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I haven't been able to find the units of the reactive cross-section (σ* = Pσ) online but when I do a unit analysis from the equation:

$$ k = PσN_A √(\frac{8k_BT}{πμ}) e^{-E_a/RT}$$

then when plotting lnk against $1$/T the intercept is equal to:

$$intercept = lnPσN_A √(\frac{8k_BT}{πμ})$$

solving Pσ then gives that the units should be [m$^2$s$^{-1}$mol$^{-1}$]. However, the units of the collisional cross-section is [m$^2$] and the reactive cross-section is by definition the collisional cross-section times a steric factor P which is a constant, so how come the units change? Shouldn't the units for the reactive cross-section also be [m$^2$]?

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  • $\begingroup$ what is the dimension of P ? $\endgroup$
    – porphyrin
    Sep 7, 2021 at 16:34
  • $\begingroup$ @porphyrin I believe it is unitless, in our lecture notes it only says its a steric factor $\endgroup$
    – katara
    Sep 7, 2021 at 16:43
  • $\begingroup$ ok, then the units of rate constant $k$ are $\mathrm{m^3/mol/s}$ which are correct. $\endgroup$
    – porphyrin
    Sep 8, 2021 at 9:20

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