LearnChemE

#### Thermal Effects in Chemical Reactions: Screencast

Applies the first law to a semibatch reactor for a fast reaction, so the conversion is limited by thermodynamics. Demonstrates how the heat of reaction appears from an energy balance.

We suggest you list the important points in this screencast as a way to increase retention.

##### Important Equations:

The equilibrium constant $$K_e$$ (dimensionless) at temperature $$T$$ (K) is:   $K_e\,=\,K_mexp{\left[\frac{\Delta H}{R}\left(\frac{1}{T_m}-\frac{1}{T}\right)\right]}$where $$K_m$$ is the equilibrium constant at $$T_m$$,
$$\Delta H$$ is the heat of reaction (J/mol)
$$R$$ is the ideal gas constant $$(\frac{J}{mol\,K})$$

The fractional conversion $$X$$, which is referred to as conversion, for a chemical reaction $$A\rightleftharpoons B$$; $X\,=\,\frac{F_{A0}-F_A}{F_{A0}}$ where $$F_{A0}$$ is the molar flow rate of A (mol/s) into the reactor and $$F_A$$ is the molar flow rate of A out of the reactor.

For the reaction $$A \rightleftharpoons B$$, the equilibrium conversion $$X_e$$ is: $X_e\,=\,\frac{K_e}{1+K_e}$ where $$K_e$$ is a function of temperature as shown above.

For an adiabatic reactor, the energy balance is; $H_{in}^{total}\,=\,H_{out}^{total}$ This energy balance yields the conversion ($$X_{energy}$$) at temperature $$T$$ for the reaction $$A \rightleftharpoons B$$ in an adiabatic reactor in which the heat capacities $$C_{PA},C_{PB}$$ are equal and independent of temperature: $X_{energy}\,=\,\frac{(C_{PA}+\alpha C_{PI})(T-T_{feed})}{-\Delta H_{rxn}}$ where $$\alpha$$ is the ratio of inert flow rate to feed flow rate of $$A$$, $$T_{feed}$$ is the feed temperature into the reactor, and $$\Delta H_{rxn}$$ is the heat of reaction (J/mol), which is independent of temperature.

Note that for constant $$C_P$$’s and constant heat of reaction, the conversion versus temperature is a straight line.

The energy balance for an isothermal reactor is; $XF_{A0}\Delta H_{rxn}\,=\,\dot Q$ where $$\dot Q$$ is the heat transfer rate (J/s).