The slope of Arrhenius Plot (In k v/s 1/T) of first order reaction is –5 × 10^3 K.

Question

The slope of Arrhenius Plot \(\left(\text{In k v/s}\, \frac{1}{T}\right)\) of first order reaction is –5 × 10³ K. The value of E_a of the reaction is. Choose the correct option for your answer.

[Given R = 8.314 JK^–1 mol^–1]

(1) 41.5 kJ mol^–1

(2) 83.0 kJ mol^–1

(3) 166 kJ mol^–1

(4) –83 kJ mol^–1

Answer 1

Correct option is (1) 41.5 kJ/mol

Arrhenius equation

k = Ae^−Ea/RT

ln k = ln A + ln e^−Ea/RT

ln k = ln A − \(\frac{E_a}R (\frac 1T)\)   .......(1)

Slope of ln k vs \(\frac 1T\) curve,

m = \(- \frac{E_a}R\)

−5 × 10³ = \(- \frac{E_a}R\)

E_a = 5 × 10³ × 8.314 J/mol

= 41.57 × 10³ J/mol

= 41.5 kJ/mol

Answer 2

Correct answer is (1).