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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?

Answer & Explanation Solved by verified expert
3.9 Ratings (500 Votes)

I+I+Ar→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+I→I2

rate =k’ [I]^2

k’=k*[Ar]

It is second order with respect to I,

So integrated rate law,

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

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

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

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

                 =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

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

             =8.47 *10^14 s

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

                                                                                          
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