Textbook Question
The tabulated data were collected for this reaction at a certain temperature: X2Y → 2 X + Y c. What is the concentration of X after 10.0 hours?
Ch.14 - Chemical Kinetics
Chapter 14, Problem 87
At 700 K, acetaldehyde decomposes in the gas phase to methane and carbon monoxide. The reaction is: CH3CHO(g) → CH4(g) + CO(g). A sample of CH3CHO is heated to 700 K and the pressure is measured as 0.22 atm before any reaction takes place. The kinetics of the reaction are followed by measurements of total pressure and these data are obtained: t (s) 0 1000 3000 7000; PTotal (atm) 0.22 0.24 0.27 0.31. Find the rate law, the rate constant, and the total pressure after 2.00 × 10^4 s.
Verified step by step guidance1
Identify the initial conditions: The initial pressure of CH3CHO is 0.22 atm, and the initial total pressure is also 0.22 atm since no reaction has occurred yet.
Determine the change in pressure due to the reaction: As the reaction proceeds, the total pressure increases due to the formation of products. Calculate the change in pressure at each time point by subtracting the initial pressure from the total pressure at that time.
Relate the change in pressure to the concentration change: Since the reaction is CH3CHO(g) → CH4(g) + CO(g), for every mole of CH3CHO that reacts, one mole each of CH4 and CO is produced, leading to a net increase of 1 mole of gas. Use this stoichiometry to relate the change in pressure to the change in concentration of CH3CHO.
Determine the order of the reaction: Use the changes in pressure over time to determine the order of the reaction. This can be done by plotting the appropriate graphs (e.g., pressure vs. time, ln(pressure) vs. time, 1/pressure vs. time) and identifying which plot gives a straight line.
Calculate the rate constant and predict future pressure: Once the order is known, use the linear plot to determine the rate constant. Then, use the rate law to calculate the total pressure after 2.00 × 10^4 s.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Chemical Kinetics
Chemical kinetics is the study of the rates of chemical reactions and the factors that affect these rates. It involves understanding how concentration, temperature, and catalysts influence the speed of a reaction. In this context, analyzing the change in total pressure over time allows us to deduce the rate of the decomposition of acetaldehyde and determine the rate law.
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03:06
Chemical Kinetics
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, and m and n are the orders of the reaction with respect to reactants A and B. For the given reaction, determining the rate law involves analyzing how the total pressure changes as the reaction proceeds.
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01:52Rate Law Fundamentals
Equilibrium and Total Pressure
In a gas-phase reaction, the total pressure is influenced by the number of moles of gas present. As acetaldehyde decomposes into methane and carbon monoxide, the total number of gas moles increases, leading to a rise in total pressure. Understanding this relationship is crucial for predicting the total pressure at a given time, such as after 2.00 × 10^4 seconds, based on the initial conditions and the reaction kinetics.
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02:09Total Pressure Example
Related Practice
Textbook Question
Consider the reaction: 2 O3(g) → 3 O2( g) The rate law for this reaction is: Rate = k [O3]2 [O2] Suppose that a 1.0-L reaction vessel initially contains 1.0 mol of O3 and 1.0 mol of O2. What fraction of the O3 will have reacted when the rate falls to one-half of its initial value?
Textbook Question
Dinitrogen pentoxide decomposes in the gas phase to form nitrogen dioxide and oxygen gas. The reaction is first order in dinitrogen pentoxide and has a half-life of 2.81 h at 25 °C. If a 1.5-L reaction vessel initially contains 745 torr of N2O5 at 25 °C, what partial pressure of O2 is present in the vessel after 215 minutes?
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Textbook Question
Iodine atoms combine to form I2 in liquid hexane solvent with a rate constant of 1.5⨉1010 L/mols. The reaction is second order in I. Since the reaction occurs so quickly, the only way to study the reaction is to create iodine atoms almost instantaneously, usually by photochemical decomposition of I2. Suppose a flash of light creates an initial [I] concentration of 0.0100 M. How long will it take for 95% of the newly created iodine atoms to recombine to form I2?