Calculate the half-life of the first-order reaction C 2 H 4 O g → C H 4 g + C O g if the initial pressure of C 2 H 4 O g is 80 mm and the total pressure at the end of 20 minutes is 120 mm.

Step-by-step solution

According to the question, p 0 - p + p = 120 mm or p 0 + p = 120 mm or p = 120 - 80 = 40 mm. For a first order reaction, k = 1 t ln ⁡ p 0 p 0 - p = 1 20 ln ⁡ 80 80 - 40 = 1 20 ln ⁡ 2 …(i) But we know that t 1 2 = 1 n 2 k …(ii) From equations (i) and (ii) k = 1 20 k t 1 2 t 1 2 = 20 min.