Question

The rate constant for the isomerisation reaction $X⟶Y$ is $4.5\times {10}^{-3}{min}^{-1}$. If the initial concentration of X is 1M. Calculate the rate of the reaction after one hour.

Answer 1

The given reaction is: $X⟶Y$

Rate of the reaction= $\frac{-d\left[X\right]}{dt}=\frac{d\left[Y\right]}{dt}$

Given, rate of constant of this isomerisation reaction is $4.5\times {10}^{-3}$ $mi{n}^{-1}$

Initial concentration of $X$ is $=1M$

$X⟶Y$

$t=0min$ $a$ $0$

$t=60min$ $a-x$ $x$

Let, at $t=0$ the concentration of $X$ is $aM$ after $t=60min$ i.e. $1$ hour $xM$ of it has reacted so, the remaining concentration of $X$ will be $(a-x)M$.

Now, for first order reaction we have:-

$K=\frac{2.303}{t}\log \left(\frac{a}{a-x}\right)$

$\Rightarrow 4.5\times {10}^{-3}=\frac{2.303}{60}\log \left(\frac{1}{1-2}\right)$ $[\because a=1M(given\left)\right]$

$\Rightarrow \frac{4.5\times {10}^{-3}\times 60}{2.303}=\log \left(1/1-x\right)$