Chapter 5: Isothermal Reactor Design: Conversion

Solve:

Combine

\(\frac{dX}{dW} = \frac{kC_{A0}^2}{F_{A0}} (1 - X)^2 (1 - \alpha W)\)

Separate

\(\frac{1}{(1 - X)^2} dX = \left[\frac{kC_{A0}^2}{F_{A0}} (1 - \alpha W)\right] dW\)

Integrate with Limits

\(\int_{0}^{X} \frac{1}{(1 - X)^2} dX = \frac{kC_{A0}^2}{F_{A0}} \int_{0}^{W} (1 - \alpha W) dW\)

\(\frac{X}{1 - X} = \frac{kC_{A0}^2}{F_{A0}} \left[W - \frac{\alpha W^2}{2}\right]\)

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