At 407 K the rate constant of a chemical reaction is 9.5 × 1 0 - 5 s - 1 and at 420 K , the rate constant is 1.9 × 1 0 - 4 s - 1 . The frequency factor of the reaction is x × 1 0 5 s - 1 .The value of 'x' is. Report your answer by rounding it up to nearest whole number.

Step-by-step solution

The Arrhenius equation is, log 10 k 2 k 1 = E a 2 .303×R T 2 − T 1 T 1 T 2 Given k 1 = 9.5 × 10 − 5 s − 1 ; k 2 = 1.9 × 10 − 3 s − 1 R = 8.314 Jmol − 1 K − 1 ; T 1 = 407 K and T 2 = 420 K Substituting the values in Arrhenius equation. lo g 10 1.9 × 1 0 - 4 9.5 × 1 0 - 5 = E a 2.303 × 8.314 420 - 407 420 × 407 E a = 75782.3 J mo l - 1 Applying now log ⁡ k 1 = log ⁡ A - E a 2.303 R T 1 log ⁡ 9.5 × 10 - 5 = log ⁡ A - 75782.3 2.303 × 8.314 × 407 log A 9.5 × 10 − 5 = 75782.3 2.303 × 8.314 × 4