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The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy Ea= 50.0 KJ/mol. If the rate constant of this reaction is 0.14M-1 s-1 at -8.0what will the rate constant be at 56.0 ?

Round your answer to significant digits

k=_________ M-1s-1

User Alex Myers
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1 Answer

3 votes

Answer: The rate constant at 56°C is
11.58M^(-1)s^(-1)

Step-by-step explanation:

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


\ln((K_(56^oC))/(K_(-8^oC)))=(E_a)/(R)[(1)/(T_1)-(1)/(T_2)]

where,


K_(-8^oC) = equilibrium constant at -8°C =
0.14M^(-1)s^(-1)


K_(56^oC) = equilibrium constant at 56°C = ?


E_a = Activation energy = 50.0 kJ/mol = 50000 J/mol (Conversion factor: 1 kJ = 1000 J)

R = Gas constant = 8.314 J/mol K


T_1 = initial temperature =
-8^oC=[273-8]K=265K


T_2 = final temperature =
56^oC=[273+56]K=329K

Putting values in above equation, we get:


\ln((K_(56^oC))/(0.14))=(50000J)/(8.314J/mol.K)[(1)/(265)-(1)/(329)]\\\\K_(56^oC)=11.58M^(-1)s^(-1)

Hence, the rate constant at 56°C is
11.58M^(-1)s^(-1)

User Ben Hall
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