An equilibrium mixture of PCl 5 ( g ) , PCl 3 ( g ) , and Cl 2 ( g ) has partial pressures of 217.0 Torr, 13.2 Torr, and 13.2 Torr, respectively. A quantity of Cl 2 ( g ) is injected into the mixture, and the total pressure jumps to 263.0 Torr at the moment of mixing. The system then re-equilibrates. The chemical equation for this reaction is PCl 3 ( g ) + Cl 2 ( g ) − ⇀ ↽ − PCl 5 ( g ) Calculate the new partial pressures, P , after equilibrium is reestablished.

Explanation:

Hello,

In this case, the undergoing chemical reaction is:

And the equilibrium constant at the reaction's temperature is:

Now, even when chlorine is added, such pressure equilibrium constant does not change, therefore, since the initial total pressure is:

The new pressures, due to the change owing to the chlorine's addition, turn out:

Therefore, the added chlorine is:

Thus, the new partial pressures are found via the law of mass action in terms of the change as follows:

Solving for one obtains:

Finally, the new partial pressures result:

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