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Chapter 2: Problem 29

For a reaction \(2 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{AB}\), it is found that doubling the concentration of both the reactants increases the rate to eight times that of initial rate but doubling the concentration of \(\mathrm{B}\) alone doubles the rate. Then the order of the reaction with respect to \(A\) and \(B\) is (a) 0,3 (b) 0,2 (c) 2,1 (d) 2,2

Short Answer

Expert verified
Answer: The order of the reaction with respect to reactant A is 2, and with respect to reactant B is 1.

Step by step solution

01

Find the general rate law equation for the reaction.

For a given reaction, the rate law equation can be represented as: Rate \(= k[\mathrm{A}]^{x}[\mathrm{B}]^{y}\) Where \(k\) is the rate constant, \([\mathrm{A}]\) and \([\mathrm{B}]\) are the concentrations of reactants A and B, and \(x\) and \(y\) are the orders of the reaction with respect to A and B, respectively.
02

Write the rate law equation for the three related scenarios.

We are given three scenarios related to the rate of the reaction when the concentration of reactants is doubled. Let's write the rate law equation for each scenario: 1. Initial rate (Before changing concentration): Rate\(_1 = k[\mathrm{A}]^{x}[\mathrm{B}]^{y}\) 2. Rate when both A and B concentrations are doubled (Rate is 8 times the initial rate): Rate\(_2 = 8 \times\) Rate\(_1 = k[(2[\mathrm{A}])]^{x}[(2[\mathrm{B}])]^{y}\) 3. Rate when only B concentration is doubled (Rate is 2 times the initial rate): Rate\(_3 = 2 \times\) Rate\(_1 = k[\mathrm{A}]^{x}[(2[\mathrm{B}])]^{y}\)
03

Divide the rate law equations to relate them to initial rate.

Now, let's divide the equations for scenarios 2 and 3 by the equation for the initial rate (scenario 1) to simplify them and get expressions for \(x\) and \(y\): Dividing Rate\(_2\) by Rate\(_1\): \(\frac{8 \times \text{Rate}_1}{\text{Rate}_1} = \frac{k[(2[\mathrm{A}])]^{x}[(2[\mathrm{B}])]^{y}}{k[\mathrm{A}]^{x}[\mathrm{B}]^{y}}\) 8 = (2)^{x}(2)^{y} Dividing Rate\(_3\) by Rate\(_1\): \(\frac{2 \times \text{Rate}_1}{\text{Rate}_1} = \frac{k[\mathrm{A}]^{x}[(2[\mathrm{B}])]^{y}}{k[\mathrm{A}]^{x}[\mathrm{B}]^{y}}\) 2 = (2)^{y}
04

Solve the simplified equations for x and y.

From the simplified equation related to Rate\(_3\): 2 = (2)^{y} Taking the log base 2 on both sides: log\(_2(2)\) = log\(_2((2)^{y})\) 1 = y Now that we know y = 1, let's substitute it into the simplified equation related to Rate\(_2\): 8 = (2)^{x}(2)^{1} 8 = (2)^{x}(2) 4 = (2)^{x} Taking the log base 2 on both sides: log\(_2(4)\) = log\(_2((2)^{x})\) 2 = x
05

Order of the reaction with respect to A and B.

From the above calculations, we find that the order of the reaction with respect to A (x) is 2, and with respect to B (y) is 1. So the correct answer is: (c) 2,1

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Most popular questions from this chapter

For each of the questions, four choices have been provided. Select the correct alternative. For a reaction \(\mathrm{A}+\mathrm{B} \rightleftarrows \mathrm{C}+\mathrm{D}\), if the activation energy of backward reaction is more than that of forward reaction, the forward reaction is (a) endothermic (b) exothermic (c) reaction need not necessarily involve heat changes (d) cannot be predicted

The slope obtained by drawing a tangent at time " \(\mathrm{t}\) " on the curve for the concentration of reactants vs time is equal to instantaneous rate.

For each of the questions, four choices have been provided. Select the correct alternative. In the formation of \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) from \(\mathrm{NO}_{2}\) the rates of production of (a) \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) are equal (b) \(\mathrm{NO}\) is double the rate of consumption of \(\mathrm{NO}_{2}\) (c) \(\mathrm{NO}\) is twice the rate of production of \(\mathrm{O}_{2}\) (d) \(\mathrm{O}_{2}\) is twice the rate of production of \(\mathrm{NO}\)

For each of the questions, four choices have been provided. Select the correct alternative. Which among the following reactions is an example of instantaneous reaction under normal conditions? (a) \(2 \mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{N}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}\) (c) \(\mathrm{NaOH}+\mathrm{HCl} \rightarrow \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)

For each of the questions, four choices have been provided. Select the correct alternative. For a chemical reaction to occur (a) the reacting molecules must collide with each other (b) reacting molecules should have sufficient energy at the time of collision (c) reacting molecules must be properly oriented (d) all of the above
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