Question

A particular first-order reaction has a rate constant of 1.35 × 102 s-1 at 25.0°c. what is the magnitude of k at 75.0°c if ea = 85.6 kj/mol?

Answer 1

According to this formula:
K= A*(e^(-Ea/RT) when we have K =1.35X10^2 & T= 25+273= 298K &R=0.0821
Ea= 85.6 KJ/mol So by subsitution we can get A:
1.35x10^2 = A*(e^(-85.6/0.0821*298))
1.35x10^2 = A * 0.03
A= 4333
by substitution with the new value of T(75+273) = 348K & A to get the new K
∴K= 4333*(e^(-85.6/0.0821*348)
  = 2.16 x10^2

Answer 2

The rate constant is a the rate of reaction for particular reaction. The magnitude of rate constant at 75$\bold {^oC}$ is $\bold {2.16 x10^2}$.

Arrhenius equation

A small increase in temperature of the reaction will produce a high increase in the magnitude of the rate constant of the reaction.

$\bold {K= Ae^-^E^a^/^R^T}$

Where,

k- rate constant

A- Frequency factor

Ea - Activation energy =  85.6 KJ/mol

R - gas constant

t - temperature =  (25+273) = 298 K

Put the value in the formula

$\bold {1.35x10^2 = A\times e^(^-^8^5^.^6^/^0^.^0^8^2^1^\times ^2^9^8^)}\\\\\bold {1.35x10^2 = A \times 0.03}\\\\\bold {A= 4333}$

The rate constant 75$\bold {^oC}$

T = (75+273) = 348K

put the values in the formula

$\bold {K= 4333\times \times e^(^-^8^5^.^6^/^0^.^0^8^2^1^\times ^3^4^8^)}\\\\\bold {K = 2.16 x10^2}$

Therefore, the magnitude of rate constant at 75$\bold {^oC}$ is $\bold {2.16 x10^2}$.

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