The equilibrium constant K changes with changes inthe temperature.
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This problem is describing the state two gases have when separated and together as shown on the attached picture. First of all, diagram 1 shows how they are separated in two containers with apparently equal volumes, whereas diagram 2 shows the removal of the barrier so that they get mixed together.
In this case, we can analyze that each gas has its own pressure and due to the removal of the barrier, both pressure and volume undergo a change. Thus, we can infer that the final volume is doubled with respected to the initial one for each gas, causing the pressure of each gas to be halved and the total pressure the half of the added ones, in agreement to the Boyle's law (inversely proportional relationship between pressure and temperature).
Therefore, the correct choice is:
C. The partial pressure of each gas in the mixture is half its initial pressure; the final total pressure is half the sum of the initial pressures of the two gases.
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