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For a reaction \frac{1}{2}A\rightarrow 2B rate of disappearance of A is related to the rate of appearance of B by the expression

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As we read for reaction      aA+ bB \rightarrowcC + dD

Dis[A] =a \times rate of reaction

Dis[B] = b \times rate of reaction

appearance[C] = c \times rate of reaction

appearance[D] = d \times rate of reaction

For the reaction 

   \frac{1}{2}A\rightarrow 2B

here rate of dis of A =  \frac{1}{2}\timesrate of reaction = \frac{1}{2}R

and rate of appearance of B = 2\timesrate of reaction = 2 R

\frac{[A]}{[B]}=    \frac{1}{4}

 

 

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Gaurav

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