b$.$ The following set of chemical reactions occurs in a well$-$mixed continuous reactor:

$A2B$

$AC$

$BC+D$

At steady$-$state, the following equations describe the mass balance for species $A,B,C$ and

$D,$ respectively:

$Q(C_{A,0}-C_A)+V(-k_1{C}_A-k_2{C}_A^{\frac{3}{2}}+k_3{C}_c^2)=0$

$-Q{C}_B+V(2k_1{C}_A-k_4{C}_B^2)=0$

$-Q{C}_c+V(k_2{C}_A^{32}-k_3{C}_c^2+k_4{C}_B^2)=0$

$-Q{C}_D+V{k}_4{C}_B^2=0$

Estimate the solution of the above system of non$-$linear equations for $C_A,C_B,C_C,C_D,$ by

performing four iterations of Gauss Newton method, given the following parameter

values;

$V=100L$

$Q=50\frac{L}{s}$

$C_{A,0}=1mo\frac{l}{L}$

$k_l=1s^{-1}$

$k_2=0\mathrm{.}2L^{\frac{1}{2}}*mo{l}^{-\frac{1}{2}}*s^{-1}$

$k_s=0\mathrm{.}05L*mo{l}^{-1}*s^{-1}$

$k_4=0\mathrm{.}4L*mo{l}^{-1}*s^{-1}$

For initial guesses use $0\mathrm{.}25mo\frac{l}{L},$ for all four species.

NOTES:

There is no need to convert units for any of the quantities.

The initial guesses do not count as one of the four iterations of the Gauss$-$Newton.