Rate of the reaction, (x A+y B z C ) is given by (r=k[A]^x[B]^y ). If the concentration of (A ) is tripled, rate of reaction increased by 27 times over the initial. Then choose the correct plot for variation of half-life ( (t_ 1 / 2 . ) on (y )-axis) of the reaction w.r.t. total initial concentration of reactants (on (x )-axis) is

Step-by-step solution

In this question, we have to assume that order of the reaction, (x A+y B z C ) with respect to (B ) is zero, i.e., (y=0 ). So, the rate expression becomes, (r=k[A]^x[B]^y=k[A]^x[B]^0=k[A]^x ) Now, according to question If the concentration of (A ) is tripled, rate of reaction increased by 27 times over the initial hence. According to available data, ( aligned & (27 r)=k[3 A]^x & 27 r r = k[3 A]^x k[A]^x or 27=(3)^3 or (3)^3=(3)^x aligned ) (x=3 ) and this order of reaction (=3 ) Now, for a third order reaction half