The following kinetic data are collected for the initial rates of a reaction 2X + Z → products: Experiment [X] (M) [Z] (M) Rate (M/s) 1 0.25 0.25 4.0 * 10^1 2 0.50 0.50 3.2 * 10^2 3 0.50 0.75 7.2 * 10^2. (c) What is the reaction rate when the initial concentration of X is 0.75 M and that of Z is 1.25 M?

Verified step by step guidance

Step 1: Determine the rate law expression for the reaction. The general form of the rate law is Rate = k[X]^m[Z]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to X and Z, respectively.

Step 2: Use the data from experiments 1 and 2 to find the order of the reaction with respect to X. Compare the rates and concentrations of X while keeping Z constant to solve for m.

Step 3: Use the data from experiments 2 and 3 to find the order of the reaction with respect to Z. Compare the rates and concentrations of Z while keeping X constant to solve for n.

Step 4: Calculate the rate constant k using the rate law expression and the data from one of the experiments, now that m and n are known.

Step 5: Substitute the given concentrations of X (0.75 M) and Z (1.25 M) into the rate law expression to calculate the reaction rate.

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]^m[B]^n, where k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are the reaction orders with respect to each reactant. Understanding the rate law is essential for predicting how changes in concentration affect the reaction rate.

Reaction Order

Reaction order refers to the exponent to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction is affected by the concentration of that reactant. For example, if the reaction is first order with respect to X, doubling the concentration of X will double the rate of reaction. Determining the reaction order is crucial for calculating the rate under different concentrations.

Method of Initial Rates

The method of initial rates involves measuring the initial rate of reaction at various concentrations of reactants to deduce the rate law and reaction orders. By analyzing how the rate changes with different concentrations, one can derive the exponents in the rate law. This method is particularly useful in experimental kinetics to establish the relationship between concentration and reaction rate.

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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. (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?

Textbook Question

The reaction 2 NO₂ → 2 NO + O₂ has the rate constant k = 0.63 M^-1s^-1.

(b) If the initial concentration of NO₂ is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

Textbook Question

Consider two reactions. Reaction (1) has a constant halflife, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?