A reaction in which A, B, and C react to form products is zero order in A, one-h

Question

A reaction in which A, B, and C react to form products is zero order in A, one-half order in B, and second order in C. What is the overall order of the reaction? By what factor does the reaction rate change if [A] is doubled (and the other reactant concentrations are held constant)? By what factor does the reaction rate change if [B] is doubled (and the other reactant concentrations are held constant)? By what factor does the reaction rate change if [C] is doubled (and the other reactant concentrations are held constant)? By what factor does the reaction rate change if the concentrations of all three reactants are doubled?

Explanation / Answer

Rate of reaction = K (Concentration)a

K = rate constant

a= order w.r.t reactant

Now as per the given information,

Rate= k [A]0 [B]0.5[C]2

Overall rate of reaction will be sum of all the order w.r.t all the reactions i.e. = 0+0.5+2=2.5.

When concentration of A i.e. [A] is doubled then:

Since w.r.t [A] rate is zero order so there will be no effect of concentration of A on rate. So, rate of reaction will be unchanged.

When concentration of [B] is doubled then:

Rate is proportional to [B]0.5 when [B] is doubled then

Rate will be [2B]0.5= [2]0.5[B]0.5= 1.41 [B]0.5 i.e. now new rate will be 1.41 of initial rate.

When concentration of [C] is doubled then :

Rate is proportional to [C]2 when [C] is doubled then:

Rate will be [2C]2=[2]2[C]2 = 4[C]2 i.e. now new rate will be 4 times of initail rate.

When all the reactant concentartion will be doubled then:

New rate will be = k [2A]0[2B]0.5[2C]2= K [2]0[A]0[2]0.5[B]0.5[2]2[C]2= [1.41][4] [A]0[B]0.5[C]2= 5.64 initial rate

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