Answer:
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
- Rate₁ = k[A]₁ᵃ[B]ᵇ → eq. 1
- Rate₂ = k[A]₂ᵃ[B]ᵇ → eq. 2
Dividing eq. 2 by eq. 1 one can get
- (Rate₂ / Rate₁) = (k [A]₂ᵃ[B]ᵇ) / (k[A]₁ᵃ[B]ᵇ)
using
- Rate₂ = 2 *Rate₁ and [A]₂ = 2 [A]₁
∴ (2 Rate₁ / Rate₁) = ( k [2]ᵃ[B]ᵇ) / (k[1]ᵃ[B]ᵇ)
- (2) = (2)ᵃ
- taking log of both sides
- log (2) = a Log (2)
- 0.693 = a * 0.693
- a =1
∴ 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
- Rate₁ = k[A]ᵃ[B]₁ᵇ → eq. 1
- Rate₂ = k[A]ᵃ[B]₂ᵇ → eq. 2
Dividing eq. 2 by eq. 1 one can get
- (Rate₂ / Rate₁) = (k [A]ᵃ[B]₂ᵇ) / (k[A]ᵃ[B]₁ᵇ)
using
- Rate₂ = Rate₁ and [B]₂ = 2 [B]₁
∴ (Rate₁ / Rate₁) = ( k [A]ᵃ[2]ᵇ) / (k[A]ᵃ[1]ᵇ)
- (1) = (2)ᵇ
- taking log of both sides
- log (1) = b Log (2)
- 0 = 0.693 * b
- b = 0
∴ 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]
