Question

A reaction has a rate constant of 0.0177 s^-1 at 400.0 K. If the reaction has activation energy of 125 kJ/mol, calculate the rate constant at 500.0 K.A reaction has a rate constant of 0.0177 s^-1 at 400.0 K. If the reaction has activation energy of 125 kJ/mol, calculate the rate constant at 500.0 K.

Answer 1

Answer -

Given,

Rate constant at 400.0 K (K₁) = 0.0177 s^-1

Activation Energy = 125 kJ/mol

Rate constant at 500.0 K (K₂) = ?

We know that,

ln(K₂/K₁) = (E_a/R)[(1/T₁)-(1/T₂)]

where,

E_a = Activation Energy

K₂ and K₁ are rate constant

T₁ and T₂ are Temperatures

R = Rate Constant (0.008314 kJ/K mol)

Put the values,

ln(K₂/0.0177 s^-1) = (125 kJ/mol/0.008314 kJ/K mol)[(1/400.0 K)-(1/500.0 K)]

ln(K₂/0.0177 s^-1) = (15034.881 K) * (0.0005 K^-1)

ln(K₂/0.0177 s^-1) = 7.517

K₂/0.0177 s^-1 = e^7.517

K₂/0.0177 s^-1 = 1839.042

K₂ = 1839.042 * 0.0177 s^-1

K₂ = 32.551 s^-1 [ANSWER]