Question

The reaction ( 2A + B → C ) is of order 1 with respect to A and order 2 with respect to B. The rate constant is ( 5.1 × 10⁻⁵ ,M^-2.5 ) at a certain temperature. Calculate the reaction rate when the concentrations of A and B are respectively, ( 0.01 ,M ) and ( 0.02 ,M ).

a) ( 2.04 × 10⁻⁸ ,M/s )
b) ( 1.53 × 10⁻⁸ ,M/s )
c) ( 1.02 × 10⁻⁸ ,M/s )
d) ( 0.51 × 10⁻⁸ ,M/s )

Answer 1

The rate of the reaction 2A + B → C, which is first order in A and second order in B, is calculated using the rate law rate = k[A][B]² with given concentrations and rate constant, resulting in a reaction rate of 2.04 × 10−8 M/s.Therefore, the correct answer is (a) 2.04 × 10−8 M/s.

Step-by-step explanation:

The question involves calculating the reaction rate for the reaction 2A + B → C, which is first order with respect to A and second order with respect to B. To calculate the rate, we use the given rate law and plug in the concentrations of A and B along with the rate constant.

The rate law is given as:

rate = k[A]1[B]2

Using the provided concentrations:

• [A] = 0.01 M
• [B] = 0.02 M
• k = 5.1 × 10−5 M−2.5

The reaction rate can be calculated as:

rate = (5.1 × 10−5 M−2.5)(0.01 M)^1(0.02 M)²

rate = (5.1 × 10−5) ×(0.01) ×(0.0004)

rate = 2.04 × 10−8 M/s

Therefore, the correct answer is (a) 2.04 × 10−8 M/s.