Question

The reaction C4H8(g)⟶2C2H4(g) C4H8(g)⟶2C2H4(g) has an activation energy of 262 kJ/mol.262 kJ/mol. At 600.0 K,600.0 K, the rate constant, ????,k, is 6.1×10−8 s−1.6.1×10−8 s−1. What is the value of the rate constant at 785.0 K?

Answer 1

Answer : The rate constant at 785.0 K is, $1.45\times 10^{-2}s^{-1}$

Explanation :

According to the Arrhenius equation,

$K=A\times e^{\frac{-Ea}{RT}}$

or,

$\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}]$

where,

$K_1$ = rate constant at $600.0K$ = $6.1\times 10^{-8}s^{-1}$

$K_2$ = rate constant at $785.0K$ = ?

$Ea$ = activation energy for the reaction = 262 kJ/mole = 262000 J/mole

R = gas constant = 8.314 J/mole.K

$T_1$ = initial temperature = $600.0K$

$T_2$ = final temperature = $785.0K$

Now put all the given values in this formula, we get:

$\log (\frac{K_2}{6.1\times 10^{-8}s^{-1}})=\frac{262000J/mole}{2.303\times 8.314J/mole.K}[\frac{1}{600.0K}-\frac{1}{785.0K}]$

$K_2=1.45\times 10^{-2}s^{-1}$

Therefore, the rate constant at 785.0 K is, $1.45\times 10^{-2}s^{-1}$

Answer 2

The rate constant at the new temperature is 1.81 ×10^−2 s−1.

We have the reaction written as follows; C4H8(g)⟶2C2H4(g) C4H8(g)⟶2C2H4(g).

We have to use the formula;

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

Now;

k2 = ?

k1 = 6.1×10−8 s−1

Ea = 262 ×10 ^3 J/mol

T1= 600.0 K

T2 = 785.0 K

R = 8.314 J/K. mol

ln (k2/6.1×10−8) = 262 ×10 ^3 /8.314 (1/600.0 - 1/785.0)

ln (k2/6.1×10−8) = 12.6

k2/6.1×10−8 = e^12.6

k2 = 6.1×10−8 (e^12.6)

k2 = 1.81 ×10^−2 s−1.

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