31. For the gas phase reaction \( A+2 B \stackrel{K}{\longrightarrow} C \), rate law is given as \( R=K[A][B]^{2} \). Reaction starts with \( 0.20 M \) of \( A \) and \( 120 M \) of B. After \( 13.86 sec \). concentration of \( A \) reduces to \( 0.10 M \), calculate the value of rate constant \( K \).
(1) \( 6.93 \times 10^{-4} M ^{-2} S ^{-1} \)
(2) \( 3.47 \times 10^{-6} M ^{-2} S ^{-1} \)
(3) \( 10.41 \times 10^{-6} M ^{-2} S ^{-1} \)
(4) \( 17.35 \times 10^{-5} M ^{-2} S ^{-1} \)
