\[(aq)\xrightarrow{{}}B(aq)+C(aq)\] is a first order reaction. Time t \[\infty \] Moles of reagent \[{{x}_{1}}\] \[{{x}_{2}}\] Reaction progress is measured with the help of titration of reagent P, if all A, B and C reacted with reagent have n factors \[\left[ \text{n factor}:n=\frac{mol.wt.}{eq.wt.} \right]\] in the ratio 1 : 2 : 3 with the reagent. The k in terms of t, \[{{x}_{1}}\] and \[{{x}_{2}}\] is

• A. \[k=\frac{1}{t}\ln \left( \frac{{{x}_{2}}}{{{x}_{2}}-{{x}_{1}}} \right)\]
• B. \[k=\frac{1}{t}\ln \left( \frac{2{{x}_{2}}}{{{x}_{2}}-{{x}_{1}}} \right)\]
• C. \[k=\frac{1}{t}\ln \left( \frac{4{{x}_{2}}}{5({{x}_{2}}-{{x}_{1}})} \right)\]
• D. \[k=\frac{1}{t}\ln \left( \frac{8{{x}_{2}}}{{{x}_{2}}-{{x}_{1}}} \right)\]