Ch.14 - Chemical Kinetics

Problem 91d

Chapter 14, Problem 91d

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?

Verified step by step guidance

Identify the rate law for the reaction. Since the reaction is second order in NO and first order in O2, the rate law can be expressed as:

Rate = k {(NO)}^{2} (O, 2)

, where k is the rate constant.

Use the given rate of disappearance of NO to find the rate constant k. Substitute the given concentrations and rate into the rate law:

9.3 \times 10^{-5} = k {(0.040)}^{2} (0.035)

. Solve for k.

Determine the new concentration of NO when it is increased by a factor of 1.8. Multiply the initial concentration of NO by 1.8:

0.040 \times 1.8

Substitute the new concentration of NO into the rate law to find the new rate. Use the previously calculated rate constant k and the unchanged concentration of O2:

Rate = k {(0.040 \times 1.8)}^{2} (0.035)

Compare the new rate to the original rate to understand the effect of increasing the concentration of NO. Since the rate is proportional to the square of the concentration of NO, increasing NO by a factor of 1.8 will increase the rate by a factor of

{1.8}^{2}

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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. For the given reaction, the rate law can be written as Rate = k[NO]^2[O2]^1, indicating that the rate is second order with respect to NO and first order with respect to O2. Understanding the rate law is crucial for predicting how changes in concentration affect the reaction rate.

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. In this case, the reaction is second order in NO, meaning that if the concentration of NO is doubled, the rate of reaction increases by a factor of four. This concept is essential for determining how changes in concentration influence the overall reaction rate.

Effect of Concentration on Rate

The effect of concentration on the rate of a reaction is determined by the reaction's order with respect to each reactant. For the given reaction, increasing the concentration of NO by a factor of 1.8 will increase the rate of disappearance of NO by a factor of (1.8)^2, since the reaction is second order in NO. This principle allows us to calculate the new rate based on changes in concentration.

Recommended video:

Guided course

02:10

Concentration Changes and Rate Law Example

Related Practice

Textbook Question

Consider the reaction A + B → C + D. Is each of the following statements true or false? (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order.

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

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?

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?

Verified video answer for a similar problem:

Key Concepts

Rate Law

Order of Reaction

Effect of Concentration on Rate

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?