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Chapter 7: Problem 13

For the chemical change \(A \rightarrow B\), it is found that the rate reaction doubles when the concentration is increased four times. The order in \(A\) for this reaction is (a) two (b) one (c) zero (d) half

Short Answer

Expert verified
The order of the reaction with respect to \(A\) is half.

Step by step solution

01

Understand the Rate Law

The rate law provides a mathematical relationship between the rate of a reaction and the concentration of the reactants. It typically has the form rate = \(k[A]^n\), where \(k\) is the rate constant, \(A\) represents the concentration of reactant \(A\), and \(n\) is the order of the reaction with respect to \(A\). The order of the reaction tells us how changing the concentration of \(A\) will affect the rate of reaction. It is determined experimentally.
02

Analyze the Given Information

In this question, we're told that the rate of reaction doubles - that is, it increases by a factor of 2 - when the concentration of \(A\) is increased four times. Thus, we can set up the equation \(2 = 4^n\), where \(n\) is the order of the reaction we're trying to find.
03

Solve the Equation for n

Solving the equation \(2 = 4^n\) for \(n\) gives the order of the reaction. Since \(4^0.5 = 2\), it can be determined that \(n = 0.5\).

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Most popular questions from this chapter

The half-life period of a first-order reaction is 10 minutes. The time required for the concentration of the reactant to change from \(0.08 \mathrm{M}\) to \(0.02 \mathrm{M}\) is (a) 10 minutes (b) 20 minutes (c) 30 minutes (d) 40 minutes

The rate constant of a reaction is equal to its rate constant at constant temperature when the concentration of the reactants is (a) unity (b) zero (c) two (d) three

In a first-order reaction, the conc. of reactant decreases from \(1.0 \mathrm{M}\) to \(0.25 \mathrm{M}\) in 20 minutes. The value of \(k\) is (a) \(0.6932\) (b) \(6.932\) (c) \(0.06932\) (d) none of these

The statement which is true in respect of order of a reaction is (a) it is always a whole number (b) it is always a fraction (c) it may be zero, a whole number or a fraction (d) it can never be a fraction

According to the collision theory, the rate of a reaction depends on (a) the average collision of molecules (b) the total number of molecules (c) the number of colliding molecules per ml per unit time. (d) none of these
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