In the reaction a + b c, doubling the concentration of a doubles the reaction rate and doubling the concentration of b does not affect the reaction rate. what is the rate law for this reaction? a. rate = k[b] b. rate = k[a]2 c. rate = k[a][b] d. rate = k[a]

rate = k[A]

Explanation:

The equation that relate reaction rate with reactant concentrations is known as the rate law.

for a reaction:

the rate law can be expressed as:  

The proportionality constant, k, is known as the rate constant, the powers a and b is the reaction order with respect to reactants A and B, respectively.

for this reaction doubling the concentration of A doubles the reaction rate that means

Rate₂ = 2 *Rate₁     and     [A]₂ = 2 [A]₁

Dividing eq. 2 by eq. 1 one can get

using

∴ (2 Rate₁ / Rate₁) = ( k [2]ᵃ[B]ᵇ) / (k[1]ᵃ[B]ᵇ)

∴ order of reaction with respect to A is first (=1)        →     (1)

Doubling the concentration of B does not affect the reaction rate.

that means

Rate₂ = Rate₁     and     [B]₂ = 2 [B]₁

Dividing eq. 2 by eq. 1 one can get

using

∴ (Rate₁ / Rate₁) = ( k [A]ᵃ[2]ᵇ) / (k[A]ᵃ[1]ᵇ)

∴ order of reaction with respect to B is zero         →     (2)

So, from 1 and 2  the right choice is rate = k[A]¹[B]⁰= k[A]

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