pls some one help me
In a reaction, A + B → Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentrations of both the reactants (A and B) are doubled, rate law for the reaction can be written as [CBSE AIPMT 2012]

A
Rate = k[A] [B]

B
Rate = k[A]2[B]

C
Rate = k[A][B]2

D
Rate = k[A]2[B]2

Question

pls some one help me
        In a reaction, A + B → Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentrations of both the reactants (A and B) are doubled, rate law for the reaction can be written as [CBSE AIPMT 2012]

A
Rate = k[A] [B]

B
Rate = k[A]2[B]

C
Rate = k[A][B]2

D
Rate = k[A]2[B]2

photon336 · Answer

$$k[a][b] = r$$

If we double the concentration of b, or multiply 2*b we get 2 times the rate. 

$$k[a][2b] = 2r$$

if we double both of them the rate goes up by a factor of 8. 

$$k[2a][2b] = 8r $$

Think about this. if we doubled both A and B right naturally It should go up by a factor of 4. but it's by a factor of 8. so we know that the concentration of [a] must be squared. 

$$[a]^{2}[b]k = r $$

photon336 · Answer

@anisedora please let me know if you have questions about this.

anonymous · Answer

@Photon336 thank you. i understand it