Question

In: Chemistry

A reaction has a rate constant of 1.19×10−2 /s at 400. K and 0.693 /s at...

A reaction has a rate constant of 1.19×10⁻² /s at 400. K and 0.693 /s at 450. K.

A) Determine the activation barrier for the reaction

B) What is the value of the rate constant at 425 K

Expert Solution

Answer – A) We are given, T1 = 400 K , T2 = 450 K

k1 = 1.19*10^-2 s^-1 , k2 = 0.693 s^-1

Ea = ?

The intergraded Arrhenius equation

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

ln 1.19*10^-2 / 0.693 = Ea/ 8.314 J/mol.K * (1/450 – 1/400)

-4.064 = Ea/ 8.314 J/mol.K * -0.00028

So, Ea = -4.064 * 8.314 J/mol.K / -0.00028

= 1.2165*10⁵ J/mol

= 121.65 kJ/mol

the activation barrier for the reaction is 121.65 kJ/mol

B) We are given, T1 = 400 K , T2 = 425 K

k1 = 1.19*10^-2 s^-1 , k2 = ?

Ea = 1.22*10⁵ J/mol

The intergraded Arrhenius equation

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

ln 1.19*10^-2 / k2 = 1.22*10⁵ J. mol^-1 / 8.314 J/mol.K * (1/425 – 1/400)

ln 1.19*10^-2 / k2 = -2.15

so taking anitln from both side

1.19*10^-2 / k2 = 0.116

So, k2 = 1.19*10^-2 / 0.116

= 0.102 s^-1

So, the value of the rate constant at 425 K is 0.102 s^-1

queen_honey_blossom answered 2 years ago

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