Chemical Kinetics — Chemistry STD 12 Science — Question
Maharashtra BoardEnglish MediumSTD 12 ScienceChemistryChemical Kinetics3 Marks
Question
Derive the integrated rate law for first order reaction.
✓
Answer
Consider following gas phase reaction,$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ A _{( g )} \longrightarrow B _{( g )}+ C _{( g )}$
$\begin{array}{llll}\text { At start } \ \ \ \ \ \ P_0 & & &0& & 0\end{array}$
At time $t\ \ \ \ \ P_0-x \ \ \ \quad x \ \ \ \ \quad x$
Let initial pressure of $A$ be $P_0$_ at $t = 0$. If after time t the pressure of a A decreases by jc then the partial pressures of the substances will be,
$P_A = P_Q – x; P_B= x$ and $P_c = x$
Total pressure will be,
$P_T + P_0 – x + x + x = Po + x$
$\therefore x = P_T – P_n$
The partial pressures at time t will be,
$\begin{aligned} {[ A ]_t } & =P_0-x=P_0-\left(P_{ T }-P_0\right)=2 P_0-P_{ T } \\ {[ A ]_0 } & =P_0 \\ \because k & =\frac{2.303}{t} \log _{10} \frac{[ A ]_0}{[ A ]_t} \\ & =\frac{2.303}{t} \log _{10}\left(\frac{P_0}{2 P_0-P_{ T }}\right)\end{aligned}$
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