4.6     Time required to decompose $SO_{2}Cl_{2}$ to half of its initial amount is $60$ minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.

We know that t(half ) for the first order reaction is  $\frac{0.693}{k} = t_{1/2}$

and we have given the value of half time $t_{1/2} = 60 min$

thus,  $k = \frac{0.693}{60}min^{-1}$

= 0.01155 /min

OR = 1.1925$\times 10^{-4}sec$

Alternative method

we can also solve this problem by using the first order reaction equation.

$k = \frac{2.303}{t}\log\frac{[R]_{0}}{[R]}$

put $[R]=[R_{0}]/2$

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