Answer:
[tex]V=5000dm^3[/tex]
Explanation:
Hello,
In this case, for the STR reactor carrying out this chemical reaction, the material balance is:
[tex]\frac{dC_A}{dt}=r_A\\\\\frac{dC_A}{dt}=-kC_A^2[/tex]
Thus, with the given information we compute the rate constant as follows:
[tex]C_A_0 \frac{dX_A}{dt}=kC_A_0^2(1-X_A)^2\\\\\int\limits^{0.5}_0 {\frac{dX_A}{(1-X_A)^2} } \,=kC_A_0t\\\\\frac{0.5}{1-0.5}=k*0.2\frac{mol}{dm^3}*1h\\ \\k=\frac{1}{(0.2\frac{mol}{dm^3})*1h} \\\\k=5\frac{dm^3}{mol*h}[/tex]
Now, for the CSTR we have the following design equation in terms of conversion for finding the volume:
[tex]V=\frac{F_A_0*X_A}{-r_A}\\\\V=\frac{F_A_0*X_A}{k*C_A_0^2(1-X_A)^2}[/tex]
Therefore, it turns out:
[tex]V=\frac{500\frac{mol}{h} *0.5}{5\frac{dm^3}{mol*h} *(0.2\frac{mol}{dm^3} )^2(1-0.5)^2}\\\\V=5000dm^3[/tex]
Best regards.
