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?

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Identify the rate law for the reaction. Since the reaction is first order in N2O5, the rate law can be expressed as: rate = k[N2O5], where k is the rate constant.

For part (c), when the concentration of N2O5 is doubled to 0.0480 M, substitute this new concentration into the rate law: rate = k[0.0480 M].

Since the rate law is first order, doubling the concentration of N2O5 will double the rate of the reaction. This is because the rate is directly proportional to the concentration of N2O5.

For part (d), when the concentration of N2O5 is halved to 0.0120 M, substitute this new concentration into the rate law: rate = k[0.0120 M].

Halving the concentration of N2O5 will halve the rate of the reaction, as the rate is directly proportional to the concentration of N2O5 in a first-order reaction.

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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 expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. For a first-order reaction, the rate is directly proportional to the concentration of the reactant raised to the first power. This means that if the concentration of the reactant is doubled, the rate of the reaction also doubles, while halving the concentration will halve the rate.

First-Order Reaction

A first-order reaction is one where the rate of reaction depends linearly on the concentration of one reactant. In this case, the rate constant (k) remains constant, and the reaction rate can be expressed as rate = k[N2O5]. This characteristic allows for straightforward predictions about how changes in concentration affect the reaction rate.

Concentration and Reaction Rate

Concentration refers to the amount of a substance in a given volume. In chemical kinetics, changes in concentration directly influence the rate of reaction. For first-order reactions, increasing the concentration of the reactant increases the rate proportionally, while decreasing the concentration reduces the rate, allowing for predictable calculations based on concentration changes.

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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. (a) Write the rate law for the reaction.

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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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