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Chemistry · Differential and integral forms of zero and first-order reactions, their characteristics and half-lives

The following data were obtained during the first order thermal composition of a

The following data were obtained during the first order thermal composition of \( S O_{2} C l_{2} \) at a constant volume. \[ \boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{S} \boldsymbol{O}_{2(\boldsymbol{g})}+\boldsymbol{C l}_{2(\boldsymbol{g})} \] Total pres Experiment \( \quad \) Time \( / \) s \( ^{-1} \) (atm) \[ 0.5 \] What is the rate of reaction when total pressure is 0.65 atm?

  • A. 0 .35 atm \( s^{-1} \)
  • B. \( 2.235 \times 10^{-3} \) atm \( s^{-1} \)
  • C. \( 7.8 \times 10^{-4} \) atm \( s^{-1} \)
  • D. \( 1.55 \times 10^{-4} \) atm \( s^{-1} \)

Step-by-step solution

Given first-order decomposition SO2Cl2 → SO2 + Cl2 with initial total pressure P0 = 0.5 atm (pure SO2Cl2). At total pressure 0.65 atm, partial pressure of SO2Cl2 is P_A = 2P0 - P_total = 0.35 atm. The rate constant k is derived from typical data (e.g., at 100 s total pressure = 0.6 atm gives k ≈ 2.235 × 10^{-3} s^{-1}). Rate = k P_A = (2.235 × 10^{-3})(0.35) = 7.8 × 10^{-4} atm s^{-1}.
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