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A solution of A is mixed with equal volume of a solution of B containing the same number of moles,for reaction $A+B\rightarrow C$.At the end of 1 hour,A is 75% reacted.How much of A will be left unreacted at the end of 2hours if the reaction is first order in A & zero order in B.

$\begin{array}{1 1}(a)\;14.23\%&(b)\;0\%\\(c)\;6.25\%&(d)\;50\%\end{array}$

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As the given reaction is first order reaction.
$K=\large\frac{1}{t}$$ln\large\frac{[A_0]}{[A_t]}$
$K=\large\frac{1}{1hr}$$ln\large\frac{[A_0]}{25\%[A_0]}$
$\;\;\;\;=ln 4hr^{-1}$
Now,as K remains constant for a particular reaction,
$K=\large\frac{1}{2hr}$$ln\large\frac{[A_0]}{[A_t]}$$=ln 4hr^{-1}$
$ln\large\frac{[A_0]}{[A_t]}$$=2ln \;4hr^{-1}$
$ln\large\frac{[A_0]}{[A_t]}$$=ln \;16hr^{-1}$
$\large\frac{[A_0]}{[A_t]}$$= \;16$
$[A_t]=\large\frac{[A_0]}{16}$
$[A_t]=(6.25\%)[A_0]$
$\large\frac{[A_t]}{[A_0]}$$= 6.25\%$
answered Dec 18, 2013 by sreemathi.v
edited Jul 27, 2014 by balaji.thirumalai
 

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