Problem

Problem

For the reaction 2A⟶3B+5C2A \longrightarrow 3B + 5C occurring at constant temperature in a constant volume container, total pressure is observed at different time interval. If the reaction is first order with respect to A, then calculate the value of rate constant ×1000\times 1000 in terms of sec−1\text{sec}^{-1}.
Timet=0t = 0t=700 sect = 700 \text{ sec}t=∞t = \infty
PtotalP_{\text{total}}80 mm147.5 mm170 mm
Intuitive explanation

The key is recognizing that for a constant-volume reaction, total pressure is proportional to total moles, which changes as reactants convert to products. Since 2A→3B+5C2A \to 3B + 5C produces 6 moles from 2 moles, pressure increases as the reaction proceeds. Use the pressure data to find how much A has reacted at each time point, then apply the first-order integrated rate law ln⁡[A]=ln⁡[A]0−kt\ln[A] = \ln[A]_0 - kt to extract kk.

Intuitive explanation

The key is recognizing that for a constant-volume reaction, total pressure is proportional to total moles, which changes as reactants convert to products. Since 2A→3B+5C2A \to 3B + 5C produces 6 moles from 2 moles, pressure increases as the reaction proceeds. Use the pressure data to find how much A has reacted at each time point, then apply the first-order integrated rate law ln⁡[A]=ln⁡[A]0−kt\ln[A] = \ln[A]_0 - kt to extract kk.

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