The decomposition reaction of N 2 O 5 in carbon tetrachloride is 2 N 2 O 5 → 4 NO 2 + O 2 . The rate law is first order in N 2 O 5 . At 64°C the rate constant is 4.82 × 10 -3 s -1 . (a) Write the rate law for the reaction.

Hello everyone. Today we have the following problem. The decomposition reaction of di nitrogen PTO pent side and carbon tetrachloride is the following the rate loss. First order in our di nitrogen pint at 64 °C, the rate constant is 4.82 times 10 to the negative third seconds, rates to the power of negative one, write the rate law for the reaction. So the rate law is written in terms of the rate and it explores the relationship between the reaction rate and the concentrations of the reactants. And so they ignore the products. So if we look at this following reaction, it was stated that it was first order. So we will write the rate constant, which is K and then we will write our first reactant, we have our diane nitrogen pint to sign and we wanna make sure that we write it in brackets and then we write its order as an exponent. And since this was first order, we can leave it as is. So we can also include our rate constant for K if we substitute 4.82 times 10 to the negative third seconds raise with the power of negative one multiplied by our concentration of our di nitrogen pint oxide. We get the following or answer choice B as our final answer overall, I hope this helped. And until next time.

Ch.14 - Chemical Kinetics

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Brown 15th Edition

Ch.14 - Chemical Kinetics

Problem 29a

Chapter 14, Problem 29a

The decomposition reaction of N₂O₅ in carbon tetrachloride is 2 N₂O₅ → 4 NO₂ + O₂. The rate law is first order in N₂O₅. At 64°C the rate constant is 4.82 × 10^-3 s^-1. (a) Write the rate law for the reaction.

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Identify the order of the reaction with respect to N2O5, which is given as first order.

Recall that the general form of a rate law for a first-order reaction is: rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Substitute the given reactant, N2O5, into the rate law expression. The rate law becomes: rate = k[N2O5].

Use the given rate constant value, k = 4.82 \times 10^{-3} \text{ s}^{-1}, to complete the rate law expression.

The final rate law for the decomposition of N2O5 is: rate = 4.82 \times 10^{-3} \text{ s}^{-1} [\text{N}_2\text{O}_5].

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Key Concepts

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

Rate Law

The rate law of a chemical reaction expresses the relationship between the rate of the reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B. In this case, since the reaction is first order in N2O5, the rate law will reflect that dependency.

Order of Reaction

The order of a reaction indicates how the rate is affected by the concentration of reactants. A first-order reaction means that the rate is directly proportional to the concentration of one reactant raised to the first power. In the given reaction, the first-order nature in N2O5 implies that doubling its concentration will double the reaction rate.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that is specific to a particular reaction at a given temperature. It reflects the speed of the reaction; higher values of k indicate faster reactions. In this scenario, the rate constant is given as 4.82 * 10^-3 s^-1 at 64°C, which is crucial for calculating the reaction rate.

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Related Practice

Textbook Question

Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (a) Write the rate law for the reaction.

Textbook Question

Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (b) How does the rate change when [A] is doubled and the other reactant concentrations are held constant? (c) How does the rate change when [B] is tripled and the other reactant concentrations are held constant? (d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

Textbook Question

Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (e) By what factor does the rate change when the concentrations of all three reactants are tripled?

Textbook Question

The decomposition reaction of N₂O₅ in carbon tetrachloride is 2 N₂O₅ → 4 NO₂ + O₂. The rate law is first order in N₂O₅. At 64°C the rate constant is 4.82 × 10^-3 s^-1. (c) What happens to the rate when the concentration of N₂O₅ is doubled to 0.0480 M? (d) What happens to the rate when the concentration of N₂O₅ is halved to 0.0120 M?

Textbook Question

Consider the following reaction:

2 NO(g) + 2 H₂(g) → N₂(g) + 2 H₂O(g)

(b) If the rate constant for this reaction at 1000 K is 6.0 × 10⁴ M^-2 s^-1, what is the reaction rate when [NO] = 0.035 M and [H₂] = 0.015 M?

(c) What is the reaction rate at 1000 K when the concentration of NO is increased to 0.10 M, while the concentration of H₂ is 0.010 M?

Textbook Question

Consider the following reaction: 2 NO1g2 + 2 H21g2¡N21g2 + 2 H2O1g2 (d) What is the reaction rate at 1000 K if [NO] is decreased to 0.010 M and 3H24 is increased to 0.030 M?

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The decomposition reaction of N2O5 in carbon tetrachloride is 2 N2O5 → 4 NO2 + O2. The rate law is first order in N2O5. At 64°C the rate constant is 4.82 × 10-3 s-1. (a) Write the rate law for the reaction.

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Key Concepts

Rate Law

Order of Reaction

Rate Constant (k)

The decomposition reaction of N₂O₅ in carbon tetrachloride is 2 N₂O₅ → 4 NO₂ + O₂. The rate law is first order in N₂O₅. At 64°C the rate constant is 4.82 × 10^-3 s^-1. (a) Write the rate law for the reaction.