- #1

EE18

- 112

- 13

Callen asks us (with respect to an ideal gas)

$$\ln K_s(T) = - \sum_j \nu_j \phi_j(T).$$

Now a reaction which is the sum of this reaction with itself (doubled reaction) has ##\nu_j \to 2\nu_j## so that its equilibrium constant obeys, by definition,

$$\ln K_d(T) = - \sum_j 2\nu_j \phi_j(T) = 2\ln K_s(T) \implies K_d = e^2K_s.$$

But when I look online it says the equilibrium constant should square in this case, ##K_d = K_s^2##. Can someone point out what I'm doing wrong?

I had thought to proceed as follow. We have the definition for the singular reaction:How is the equilibrium constant of a reaction related to that for the same reaction when written with stoichiometric coefficients twice as large? Note this fact with caution!

$$\ln K_s(T) = - \sum_j \nu_j \phi_j(T).$$

Now a reaction which is the sum of this reaction with itself (doubled reaction) has ##\nu_j \to 2\nu_j## so that its equilibrium constant obeys, by definition,

$$\ln K_d(T) = - \sum_j 2\nu_j \phi_j(T) = 2\ln K_s(T) \implies K_d = e^2K_s.$$

But when I look online it says the equilibrium constant should square in this case, ##K_d = K_s^2##. Can someone point out what I'm doing wrong?

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