Question
How is the integrated rate equation for the first order reaction represented by considering the concentration of the product?
✓
Answer
The integrated rate equation for the first order reaction can be represented as,
$k=\frac{2.303}{t} \log _{10} \frac{[ A ]_0}{[ A ]_t}$ where $[ A ]_0$ is the initial concentration of the reactant (at time, $1=0$ ) and $[ A ]_t$ is that at time $t$. Consider the reaction, $A \rightarrow B$
If $a$ is the initial concentration of the reactant $A$ and $x$ is the concentration of the product $B$ after time $t$, then
$[ A ]_0=a$ and $[ A ]_t=a-x$ (for $A$ )
$\therefore k=\frac{2.303}{t} \log _{10}\left(\frac{a}{a-x}\right) \text {. }$
$k=\frac{2.303}{t} \log _{10} \frac{[ A ]_0}{[ A ]_t}$ where $[ A ]_0$ is the initial concentration of the reactant (at time, $1=0$ ) and $[ A ]_t$ is that at time $t$. Consider the reaction, $A \rightarrow B$
If $a$ is the initial concentration of the reactant $A$ and $x$ is the concentration of the product $B$ after time $t$, then
$[ A ]_0=a$ and $[ A ]_t=a-x$ (for $A$ )
$\therefore k=\frac{2.303}{t} \log _{10}\left(\frac{a}{a-x}\right) \text {. }$
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