An organic compound undergoes first order decomposition. The time taken for decomposition to ( 1 8 )^ th and ( 1 10 )^ th of its initial concentration are t _ 1 / 8 and t _ 1 / 10 respectively. What is the value of t _ 1 / 8 t _ 1 / 10 10 ? ( 2=0.3 )

Step-by-step solution

For first-order decomposition with rate equation [A] = [A]₀ e^ -kt , the time for concentration to reduce to fraction f is: t = 1 k 1 f = (1/f) k For reduction to 1/8: t_ 1/8 = 8 k = 3 2 k For reduction to 1/10: t_ 1/10 = 10 k Therefore: t_ 1/8 t_ 1/10 = 8 10 = 3 2 10 = 3 0.3 1 = 0.9 Thus: t_ 1/8 t_ 1/10 10 = 0.9 10 = 9