In a reaction, A + B → Product, rate is doubled when the concentration of B is doubled, and ra

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In a reaction, A + B &#8594; Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentration of both the reactants (A and B) are doubled. Rate law for the reaction can be written as

Accepted Answer

Let the order of reaction with respect to A and B is x and y respectivel. So, the rate law can be given as
        R = k [ A ]^X [ B ]^Y          ......(i)
When the concentration of only B is doubled the rate is doubled, so
       R₁ = k [ A ]^X [ B ]^X = 2R           ......(ii)
If concentration of both the reactents A and B are doubled, the rate increases by a factor of 8, so
       R′′ = k [ A ]^X [ B ]^y = 8R           ......(iii)
⇒      k 2^x 2^y [ A ]^X [ B ]^y = 2R           ......(iv)
From Eqs. (i) and (ii), we get
⇒

      2 = 2^Y
∴      y = 1
From Eqs. (i) and (ii), we get
⇒

or    8 = 2^x 2^y
Substitution of the value of y gives,
      8 = 2^x 2¹
       4 = 2^x
       (2)² = 2^x
∴       x = 2
Substitution of the value of x and y in Eq. (i) gives,
    R = k [ A ]² [ B ]

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