For gaseous reaction- following data is given- A- B- k1-1015 e-2000-T C- D- k2-1014 e-1000-TThe temperature at which k1-k2 is-

According to Arrhenius equation, nbsp; nbsp; k=Ae^ E_a/RT where, nbsp; k nbsp;: Rate constant A : Arrhenius factor or frequency factor or pre expone ...

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Byju's Answer

Standard XII

Chemistry

Arrhenius Equation

For gaseous r...

Question

For gaseous reaction, following data is given:
$A \to B, k_{1} = 10^{15} e^{- 2000 / T}$
$C \to D, k_{2} = 10^{14} e^{- 1000 / T}$
The temperature at which $k_{1} = k_{2}$ is:

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Solution

According to Arrhenius equation,
$k = A e^{- E_{a} / R T}$
where,
k : Rate constant
A : Arrhenius factor or frequency factor or pre-exponential factor
$E_{a}$ : Activation energy (in J/mol)
R : Gas constant
T : Temperature of reaction (in Kelvin(K))

When $k_{1} = k_{2}$

$10^{15} e^{- 2000 / T} = 10^{14} e^{- 1000 / T}$
$10 = e^{- 1000 / T} e^{2000 / T}$
$10 = e^{⎛ ⎝ \frac{- 1000}{T} + \frac{2000}{T} ⎞ ⎠}$
$10 = e^{1000 / T}$
Taking $l n$ on both sides
$\Rightarrow l n 10 = \frac{1000}{T}$
$\Rightarrow 2.303 l o g 10 = \frac{1000}{T}$
$\Rightarrow T = \frac{1000}{2.303}$

$Hence, T = 434.2 K$

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For gaseous reaction, following data is given: A→B,k1=1015e−2000/T C→D,k2=1014e−1000/T The temperature at which k1=k2 is:

For gaseous reaction, following data is given:
$A \to B, k_{1} = 10^{15} e^{- 2000 / T}$
$C \to D, k_{2} = 10^{14} e^{- 1000 / T}$
The temperature at which $k_{1} = k_{2}$ is: