A 20 litre container at 400 K contains $CO_2(g)$ at pressure 0.4 atm and an excess of SrO (neglect the volume

Question

A 20 litre container at 400 K contains $CO_2(g)$ at pressure 0.4 atm and an excess of SrO (neglect the volume of solid SrO). The volume of the container is now decreased by moving the movable piston fitted in the container. The maximum volume of the container, when the pressure of $CO_2$ attains its maximum value, will be (Given that: $SrCO_3(s) ightleftharpoons SrO(s) + CO_2(g)$, ($K_p = 1.6	ext{ atm}$))

Accepted Answer

The maximum pressure of $CO_2$ in the container is determined by the equilibrium constant $K_p$ of the given reaction.
For the reaction: $SrCO_3(s) ightleftharpoons SrO(s) + CO_2(g)$
$K_p = p_{CO_2} = 1.6	ext{ atm}$.
Thus, the maximum pressure of $CO_2$ that can be attained is $1.6	ext{ atm}$.
Applying Boyle's law ($p_1V_1 = p_2V_2$) to find the volume at which this maximum pressure is reached:
$0.4	ext{ atm} 	imes 20	ext{ L} = 1.6	ext{ atm} 	imes V_2$
$V_2 = \frac{0.4 	imes 20}{1.6} = 5	ext{ L}$.

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