Catalyst efficiency

The catalyst efficiency is an important parameter for catalysts , which establishes a relationship between the effective (i.e. the observable) speed of a catalyzed chemical reaction and the so-called intrinsic reaction speed, which depends on the structure of the catalyst and the nature of its surface.

Equation 1: ${\displaystyle \eta ={\frac {r_{\text{eff}}}{r_{\text{int}}}}}$

• η : catalyst efficiency
• r _eff : Effective reaction rate / average reaction rate in a catalyst pellet
• r _int : intrinsic reaction rate

In other words, the effective reaction rate can thereby be calculated by the intrinsic reaction rate with a correction factor , the catalyst efficiency, multiplied is.

Equation 2: ${\displaystyle {r_{\text{eff}}}=\eta \cdot r_{\text{int}}=\eta \cdot k\cdot m_{\text{K}}\cdot c_{\text{S}}}$

• k : rate constant
• m _K : mass of the catalyst
• c _S : concentration of the respective substrate

To explain this, imagine a catalyst as it is used in heterogeneous catalysis . The catalyst is a porous solid (e.g. a zeolite ), the other reactants are dissolved in the liquid phase. The molecules whose reaction is to be catalyzed must penetrate the cavities of the catalyst, react there with one another and leave the solid again. If these transport processes were to take place unhindered or take place faster than the chemical reaction takes place, the catalyst efficiency , i.e. the value of the quotient, would be almost or equal to one (effective and intrinsic reaction rates are the same).

Equation 3: ${\displaystyle \eta ={\frac {r_{\text{eff}}}{r_{\text{int}}}}=1}$

• The catalyst efficiency with unhindered pore diffusion

In this case one speaks of a kinetically controlled reaction. Equation 2 is reduced by the catalyst efficiency, since this is one, and the effective reaction rate is calculated as follows:

Equation 4: ${\displaystyle {r_{\text{eff}}}=k\cdot m_{\text{K}}\cdot c_{\text{S}}}$

If the diffusion in the pores of the catalyst is hindered by their size and wall properties, so that at least one reactant diffuses through the pores more slowly than it is consumed in the reaction, this leads to a deficiency of this substance in the interior of the catalyst. The catalyst efficiency is less than one. The correction factor, which takes into account the most common conditions when calculating the catalyst efficiency, is determined with the help of the Weisz-Prater criterion .

Relationships with other metrics

${\displaystyle \eta ={\frac {\Psi }{\Phi ^{2}}}}$

• ${\displaystyle \Psi }$: Weisz module
• ${\displaystyle \Phi }$: Thiele module

${\displaystyle \eta ={\frac {3}{\Phi }}\left({\frac {1}{\tanh \Phi }}-{\frac {1}{\Phi }}\right)}$

This relationship is simplified for (because of ) to ${\displaystyle \Phi >3}$ ${\displaystyle \tanh \Phi \approx 1}$

${\displaystyle \eta ={\frac {3}{\Phi }}}$

literature

• Jens Hagen: Chemical reactors. Wiley-VCH, 2004, ISBN 978-3-527-30827-9 , p. 265 ( limited preview in Google book search).