1. **Problem statement:** We are given the conductivity $\sigma$ of a reaction mixture over time $t$ during the hydrolysis of 2-chlorobutane ($\mathrm{C_4H_9Cl}$) to 2-butanol ($\mathrm{C_4H_9OH}$). The goal is to analyze the kinetics of the reaction using the conductivity data. 2. **Given data:** - Initial volume $V_0 = 50$ mL - Volume $V_1 = 25$ mL - Volume $V_2 = 1$ mL - Temperature $20^\circ$C - Molar mass $M(\mathrm{C_4H_9Cl}) = 92.57$ g/mol - Density of water $\rho(\mathrm{H_2O}) = 1$ g/cm$^3$ - Distance between electrodes $d = 0.84$ m - Conductivity $\sigma$ (S/m) at times $t$ (s) given in the table 3. **Understanding the reaction:** $$\mathrm{C_4H_9Cl + 2H_2O \rightarrow C_4H_9OH + Cl^- + H_3O^+}$$ The conductivity increases as ions $\mathrm{Cl^-}$ and $\mathrm{H_3O^+}$ are produced. 4. **Calculate the maximum conductivity $\sigma_\infty$:** From the data, conductivity plateaus at $\sigma_\infty = 1.955$ S/m after 1800 s. 5. **Calculate the degree of reaction progress $\alpha(t)$:** $$\alpha(t) = \frac{\sigma(t)}{\sigma_\infty}$$ This represents the fraction of reaction completed at time $t$. 6. **Calculate $\alpha(t)$ for each time point:** For example, at $t=200$ s: $$\alpha(200) = \frac{0.489}{1.955} \approx 0.250\quad (25\%)$$ Similarly for other times. 7. **Determine the reaction kinetics:** Assuming a first-order reaction, the concentration of $\mathrm{C_4H_9Cl}$ decreases as: $$[\mathrm{C_4H_9Cl}] = [\mathrm{C_4H_9Cl}]_0 (1 - \alpha(t))$$ The rate law is: $$\ln\left(\frac{[\mathrm{C_4H_9Cl}]_0}{[\mathrm{C_4H_9Cl}]_0 (1 - \alpha(t))}\right) = kt$$ which simplifies to: $$-\ln(1 - \alpha(t)) = kt$$ 8. **Plot or calculate $-\ln(1 - \alpha(t))$ vs $t$ to find rate constant $k$:** Using the data, calculate $-\ln(1 - \alpha(t))$ for each $t$ and perform linear regression to find slope $k$. 9. **Summary:** - The reaction progress is monitored by conductivity. - The degree of reaction $\alpha(t)$ is the ratio of conductivity at time $t$ to maximum conductivity. - The reaction follows first-order kinetics with rate constant $k$ obtained from the slope of $-\ln(1 - \alpha(t))$ vs $t$. **Final answer:** The reaction is first-order with respect to $\mathrm{C_4H_9Cl}$, and the rate constant $k$ can be determined from the conductivity data using: $$k = \frac{-\ln(1 - \alpha(t))}{t}$$ where $$\alpha(t) = \frac{\sigma(t)}{1.955}$$