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  •  If 50% of the reactant that follows first order kinetics is converted into product(s) in 25 min, how much of it would react in 100 min?  <div

 If 50% of the reactant that follows first order kinetics is converted into product(s) in 25 min, how much of it would react in 100 min?

 

Option: 1

93.75%


Option: 2

87.5%


Option: 3

75%


Option: 4

100%


Answers (1)

best_answer

For any reaction, time taken for 50 %  of a reactant to convert into product(s) is called the half life \mathrm{\left(t_1\right)}  For a first order reaction:

\mathrm{ t_{\frac{1}{2}}=\frac{\ln 2}{k}=25 \min }
\mathrm{k=\frac{\ln 2}{25} \min ^{-1} }
\mathrm{ k=\text { Rate constant } }

Also,
For a first order reaction:
\mathrm{ A \rightarrow \text { Products } }
\mathrm{ [A]=\left[A_0\right] e^{-k t} \ldots }.......(i)

Here,
\mathrm{ [A] }= Concentration of \mathrm{ \mathrm{A} }  at time \mathrm{ \mathrm{t} }
\mathrm{ \mathrm{\left[A_0\right]=} } Concentration of \mathrm{ \mathrm{\mathrm{A}} } initially
Putting \mathrm{ \mathrm{t=100 \min and~ k=\frac{\ln 2}{25}} }    in (i)

\mathrm{ \mathrm{ {[A]=\left[A_0\right] e^{\frac{\ln 2}{25} \times 100}} } }
\mathrm{ \mathrm{ {[A]=\left[A_0\right] e^{-\ln 2^4}} } }
\mathrm{ \mathrm{{[A]=\frac{1}{16} \times\left[A_0\right]} } }

\mathrm{ \mathrm{\% \text { reacted }=\frac{\left[A_0\right]-[A]}{\left[A_0\right]} \times 100 \%=\frac{\left[A_0\right]-\frac{\left[A_0\right]}{16}}{\left[A_0\right]} \times 100 \%}}
\mathrm{\%~reacted =93.75 \%}.

 

Posted by

Rishi

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