Question 3 of 37beginner💡 UnderstandShort Answer1 mark

For a reaction, A+B→ProductA + B \rightarrow Product; the rate law is given by, r=k[A]1/2[B]2r = k [A]^{1/2} [B]^2. What is the order of the reaction?

Correct Answer

The order of the reaction is 5/2 (or 2.5).

According to the definition of order of a reaction, the sum of powers of the concentration of the reactants in the rate law expression gives the overall order. For the given rate law, r=k[A]1/2[B]2r = k [A]^{1/2} [B]^2, the order with respect to A is 1/2 and with respect to B is 2. Therefore, the overall order of the reaction = 1/2 + 2 = 5/2.

Exercise: Intext Questions | Q: 3.3 | (Page 11)
For More Understanding

Explanation

The textbook clearly defines order of a reaction in section 3.2.3 as 'the sum of powers of the concentration of the reactants in the rate law expression.' Example 3.3 demonstrates this calculation where order = x + y for Rate = k[A]^x[B]^y. Applying this to the given rate law r = k[A]^(1/2)[B]^2, we add the exponents: 1/2 + 2 = 5/2. The context also notes that 'Order of a reaction can be 0, 1, 2, 3 and even a fraction,' confirming that fractional orders like 5/2 are valid.

Solution Steps

  1. Step 1: Identify the exponents in the rate law expression r=k[A]1/2[B]2r = k [A]^{1/2} [B]^2. The exponent for [A] is 1/2 and for [B] is 2.

  2. Step 2: Apply the definition of order: Order = Sum of powers of concentration terms = 1/2 + 2.

  3. Step 3: Calculate the sum: 1/2 + 2 = 1/2 + 4/2 = 5/2 or 2.5.

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