Benzene diazonium chloride in aqueous solution decomposes according to the equation C_6H_5N_2Cl rarrC_6H_5Cl+N_2 . Starting with an initial concentration of 10 "g L"^(-1),the volume of N_2 gas obtained at 50^@C at different intervals of time was found to be as under : {:(t(min):,6,12,18,24,30,oo),("Vol. of "N_2(ml):,19.3,32.6,41.3,46.5,50.4,58.3):} Show that the above reaction follows the first order kinetics. What is the value of the rate constant ?

Benzene diazonium chloride in aqueous solution decomposes according to

1.	Benzene diazonium chloride in aqueous solution decomposes according to the equation C_6H_5N_2Cl rarrC_6H_5Cl+N_2 . Starting with an initial concentration of 10 "g L"^(-1),the volume of N_2 gas obtained at 50^@C at different intervals of time was found to be as under : {:(t(min):,6,12,18,24,30,oo),("Vol. of "N_2(ml):,19.3,32.6,41.3,46.5,50.4,58.3):} Show that the above reaction follows the first order kinetics. What is the value of the rate constant ?
Answer» Solution :For a FIRST order reaction `k=(2.303)/tlog.(a)/((a-x))` `k=2.303/tlog.(V_oo)/(V_oo-V_t)` In this case, `V_oo=58.3` ml The value of k at DIFFERENT time can be CALCULATED as FOLLOWS : Since the value of k comes out to the nearly constant , the given reaction is of the first order. The mean value of `k=0.0674 "min"^(-1)`.