) is given by = -r = K[C]n, n is order and K is rate constant.
to determine the order of reaction n=1 , a plot of concentration vs time gives an idea. If the graph is exponential, it suggests that the reaction is 1st order. If not , we have to adopt integral method of analysis. the plot of C vs t drawn is shown below and it can be concluded from the plot that the reaction is 1st order. for zero order, the plot of C vs t is straight line and for second order 1/C vs t has to give straight line. all the three cases are drawn and shown below.
since the plot of concentration vs tiime is not straight line, it is not zero order.
the plot of 1/C vs t is shown below. this has got R2 value of 0.916
the plot of Concentration vs time is drwan and found to be exponential. This is shown below with R2 value of 0.976.
this suggests that the data is best fit into 1st order equation.
for 1st order equation,
-dC/dt= KC
when integrated C = Co*exp(-Kt), Co= initial concentration and K= rate constant ( from the graph), K= 0.16/hr
for a CSTR, T = space time = V/Vo = (CO-C1)/KC1
where Co= initial concentration=50 mg/L, C1= concentration to be achieved at the outlet of reactor=5 mg/L
K=0.16/hr, V= volume of reactor and Vo= volumetric flow rate = 500m3/day= 500/24 m3/hr =20.83 m3/hr
Hence 0.16*V/20.83= (50-5)/5= 9
V= 9*20.93/0.16=1172m3
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