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Initially, I found that $K_\mathrm{p}$ depends only on temperature; but later I found that it depends on pressure of $\ce{CO2}$ gas in case of $\ce{CaCO3 (s, aragonite) → CaO (s) + CO2}$.

How do we know whether it depends upon partial pressure of reactants and products or not? Or, this is a special scenario?

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If there is a high gas pressure in the environment the reaction is taking place in, $K_\mathrm{p}$ will shift towards the side of the reaction that has fewer gas molecules, as it is "fighting against" the high pressure, in a way. So in your case, since only one side has gas (the product side) if you increase the pressure of $\ce{CO2}$ or any other gas, the equilibrium will shift towards the reactant side.

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    $\begingroup$ I am sorry. But does this answer the question? $\endgroup$ Jul 6, 2017 at 15:28
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    $\begingroup$ It seemed to me he was asking if $K_p$ depends on partial pressure of reactants/products, so I was posting about how the equilibrium ($K_p$) shifts due to pressure (which could be partial pressure of a reactant/product, or pressure of some other gas). I hope I didn't misinterpret the question, but I think my post goes some way to answering. $\endgroup$
    – iammax
    Jul 6, 2017 at 15:52
  • $\begingroup$ Sir I want to ask that generally we say that K of a reaction depends only on temperature but in this case it is also depending on pressure of CO2 gas.Why is it so? $\endgroup$ Jul 7, 2017 at 5:14

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