Question

In: Chemistry

The gas phase decomposition of hydrogen iodide to hydrogen gas and iodine gas occurs with a...

The gas phase decomposition of hydrogen iodide to hydrogen gas and iodine gas occurs with a rate of 2.35x10^-7 M^-1s^-1 at 283 degree C and 1.62x10^-3 M^-1s^-1 at 427 degree C.

A. What is the activation energy of this reaction in kJ/mole?

B. What is the temperature in Celsius of a reaction that has a rate constant of 2.91x10^-4 M^-1s^-1?

Expert Solution

A) 2HI(g)H2(g)+I2(g)

rate of reaction=r=-d[HI]/dt=k[HI]^2, k=rate constant

given

r1=-d[HI]/dt=k1[HI]^2=2.35*10^-7 (at 283k)

r2=-d[HI]/dt=k2[HI]^2=1.62*10^-3 (at 427k)

taking ratio,

r1/r2=k1/k2=2.35*10^-7/1.62*10^-3 =1.45*10^-4

A) Arrhenius equation,

lnK=lnA-Ea/RT

so ln(k1/k2)=Ea/R(1/T2-1/T1)

T1=283+273=556K , T2= 427+273=700K T=temperature,Ea=activation energy,R=gas constant

ln(1.45*10^-4)=Ea/8.314J/K mol(1/700-1/556)

-8.873=Ea/8.314J/K mol(0.00143-0.00180)

-8.873=Ea/8.314J/K mol(-0.00037)

Ea=-8.873*8.314J/K mol/(-0.00037)=199378.708 J/mol=199.379 KJ/mol

B)k3=2.91*10^-4

let T=T3 for this reaction

k1/k3=2.35*10^-7/2.91*10^-4=0.807*10^-3

ln(k1/k3)=Ea/R(1/T3-1/T1)

ln(0.807*10^-3)=199378.708 J/mol/8.314J/k mol(1/T3-1/556)

-7.122=23981.081(1/T3-0.00180)

-2.970*10^-4=(1/T3-0.00180)

1/T3=-2.970*10^-4+0.00180=0.00150

T3=666.667K

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