Question

the activation energy (ea) of a first order reaction is 70 kj mol-1. the rate constant (k1) at 25 c is 2.25 10-5 s-1. what is the rate constant (k2) (s-1) at 70 c?

Answer 1

I don't know answer sorry

Answer 2

The rate constant at 70°C is $9.16\times 10^{-4}s^{-1}$

Explanation:

To calculate rate constant at two different temperatures of the reaction, we use Arrhenius equation, which is:

$\ln(\frac{K_{70^oC}}{K_{25^oC}})=\frac{E_a}{R}[\frac{1}{T_1}-\frac{1}{T_2}]$

where,

$K_{70^oC}$ = equilibrium constant at 70°C = ?

$K_{25^oC}$ = equilibrium constant at 25°C = $2.25\times 10^{-5}s^{-1}$

$E_a$ = Activation energy = 70 kJ/mol = 70000 J/mol   (Conversion factor:  1 kJ = 1000 J)

R = Gas constant = 8.314 J/mol K

$T_1$ = initial temperature = $25^oC=[25+273]K=298K$

$T_2$ = final temperature = $70^oC=[70+273]K=343K$

Putting values in above equation, we get:

$\ln(\frac{K_{70^oC}}{2.25\times 10^{-5}})=\frac{70000J}{8.314J/mol.K}[\frac{1}{298}-\frac{1}{343}]\\\\K_{70^oC}=9.16\times 10^{-4}s^{-1}$

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