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A cascade of three isothermal CSIRs in series is used to carry out a liquid - phase reaction. A k B The dynamic equations that

A cascade of three isothermal CSIRs in series is used to carry out a liquid-phase reaction.
AkB
The dynamic equations that govern the system are given by carrying out the molar balance for component A for each CSTR: Accumulation = ln - Out + Generation-Consumption
V(i)dCA(i)dt=FCA(i-1)-FCA(i)-kCA(i)V(i), for i=1,2,3.
Using the residence time =VF the equation can be transformed to
dCA(i)dt=1iCA(i-1)-(1i+ki)CA(i), for ,i=1,2,3.
If we set up the left-hand side of each equation to zero, then we will end up with a set of three linear algebraic equations that describe the three CSTRs under a state-state condition. Notice that each CSTR has its own residence time and rate constant.
Assume: 1=1s;2=2s;3=3s;CA0=100molL;k1=1s-1;k2=2s-1;k3=3s-1
1.1 Compute the set of linear equations in a matrix/vector form as [10 Marks]
Ax=b
1.2 Use the Gauss-Jordan reduction method to solve the three equations with three unknowns CA1,CA2, and CA3.20 Marks]
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