A reaction can take place by two paths, k_1 and k_2 are rate constants for the two paths & E_1 and E_2 are their respective activation energies. At temperature T_a: k_1gtk_2, E_1ltE_2. if temperature is raised to T_b, the rate constants change to k_1 & k_2 Which relation is correct between k_1,k_2,k_1 & k_2 (considering activation energy does not change with temperature )

A reaction can take place by two paths, k_1 and k_2 are rate constants

1.	A reaction can take place by two paths, k_1 and k_2 are rate constants for the two paths & E_1 and E_2 are their respective activation energies. At temperature T_a: k_1gtk_2, E_1ltE_2. if temperature is raised to T_b, the rate constants change to k_1 & k_2 Which relation is correct between k_1,k_2,k_1 & k_2 (considering activation energy does not change with temperature )
Answer» `k_1/k_1gtk_2/k_2` `k_1/k_1=k_2/k_2` `k_1/k_1ltk_2/k_2` `k_1/k_2gtk_1/k_2` Solution :`k_1=Ae^((-E_(1))/(RT_a)) "" k_2=Ae^((-E_2)/(RT_a)) " " IMPLIES (k'_(1))=Ae^((-E_1)/(RT_b)) " " k'_2=Ae^((-E_2)/(RT_b))` `k_1/k_1'=(Ae^((-E_1)/(RT_a)))/(Ae^((-E_1)/(RT_b))) "" k_1/k_1'=E^((-E_1)/R(1/T_a-1/T_b))` `(k_1')/k_1=e^((E_1)/R(1/T_a-1/T_b))` Similarly `(k_2')/k_2=e^((E_2)/R(1/T_a-1/T_b))` `E_1ltE_2 implies e^((E_1)/R(1/T_a-1/T_b)) " " lt e^((E_2)/R(1/T_a-1/T_b))` `implies k_1^'/k_1ltk_2^'/k_2`