For an elementary reaction, X ( g ) ⟶ Y ( g ) + Z ( g ) , the t 1 / 2 is 10 minutes. In what period of time would the concentration of X be reduced to 10 % of its original concentration?

Step-by-step solution

X ( g ) ⟶ Y ( g ) + Z ( g ) Let the concentration at   t = 0   =   x The concentration after time t = t   =   a - x = 10 % x   =   0 . 1 x K = 0 . 693 t 1 2 = 0 . 693 10 = 0 . 0693 According to the integrated rate law, t = 1 K ln a a - x = 1 0 . 0693 ln 1 0 . 1 = 1 0 . 0693 ln 10 = 2 . 303 0 . 0693 = 33 . 2 Hence, the time is equal to the 33 . 2   minutes