#### 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.

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##### 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).