You perform a series of experiments for the reaction A → B + C and find that the rate law has the form rate = k[A]^x. Determine the value of x in each of the following cases: (a) There is no rate change when [A] is tripled. (b) The rate increases by a factor of 9 when [A] is tripled. (c) When [A] is doubled, the rate increases by a factor of 8.

Verified step by step guidance

Step 1: Understand the rate law expression. The rate law for the reaction is given as rate = k[A]^x, where k is the rate constant, [A] is the concentration of reactant A, and x is the order of the reaction with respect to A.

Step 2: Analyze case (a). If there is no rate change when [A] is tripled, it implies that the rate is independent of [A]. Therefore, x must be 0, as any change in [A] does not affect the rate.

Step 3: Analyze case (b). If the rate increases by a factor of 9 when [A] is tripled, set up the equation: (3[A])^x = 9[A]^x. Simplify to find x by solving 3^x = 9.

Step 4: Analyze case (c). If the rate increases by a factor of 8 when [A] is doubled, set up the equation: (2[A])^x = 8[A]^x. Simplify to find x by solving 2^x = 8.

Step 5: Conclude the values of x for each case based on the simplified equations from steps 2, 3, and 4.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^x, where k is the rate constant, [A] is the concentration of reactant A, and x is the reaction order with respect to A. Understanding the rate law is essential for determining how changes in concentration affect the reaction rate.

Reaction Order

The reaction order is the exponent x in the rate law that indicates how the rate of reaction depends on the concentration of a reactant. It can be determined experimentally and can be zero, positive, or even fractional. The value of x provides insight into the mechanism of the reaction and how the concentration of reactants influences the rate.

Method of Initial Rates

The method of initial rates involves measuring the initial rate of reaction at varying concentrations of reactants to deduce the rate law and reaction order. By analyzing how the rate changes with different concentrations, one can determine the value of x. This method is crucial for understanding the kinetics of a reaction and allows for the systematic investigation of how concentration affects reaction speed.

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Rate Law Determination

Related Practice

Textbook Question

The reaction 2 NO(g) + O₂(g) → 2 NO₂ (g) is second order in NO and first order in O₂. When [NO] = 0.040 M, and [O₂] = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10^-5 M/s. (b) What is the value of the rate constant?

Textbook Question

The reaction 2 NO(g) + O₂(g) → 2 NO₂ (g) is second order in NO and first order in O₂. When [NO] = 0.040 M, and [O₂] = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10^-5 M/s. (c) What are the units of the rate constant?

Textbook Question

The reaction 2 NO(g) + O₂(g) → 2 NO₂ (g) is second order in NO and first order in O₂. When [NO] = 0.040 M, and [O₂] = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10^-5 M/s. (d) What would happen to the rate if the concentration of NO were increased by a factor of 1.8?

Textbook Question

Consider the following reaction between mercury(II) chloride and oxalate ion:

2 HgCl₂(aq) + C₂O₄^2-(aq) → 2 Cl^-(aq) + 2 CO₂(g) + Hg₂Cl₂(s)

The initial rate of this reaction was determined for several concentrations of HgCl₂ and C₂O₄^2-, and the following rate data were obtained for the rate of disappearance of C₂O₄^2-:

Experiment [HgCl₂] (M) [C₂O₄^2-] (M) Rate (M/s)

1 0.164 0.15 3.2 × 10^-5

2 0.164 0.45 2.9 × 10^-4

3 0.082 0.45 1.4 × 10^-4

4 0.246 0.15 4.8 × 10^-5

(b) What is the value of the rate constant with proper units?

(c) What is the reaction rate when the initial concentration of HgCl₂ is 0.100 M and that of C₂O₄^2- is 0.25 M if the temperature is the same as that used to obtain the data shown?

Textbook Question

The reaction 2 NO₂ → 2 NO + O₂ has the rate constant k = 0.63 M^-1s^-1. (a) Based on the units for k, is the reaction first or second order in NO₂?