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The van't Hoff equation describes how equilibrium constants vary with temperature. Which of the following correctly expresses the temperature dependence of Kp and Kc?

1. d(ln Kp)/dT = delta_H / (RT²) and Kp = Kc(RT)^(deltaₙ)
2. d(ln Kp)/dT = -delta_H / (RT²) and Kp = Kc(RT)^(deltaₙ)
3. d(ln Kc)/dT = delta_H / (RT²) and Kp = Kc * T^(deltaₙ)
4. d(ln Kp)/dT = delta_H / RT and Kp = Kc(R)^(deltaₙ)

Correct answer: d(ln Kp)/dT = delta_H / (RT²) and Kp = Kc(RT)^(deltaₙ)

Solution

The van't Hoff equation is: d(ln Kp)/dT = delta_H_rxn / (RT²), where delta_H_rxn is the standard enthalpy of reaction and R is the gas constant. For exothermic reactions (delta_H < 0), K decreases with increasing T. The relation between Kp and Kc is: Kp = Kc * (RT)^(deltaₙ), where deltaₙ = moles of gaseous products - moles of gaseous reactants. Both Kp and Kc obey the same van't Hoff equation form since they differ only by a factor that depends on T through a power law.

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