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For general reaction $\mathrm{X\rightarrow Y, }$ the plot of concentration of X vs time is given in the figure. What is the order of the reaction and what is the units of rate constant?

Option: 1
$\mathrm{Zero, mol L { }^{-1} \mathrm{~s}^{-1} }$

Option: 2
$\mathrm{First, mol L s { }^1 }$

Option: 3
$\mathrm{First, \mathrm{s}^{-1} }$

Option: 4
$\mathrm{Zero, L mol s { }^{-1}}$

Answers (1)

best_answer

For a zero-order reaction, concentration versus time graph is a straight line with a negative slope.

Consider a zero order reaction,

Rate, $\mathrm{R=K[A]^0}$

$\mathrm{-\frac{d[A]}{d t} =K[A]^0 }$

$\mathrm{-\frac{d[A]}{d t} =K \times 1 \\ }$

$\mathrm{-d[A] =K d t }$

Taking limit on both side

$\mathrm{-\int_{[A]_0}^{[A]_t} d[A]=K \int_0^t d t }$

When
$\mathrm{ \text { time }=0, \quad A=[A]_o \\ }$

$\mathrm{ \text { time }=t, \quad A=[A]_t \\ }$

$\mathrm{ -[A]_{[A]_o}^{[A]_t}=K[t]_0^t \\ }$

$\mathrm{ {[A]_0-[A]_t=K t} \\ }$

$\mathrm{ {[A]_t=[A]_0-K t} }$

Its in y=m x form.

Hence, Plot between $\mathrm{ [A]_t }$ vs time :

Hence,
Order of the given reaction is zero
$\mathrm{ \text { Rate }=\text { Rate constant }=\frac{d x}{d t} }$
units of $\mathrm{ \mathrm{K}=m o l L^{-1} s^1 }$ .

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Rishi

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