Question

Assume that k and V0 are constant and are, respectively, 0.02, and 7. The parameter CA varies from an initial value CA0 = 100 to a final value of CA = 7. What is the value of V given the following equation and assuming that the integral of dV equals V. Express your answer rounded to one decimal place.
dCA/dV = -kCA/V0

Answer 1

Answer:

V = 929.7

Step-by-step explanation:

Given the equation:

$\frac{dCA}{dV}$ = $\frac{-kCA}{V0}$

The integral of the above equation is:

$\int\limits {\frac{dCA}{dV} }$ = $\int\limits{\frac{-kCA}{V0} }$

Re-organizing the integrals:

$\int\limits {\frac{dCA}{CA} }$ = $\int\limits {\frac{-kdV}{V0} }$

Integrating:

ln(CA) - ln(CA0) = $\frac{-kV}{V0}$

Inputting the initial conditions of CA and the values of k and V0:

ln(7) - ln(100) = $\frac{-0.02V}{7}$

1.946 - 4.605 = -0.00286V

-2.659 = -0.00286V

=> V = $\frac{2.659}{0.00286}$

V = 929.720

Approximating to one decimal place,

V = 929.7