Under the same reaction conditions, initial concentration of $1.386$ $m o l$ ${d m}^{- 3}$ of a substance becomes half in $40$ seconds and $20$ seconds through first order and zero order kinetics respectivley. Ratio $(\frac{k_{1}}{k_{0}})$ of the rate constant for first order $(k_{1})$ and zero order $(k_{0})$ of the reaction is:

0.5 {m o l}^{- 1} {d m}^{3}

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1 m o l {d m}^{- 3}

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1.5 m o l {d m}^{- 3}

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2 {m o l}^{- 1} {d m}^{3}

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Solution

The correct option is C $0.5 {m o l}^{- 1} {d m}^{3}$
$t_{1 / 2} = \frac{0.693}{k_{1}}$ , $t_{1 / 2} = \frac{a_{0}}{2 k_{0}}$
$40 = \frac{0.693}{k_{1}}$ , $20 = \frac{1.386}{2 k_{0}} = \frac{0.693}{k_{0}}$
$\frac{20}{40} = \frac{0.693 / k_{0}}{0.693 / k_{1}} = \frac{k_{1}}{k_{0}}$
$\frac{k_{1}}{k_{0}} = 0.5 \frac{{s e c}^{- 1}}{m o l {d m}^{- 3} {s e c}^{- 1}} = 0.5 {m o l}^{- 1} {d m}^{3}$

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Under the same reaction conditions, initial concentration of 1.386 $m o l d m^{- 3}$ of a substance becomes half in 40 s amd 20 s through first order and zero order kinetics respectively. Ratio $(\frac{k_{1}}{k_{0}})$ of the rate constants for first order $(k_{1})$ and zero order $(k_{0})$ of the reaction is:

Under the same reaction conditions, the initial concentration of 1.386 mol $d m^{- 3}$ of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively.

The ratio $(k_{1} / k_{0}$ ) of the rate constants for first order $(k_{1})$ and zero order $(k_{0})$ of the reaction is

Under the same reaction conditions, the initial concentration of 1.386 mol $d m^{- 3}$ of a substance becomes half in 40 s and 20 s through first order and zero order kinetics, respectively.

The ratio $(k_{1} / k_{0}$ of the rate constants for first order $(k_{1})$ and zero order $(k_{0})$ of the reaction is

The ratio $(k_{1} / k_{0}$ ) of the rate constants for first order $(k_{1})$ and zero order $(k_{0})$ of the reaction is

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Under the same reaction conditions, initial concentration of 1.386 mol dm−3 of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics respectivley. Ratio (k1k0) of the rate constant for first order (k1) and zero order (k0) of the reaction is:

The correct option is C 0.5 mol−1dm3t1/2=0.693k1, t1/2=a02k040=0.693k1, 20=1.3862k0=0.693k02040=0.693/k00.693/k1=k1k0k1k0=0.5sec−1moldm−3sec−1=0.5mol−1dm3