The rate costant K₁ of a reaction is found to be double of that of rate constant K₂ of another reaction .What is the relationship between corresponding activation energies of the to reactions .The Arrhenius constant is same for the reactions.

(A)E₂ = E₁ - ln 2 /RT

(B)E₂=E₁ ln 2/RT

(C)E₂ + E₁ = ln 2/RT

(D) E₂ =E₁ + RTln 2

Ans:(C)

Thanks in advance.

Given is that

k1  = 2*k2               .................(1)

Let A be the arrhenius constant for both the reactions . Then using arrhenius equation,       

k1=A*exp(-E1/RT)    ..............(2)

k2=A*exp( -E2/RT)  ...............(3)

[ where exp stands for 'e' raised to the power of ]

Divide (2) by (3)

k1/k2=exp(E2-E1)/RT

OR exp(E2-E1)/RT= 2   [ from equation (1)  ]

Taking log both sides to the base e ,

(E2-E1)/RT = ln2

E2 = E1 + RTln2

Ans is (D ) & not (C)

If you watch all four options, equations given in (B) & (C) are dimensionally incorrect . So they should be ruled out at once.

Calculations show answer to be (D) as above.