The rate consant for the reaction I+I+Ar---->I2+Ar is 0.59 x 1016 cm6mol-2s-1 at 293K. What is the half-life of...

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Chemistry

The rate consant for the reaction
I+I+Ar---->I₂+Ar
is 0.59 x 10¹⁶cm⁶mol^-2s^-1 at 293K. What is thehalf-life of I is [I]_o= 2 x 10^-5 molL^-1 and [Ar]= 5 x 10^-3 molL^-1?

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3.9 Ratings (500 Votes)

I+I+Arâ†’I₂+Ar

Rate=k[I]^2 [Ar]

As Ar is constant ,so the rxn is independent of concentration of Ar,[Ar]

Can be represented as I+Iâ†’I₂

rate =kâ€™ [I]^2

kâ€™=k*[Ar]

It is second order with respect to I,

So integrated rate law,

t(1/2) =1/k[I]o

given, kâ€™=rate constant=0.59*10^16 cm⁶ mol^-2 s^-1=k*[Ar]

k=kâ€™/[Ar]=( 0.59*10^16 cm⁶ mol^-2 s^-1)/(5*10^-3 mol/L*1000cm^3/L)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =( 0.59*10^16 cm⁶ mol^-2 s^-1)/(5 mol/cm^3)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =0.118 *10 ^16 cm³ mol^-1 s^-1

[I]o=2*10^-5 mol/L=2*10^-5 mol/L*1000cm3/L=2*10^-2 mol/cm

t(1/2) =1/k[I]o

Â Â Â Â Â Â Â Â Â Â Â =1/(0.118* 10^16 cm³ mol^-1 s^-1 )*( 2*10^-2 mol/cm³)

Â Â Â Â Â Â Â Â Â Â Â Â =8.47 *10^14 s

Â Â Â Â Â Â Â Â Â Â Â Â Â Â t(1/2)Â Â Â =8.47 *10^14 s

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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