Phosphorus pentachloride interconverts with its decomposition products according to…

CHEMISTRY · Multi-part · AP · Chemistry · Equilibrium · Equilibrium

Problem

Phosphorus pentachloride interconverts with its decomposition products according to PCl

_5

(g) ⇌ PCl

_3

(g) + Cl

_2

(g) A sealed 10.0 L vessel at 450 K initially contains the equilibrium mixture whose partial pressures are

P

(PCl

_5

) = 0.80 atm

P

(PCl

_3

) = 0.60 atm

P

(Cl

_2

) = 0.60 atm At time

t=0

the vessel volume is suddenly compressed to 5.0 L while the temperature is held constant. Immediately afterward, but before the system can respond chemically, an additional 0.40 atm of PCl

_3

(g) is injected (the volume remains 5.0 L). Throughout the experiment the temperature stays at 450 K, so the rate constants

k_{\text{f}}

and

k_{\text{r}}

are unchanged. The elementary rate laws are Rate

_{\text{forward}} = k_{\text{f}}[\text{PCl}_5]

Rate

_{\text{reverse}} = k_{\text{r}}[\text{PCl}_3][\text{Cl}_2]

(a) Write an expression for the ratio

R = \dfrac{\text{Rate}_{\text{forward}}}{\text{Rate}_{\text{reverse}}}

in terms of the partial pressures of the three species. (b) Calculate the value of

R

immediately after the compression but before the PCl

_3

injection. Indicate the resulting direction of net conversion and justify your choice. (c) After the 0.40 atm of PCl

_3

is added (still at 5.0 L), determine the new value of

R

. Identify the new direction of net conversion and justify your answer. (d) Explain qualitatively how the composition of the gas mixture will evolve over time after the events in parts (b) and (c) until equilibrium is re-established. In your explanation refer explicitly to how the forward and reverse rates change as the partial pressures change.

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