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(A) Let the initial pressure of $A$ be $P_0$.Reaction: $A(g) \rightarrow 2B(g) + C(g)$At $t=0$: $P_0, 0, 0$ (Total pressure $= P_0$)At $t=10 \, min$:

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$90 \, mm, 47 \, mm, 6.496 	imes 10^{-2} \, min^{-1}$

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(A) Let the initial pressure of $A$ be $P_0$.Reaction: $A(g) ightarrow 2B(g) + C(g)$At $t=0$: $P_0, 0, 0$ (Total pressure $= P_0$)At $t=10 \, min$: $P_0-x, 2x, x$ (Total pressure $= P_0 + 2x = 176 \, mm$)At $t=\infty$: $0, 2P_0, P_0$ (Total pressure $= 3P_0 = 270 \, mm$)$(1)$ Initial pressure $P_0 = 270 / 3 = 90 \, mm$.$(2)$ At $t=10 \, min$,$P_0 + 2x = 176 \implies 90 + 2x = 176 \implies 2x = 86 \implies x = 43 \, mm$.Pressure of $A$ remaining $= P_0 - x = 90 - 43 = 47 \, mm$.$(3)$ Rate constant $k = \frac{2.303}{t} \log \frac{P_0}{P_0-x} = \frac{2.303}{10} \log \frac{90}{47} = \frac{2.303}{10} 	imes 0.2821 = 6.496 	imes 10^{-2} \, min^{-1}$.

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