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in Chemical kinetics by (30 points)
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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) \( 17.35 \times 10^{-5} M ^{-2} S ^{-1} \)

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\(A\,+\,2B\,\longrightarrow\,C\)

Rate of reaction \(r=\frac{-d[A]}{dt}=\frac{-1}{2}\frac{d[B]}{dt}=\frac{d[C]}{dt}\)

\(R=K[A][B]^2\)

\(\therefore\) Rate of reaction \(=-\frac{(0.10-0.20)}{13.06}\)

\(R=\frac{0.10}{13.06}\)

\(R=7.2\times10^{-3}\,MS^{-1}\)

\(R=K[A][B]^2\)

\(7.2\times10^{-3}=K\times0.20\times(120)^2\)

\(K=\frac{7.2\times10^{-3}}{0.20\times120}\)

\(K=2.5\times10^{-6}\,M^{-2}S^{-1}\)

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