Given the initial rate data for the reaction A + B –––> C, determine the rate expression for the reaction.

Answer:

The accurate answer is E) (Δ[C]/Δt) = 8.37 x 10–2 M –2 s –1 [A]2 [B]

Explanation:

To ascertain the rate expression for the reaction, employing the initial rate methodology is necessary. This approach involves measuring the initial rate (Δ[C]/ Δt) by varying the concentration of reactants one at a time. If high concentrations of A and B are utilized in experimentation, their values will change little from their initial status, particularly in the early moments of the reaction. Under these circumstances, the initial velocity will approximate a constant.

The general rate expression for the reaction can be represented as

(Δ[C]/Δt) =

where k denotes the rate constant, while [A] and [B] refer to the concentrations of A and B, respectively, with α and β representing the order of the reaction concerning A and B, respectively.

To determine the orders of reaction, it is essential to write the ratio between Conditions one and two:

Determining that β = 1 indicates that B is of first order.

In addition, the ratio between the first and third conditions must be noted:

This indicates α = 2, indicating that A is of second order.

Consequently, the rate expression is

(Δ[C]/Δt) =

Replacing the data from the first conditions allows for the determination of the rate constant:

Answer:

B) Δ[C]/Δt = 3.60x10⁻² M⁻¹s⁻¹ [A] [B]

Explanation:

For the reaction A + B → C

The expression for the reaction's rate is:

Δ[C]/Δt = k [A] [B]

Utilizing the values for [A], [B], and Δ[C]/Δt, multiply [A] by [B] to acquire a value of X and consider Δ[C]/Δt as Y. The slope derived from this linear regression will yield k.

Therefore, the results you should have are:

y = 3.60x10⁻² X

Thus, the reaction's rate is:

B) Δ[C]/Δt = 3.60x10⁻² M⁻¹s⁻¹ [A] [B]

I hope this assists you!